Recent development in GFD and remote sensing. Nonlinear and turbulent processes under high wind conditions

The multitude of processes of various scales occurring simultaneously under strong winds in the air and sea boundary layers presents a true challenge for nonlinear science. We want to understand the physics of these processes, their specific role, their interactions and how they can be probed remotely, how these processes differ from their counterparts under moderate/weak winds. We welcome theoretical, experimental and numerical works on all aspects of processes in turbulent boundary layers above and below the ocean surface. Although we are particularly interested in the processes and phenomena occurring under strong wind conditions, the works concerned with similar processes under weaker winds which might provide an insight for rough seas are also welcomed. We are also very interested in works on remote sensing of these processes.
The areas of interest include the processes at and in the vicinity of the interface (nonlinear dynamics of surface water, wave-turbulence interactions, wave breaking, generation and dynamics of spray and air bubbles, thermodynamics of the processes in the boundary layers, heat and gas exchange), all the processes above and below the aIr/water interface, as long as they are relevant for strong wind conditions (such as, e.g. inertial waves generated by changing winds). Relevant nonlinear biological phenomena are also welcomed.
The main aims of the session is to initiate discussion of the multitude of processes active under strong winds across the narrow specializations as a step towards creating an integrated picture. Theoretical, numerical, experimental and observational works are welcomed.

Geophysical Fluid Dynamics (GFD) is a truly interdisciplinary field, including different topics dealing with rotating stratified fluids. It emerges in the late 50s, when scientists from meteorology, oceanography, astrophysics, geological fluid dynamics, and applied mathematics began to mathematically model complex flows and thereby unify these fields. Since then many new aspects were added and deeper insight into many problems has been achieved. New mathematical and statistical tools were developed, standard techniques were refined, classical problems were varied. In this session we primarily focus on contributions from dynamic meteorology and physical oceanography that model flows by mathematical analysis. However, it is also a forum for experimental GFD and for astrophysical and geological aspects of GFD as well.

Co-organized by AS2/NH5/OS4
Convener: Yuliya Troitskaya | Co-conveners: Uwe Harlander, Victor Shrira, Michael Kurgansky, Wu-ting Tsai, Claudia Cherubini, Daria GladskikhECSECS, Costanza Rodda
vPICO presentations
| Mon, 26 Apr, 09:00–12:30 (CEST), 13:30–15:00 (CEST)

vPICO presentations: Mon, 26 Apr

Chairpersons: Uwe Harlander, Michael Kurgansky, Costanza Rodda
Recent developments in GFD: Ocean
Hemant Khatri, Stephen Griffies, Takaya Uchida, Han Wang, and Dimitris Menemenlis

In the upper ocean, submesoscale turbulence shows seasonal variability and is pronounced in winter. We analyze geostrophic KE spectra in a submesoscale-permitting global ocean model to study the seasonal variability in the upper ocean turbulence. Submesoscale processes peak in winter and, consequently, geostrophic kinetic energy (KE) spectra tend to be relatively shallow in winter (k-2) with steeper spectra in summer (k-3). The roles of frontogenesis processes and mixed-layer instabilities in submesoscale turbulence and their effects on the evolution of KE spectra over an annual cycle are discussed. It is shown that this transition in KE spectral scaling has two phases. In the first phase (late autumn), KE spectra show a presence of two spectral regimes: k-3 scaling in mesoscales (100-300 km) and k-2 scaling in submesoscales (< 50 km), indicating the coexistence of QG, surface-QG, and frontal dynamics. In the second phase (late winter), mixed-layer instabilities convert available potential energy into KE, which cascades upscale leading to flattening of the KE spectra at larger scales, and k-2 power-law develops in mesoscales too.

How to cite: Khatri, H., Griffies, S., Uchida, T., Wang, H., and Menemenlis, D.: A synthesis of upper ocean geostrophic kinetic energy spectra from a global submesoscale permitting simulation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-19,, 2020.

Georgi Sutyrin, Jonas Nycander, and Timour Radko

Baroclinic vortices embedded in a large-scale vertical shear are examined. We describe a new class of steady propagating vortices that radiate Rossby waves but yet do not decay. This is possible since they can extract available potential energy (APE) from a large-scale vertically sheared flow, even though this flow is linearly stable. The vortices generate Rossby waves which induce a meridional vortex drift and an associated heat flux explained by an analysis of pseudomomentum and pseudoenergy. An analytical steady solution is considered for a marginally stable flow in a two-layer model on the beta-plane, where the beta-effect is compensated by the potential vorticity gradient (PVG) associated with the meridional slope of the density interface. The compensation occurs in the upper layer for an upper layer westward flow (an easterly shear) and in the lower layer for an upper layer eastward flow (the westerly shear). The theory is confirmed by numerical simulations indicating that for westward flows in subtropical oceans, the reduced PVG in the upper layer provides favorable conditions for eddy persistence and long-range propagation. The drifting and radiating vortex is an alternative mechanism besides baroclinic instability for converting background APE to mesoscale energy. 

How to cite: Sutyrin, G., Nycander, J., and Radko, T.: Steady radiating baroclinic vortices in vertically sheared flows, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3836,, 2021.

Elnaz Naghibi, Elnaz Naghibi, Sergey Karabasov, Vassili Toropov, and Vasily Gryazev

In this study, we investigate Genetic Programming as a data-driven approach to reconstruct eddy-resolved simulations of the double-gyre problem. Stemming from Genetic Algorithms, Genetic Programming is a method of symbolic regression which can be used to extract temporal or spatial functionalities from simulation snapshots.  The double-gyre circulation is simulated by a stratified quasi-geostrophic model which is solved using high-resolution CABARET scheme. The simulation results are compressed using proper orthogonal decomposition and the time variant coefficients of the reduced-order model are fed into a Genetic Programming code. Due to the multi-scale nature of double-gyre problem, we decompose the time signal into a meandering and a fluctuating component. We next explore the parameter space of objective functions in Genetic Programming to capture the two components separately. The data-driven predictions are cross-compared with original double-gyre signal in terms of statistical moments such as variance and auto-correlation function.


How to cite: Naghibi, E., Naghibi, E., Karabasov, S., Toropov, V., and Gryazev, V.: On the use of the data- and physics-driven approaches for quasi-geostrophic double-gyre problem: application of Genetic Programming, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8093,, 2021.

Julia Draeger-Dietel and Alexa Griesel

We derive the energy transfer rate ε from the 3rd order relative (longitudinal)  velocity structure function <Δul3>=(3/2)εs from ocean surface drifter trajectories in the turbulent mixed layer of the Benguela upwelling region off the coast of Namibia.  Combination with the  mean squared pair separation<s2(t)> =gεt3 reveals the Richardson-Obhukov constant g≅0.5, which is remarkably close to the one measured in  controlled two-dimensional turbulent flows in laboratory. We verify the  two coupled  cascades of energy (upscale/inverse) and enstrophy (downwscale) by  the  theoretically predicted  slope 1  for <Δul3> for inertial scales (above the injection scale) and slope 2 for  the 2nd order structure function <Δul2> for non-local scales (below the injection scale) respectively. We detect  additional 'ballistic contributions' in the central regime of the corresponding probability distribution P(st) of relative separations s for fixed time t, leading to an additional  power law factor s with  α ≅ 5/3. The algebraic decay with 1<α <2 revives  to the relevance of Levy distributions in the stochastic description of the turbulent transport process in contrast to former claims. Our findings  of a positively skewed   probability distribution P(Δuls) of relative longitudinal velocity Δul  for inertial scales s renews the question of intermittency in the  inverse energy cascade.

How to cite: Draeger-Dietel, J. and Griesel, A.: Inverse energy cascade in ocean macroscopic turbulence:      Energy transfer rate ε and Richardson-Obhukov  constant g from an surface drifter experiment in the Benguela upwelling system, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10184,, 2021.

Leo Middleton, Elizabeth Fine, Jennifer MacKinnon, Matthew Alford, and John Taylor

Understanding the transport of heat in the Arctic ocean will be vital for predicting the fate of sea-ice in the decades to come. Small-scale turbulence is an important driver of heat transport and one of the major forms of this turbulence is known as `double-diffusive convection'. Double diffusion refers to a variety of turbulent processes in which potential energy is released into kinetic energy, made possible in the ocean by the difference in molecular diffusivities between salinity and temperature.  The most direct measurements of ocean mixing require sampling velocity or temperature gradients on scales <1mm, so-called microstructure measurements. Here we present a new method for estimating the energy dissipated by double-diffusive convection using temperature and salinity measurements on larger scales (100s to 1000s of metres). The method estimates the up-gradient diapycnal buoyancy flux, which is hypothesised to balance the dissipation rate. To calculate the temperature and salinity gradients on small scales we apply a canonical scaling for compensated thermohaline variance (or `spice') and project the gradients down to small scales. We apply the method to a high-resolution survey of temperature and salinity through a subsurface Arctic eddy (Fine et al. 2018) and compare the results with simultaneous microstructure measurements. The new technique can reproduce up to 70% of the observed dissipation rates to within a factor of 3. This suggests the method could be used to estimate the dissipation and heat fluxes associated with double-diffusive convection in regions without microstructure measurements. Finally, we show the method maintains predictive skill when applied to a sub-sampling of the CTD data at lower resolutions.

How to cite: Middleton, L., Fine, E., MacKinnon, J., Alford, M., and Taylor, J.: New Method for Estimating Double-Diffusive Dissipation Rates, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11054,, 2021.

Ana M Ricardo, Giovanni Di Lollo, Moisés Brito, Claudia Adduce, and Rui M.L. Ferreira

Flow around bluff bodies have been attracting the interest of the research community for more than a century. The physical mechanisms associated with the vortex shedding in the wake of bluff bodies is still of fundamental research interest. However, flow-structure interaction in density currents has not received enough attention. The transient nature of the interaction between the density driven flow and a stationary object constitutes the motivation for the present laboratory study aiming at investigating the vortex generation and fate on the wake of a circular cylinder in a density current.

The experiments were conducted in a horizontal and rectangular cross-section channel with 3.0 m long, 0.175 m wide and 0.4 m deep. The gravity current was generated using the classic lock-exchange configuration. A sliding stainless-steel gate with 1 mm thickness, sealed by PVC board glued in the sidewall, was positioned at 0.3 m from the left hand side of the channel. The experiment starts when the gate is suddenly removed, leaving the dense fluid to flow along the bottom of the channel, while the ambient fluid moves above in the opposite direction. The dense fluid consists in a mixture of fresh water and salt while the ambient fluid is a solution fresh water and ethanol (96%). The amount of salt and alcohol added in each mixture was determined in order to obtain a given density difference and to ensure the same refractive index in both fluids. Two different currents were tested with reduced gravity equal to 0.06 ms-2 and 0.24 ms-2. For each test ten repetitions were carried out. Instantaneous velocity maps were acquired with a Particle Image Velocimetry system at 15 Hz. Polyamide seeding particles of density equal to 1.03 were added in both dense and ambient fluids.

 The Reynolds number varied between 1500 and 4000. The results show that vortex shedding varies as the current reaches and overtakes the cylinder. Boundary layer detachment and shear instability is initiated shortly before the snout reaches the cylinder. A pattern of well-defined symmetrical vortexes is formed as a result of the initial shear instability. As the head of the current engulfs the cylinder, stronger turbulence diffusion contributes to reduce vortex coherence. Vortexes are smaller and detach sooner, while is not clear if shedding is alternate or simply random. The formation length is smaller than that of a steady flow with the same Re. When the back of the current passes, the formation length is increased and vortex shedding becomes periodical again. A striking feature is that the Von Kármán street is frequently symmetrical rather than exhibiting a pattern of alternate vortices.

This research was funded by national funds through Portuguese Foundation for Science and Technology (FCT) project PTDC/CTA-OHR/30561/2017 (WinTherface).

How to cite: Ricardo, A. M., Di Lollo, G., Brito, M., Adduce, C., and Ferreira, R. M. L.: Vortex shedding by a circular cylinder in lock-exchange density current , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13453,, 2021.

Elizabeth Yankovsky, Laure Zanna, and Shafer Smith

The representation of energetic transfers associated with ocean mesoscale eddies is a leading challenge in the development of modern climate models. Here we investigate the relationships between eddy representation and vertical structure. We employ the GFDL-MOM6 in an idealized, one-basin, stacked-shallow water configuration and consider four resolutions of otherwise-identical simulations: 1/4, 1/8, 1/16, and 1/32 degree. We assess the degree of eddy representation by: (1) the ratio of the deformation scale to the model grid spacing; and (2) using linear QG instability analysis to compute the fastest growing wavenumber and comparing it to the model resolution. We then analyze the available potential energy (APE) and kinetic energy (KE) distributions for each simulation. KE is found to broadly increase with increasing resolution. The KE is decomposed into barotropic (BT) and baroclinic (BC) components, which are further split into temporally-defined “eddy” and “mean” parts. The dominant trend in eddy representation vs. vertical structure is an increasing fraction of KE going into the BT mode, particularly the BT-eddy component, as eddy representation increases. We attribute this to the inaccurate representation of BC energy transfers in the low-resolution models which leads to buildup of BC energy and lack of barotropization. The end goal of this work is contributing to the development of scale-aware, energetically-consistent mesoscale eddy parameterizations by constraining the vertical structure of eddy energy.

How to cite: Yankovsky, E., Zanna, L., and Smith, S.: Relationships between eddy representation and vertical structure, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14098,, 2021.

Luna Hiron, David Nolan, and Lynn Shay

Mesoscale eddies drive a large fraction of the variability in the ocean. Eddies with strong tangential velocity compared to their translation speed are able to stay coherent and travel long distances, carrying water mass properties, heat, nutrients, and particles around the ocean. The nonlinearity of these mesoscale features is greater for stronger flow and greater curvature, which, consequently, is associated with greater centrifugal force.

The Gulf of Mexico Loop Current (LC) system has long been assumed to be close to geostrophic balance despite its strong flow and the development of large meanders and strong frontal eddies during unstable phases. The region between the LC meanders and its frontal eddies was shown to have high Rossby numbers indicating nonlinearity; however, the effect of the nonlinear term on the flow has not been studied so far. In this study, the ageostrophy of the LC meanders is assessed using a high-resolution numerical model and geostrophic velocities from altimetry. The method used in this study can be applied in any region where the centrifugal force is important. A formula to compute the radius of curvature of the flow from the velocity field is also presented.

The results indicate that during strong meandering, especially before and during LC shedding and in the presence of frontal eddies, the centrifugal force becomes as important as the Coriolis force and the pressure-gradient force: LC meanders are in gradient-wind balance. The centrifugal force modulates the balance and modifies the flow speed, resulting in a subgeostrophic flow in the LC meander trough around the frontal eddies and supergeostrophic flow in the LC meander crest. The same pattern is found when correcting the geostrophic velocities from altimetry to account for the centrifugal force. The ageostrophic percentage in the cyclonic and anticyclonic meanders is 47% ± 1% and 78% ± 8% in the model and 31% ± 3% and 78% ± 29% in the altimetry dataset, respectively. Thus, the ageostrophic velocity is an important component of the LC flow and cannot be neglected when studying the LC system.




How to cite: Hiron, L., Nolan, D., and Shay, L.: Study of ageostrophy during strong, nonlinear eddy-front interaction in the Gulf of Mexico, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14054,, 2021.

Recent developments in GFD: Atmosphere
Andrei Sukhanovskii and Elena Popova

The present laboratory study is focused on the role of convective rolls in enhancement of the heat flux from the sea and triggering of the process of rapid intensification of tropical cyclones. The appearance of coherent convective structures such as thermals and rolls are registered by different optical techniques and temperature measurements. Two-dimensional velocity fields are used for the study of the structure and characteristics of the flow. The heat flux from the heating plate to the fluid is measured directly. Obtained results clearly show that rapid intensification of a laboratory analog of a tropical cyclone is tightly linked with the heat transfer process in the boundary layer. Formation of secondary convective structures strongly increases the heat transfer and intensity of convective circulation. Intensity of radial inflow is a crucial aspect for the intensification of cyclonic vortex, hence rapid variation of the heat transfer is a factor that has a substantial influence on the dynamics of a laboratory vortex.

How to cite: Sukhanovskii, A. and Popova, E.: The role of horizontal rolls in rapid intensification of cyclonic vortex, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1929,, 2021.

Stéphane Abide, Gabriel Meletti, Raspo Isabelle, Stéphane Viazzo, Andreas Krebs, Anthony Randriamampianina, and Uwe Harlander

Using high-order discretization on a High-Performance Computing framework, direct numerical simulations of a differentially heated rotating annulus are performed. The geometry of the baroclinic wave tank is similar to the new atmospheric-like experiment designed at BTU Cottbus-Senftenberg (Rodda et al., 2020), which also consists of a differentially heated rotating annulus. The experimental observations reveal  spontaneous emissions of inertial-gravity waves in the baroclinic wave jet front in accordance with Hien et al. (2018). The different length scales of inertial-gravity instabilities and the baroclinic waves make direct numerical simulation challenging. This motivates the current design of a new higher-order/HPC solver devoted to stratified rotating flows (Abide et al., 2018). Specifically, some features of compact scheme discretizations are used to combine efficiently parallel computing and accuracy for reducing DNS wall times. The ability to reproduce experimentally measured flow regimes with non-axisymmetric regular steady waves to the vacillation regimes is also discussed.

S. Abide et al. (2018), Comput Fluids 174:300-310.
S. Hien et al. (2018), J Fluid Mech 838:5–41.
C. Rodda et al. (2020), Exp Fluids 61:2.

How to cite: Abide, S., Meletti, G., Isabelle, R., Viazzo, S., Krebs, A., Randriamampianina, A., and Harlander, U.: Direct Numerical Simulation of an atmospheric-like differentially heated rotating annulus, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7003,, 2021.

Peter Szabo and Wolf-Gerrit Früh

The earth, a sphere consisting of several layers like an onion is still up to now not fully understood. Gaining the fundamental knowledge to understand the mystery of global cell formation and large-scale convection in the interior or at the surface e.g. in our atmosphere is still of great interest from a meteorological point of view and of course in geophysics. However, laboratory experiments are still exposed to a significant problem – gravity. Establishing a radial force field e.g. in a sphere or annulus is still overpowered by gravity unless the experiment is carried out in a microgravity environment. Here, we show a potential application of a central force field induced by magnetic forces that acts on a magnetic fluid in a rotating thermally heated annulus to induce thermomagnetic convection and waves that are similar to the baroclinic annulus with the focus to study large scale atmospheric flow fields in a small laboratory system.


Thermomagnetic convection is based on non-isothermal variation of fluid magnetisation induced e.g. by a temperature gradient in the presence of an external magnetic field. After Currie’s law colder magnetic fluid exhibits a larger fluid magnetisation and is therefore attracted to higher magnetic field intensities. This phenomenon is used to induced convection in a thermally heated annulus filled with a magnetisable ferro-magnetic fluid. Here, we study a 2-dimensional numerical problem geometry where the fluid is cooled at the inner and heated at the outer cylinder. The system is forced with an increasing central force field such that colder fluid is attracted towards the outer boundary when a critical threshold is exceeded – the critical magnetic Rayleigh number an equivalent non-dimensional parameter to the classical Rayleigh number for natural convection.


Numerical results are obtained for two different radii ratios (0.35, 0.5). The parametric study included a range of magnetic Rayleigh numbers between 103 to 7.5x105 to induce a range of thermomagnetic convective cases. In addition, the thermally annulus is rotated at different speeds expressed via the Taylor number ranging from 105 to 106. The observed flow fields reveal similar flow structures as seen in the classical baroclinic wave tank but have a different physically interpretation. The observed modes range from mode number 2 to 8 with stable symmetric to oscillatory and chaotic behaviours. The results are summarised in a regime diagram that is spanned in the thermally forcing and rotation speed space. This may be able to classify certain structures that are used to study atmospheric flow fields for different rotation and thermal forcing states e.g. planetary waves.

How to cite: Szabo, P. and Früh, W.-G.: Convective pattern formation in a thermally heated rotating annulus with magnetic central force field , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7745,, 2021.

Janet Peifer, Onno Bokhove, and Steve Tobias

Rayleigh-Bénard convection (RBC) is a fluid phenomenon that has been studied for over a century because of its utility in simplifying very complex physical systems. Many geophysical and astrophysical systems, including planetary core dynamics and components of weather prediction, are modeled by including rotational forcing in classic RBC. Our understanding of these systems is confined by experimental and numerical limits, as well as theoretical assumptions. 

The role of thermal boundary condition choice on experimental studies of geophysical and astrophysical systems has been often been overlooked, which could account for some lack of agreement between experimental and numerical models as well as the actual flows. The typical thermal boundary conditions prescribed at the top and the bottom of a convection system are fixed temperature conditions, despite few real geophysical systems being bounded with a fixed temperature. A constant heat flux is generally more applicable for real large-scale geophysical systems. However, when this condition is applied in numerical systems, the lack of fixed temperature can cause a temperature drift. In this study, we seek to minimize temperature drifting by applying a fixed temperature condition on one boundary and a fixed thermal flux on the other.

Experimental boundary conditions are also often assumed to be a fixed temperature. However, the actual condition is determined by the ratio of the height and thermal conductivity of the boundary material to that of the contained fluid, known as the Biot number. The relationship between the Biot number and thermal boundary condition behavior is defined by the Robin, or 'thin-lid', boundary condition such that low Biot number boundaries are essentially fixed thermal flux and high Biot number boundaries are essentially fixed temperature. 

This study seeks to strengthen the link between numerical and experimental models and geophysical flows by investigating the effects of thermal boundary conditions and their relationship to real-world processes. Both fixed temperature and fixed flux boundary conditions are considered. In addition, the Robin boundary condition is studied at a range of Biot numbers spanning from fixed temperature to fixed flux, allowing intermediate conditions to be investigated. Each system is studied at increasingly rapid rotation rates, corresponding to decreasing Ekman numbers as low as Ek=10-5 Heat transport is analyzed using the Nusselt number, Nu, and the form of the solution is described by the number of convection rolls and time-dependency. Further investigations will analyze Nu and fluid movement within a system with heterogeneous heat flux condition on the  sidewall boundary conditions, which is useful in the study of planetary core dynamics. The results of this study have implications for improvements in modeling geophysical systems both experimentally and numerically. 

How to cite: Peifer, J., Bokhove, O., and Tobias, S.: Effects of thermal boundary conditions on rotating Rayleigh-Bénard convection with implications on geophysical and astrophysical systems, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9511,, 2021.

Florian Zaussinger, Peter Haun, Peter Szabo, and Christoph Egbers

Electro-hydrodynamics (EHD) plays an important role in many industrial applications. Ink-jet printers, microwave drying facilities, and lab-on-a-chip devices utilize dielectric properties of the working fluids and their manipulation without moving parts. Another application is found in heat exchangers, where the dielectrophoretic force is used to increase heat transfer due to thermal buoyancy. In particular, the dielectrophoretic force has great advantages in low- and micro-gravity conditions since the force can be used to mimic a gravitational force field. Hence, convection in a rectangular cavity induced by EHD is a model system comparable to Rayleigh-Benard (RB) convection. However, the electric-driven buoyancy term and dielectric heating make the system more complex. The direction of the triggering dielectrophoretic force depends mainly on the temperature gradient which can be used to manipulate the heat flux or the entire structure of the convective flow. Layer formation, comparable to double-diffusive convection, and convective overshooting are two representative cases which can be established by EHD, too. We will present first results of turbulent convection induced by EHD in the rectangular cavity and the impact of volumetric heating. For this purpose, the Boussinesq approximation, as well as compressible models for EHD, are tested also for applicability in geophysical relevant regimes. This is a crucial point as the limitations by incompressible modeling are not well-understood for EHD. The main focus of the study is the analysis of the heat flux as a function of the thermo-electric feedback and the dielectric heating rate. Convective overshooting and layer formation are examined closely. Results of this study are used to estimate transport properties and time scales. Applications using EHD are the GeoFlow and AtmoFlow experiments. The GeoFlow experiment was conducted several years on the International Space Station and gained deep insight into EHD driven convection in the spherical shell geometry. The AtmoFlow experiment is under construction and is planned for operations on the ISS in 2024. This experiment is designed to study atmospheric like flows in the spherical shell.

How to cite: Zaussinger, F., Haun, P., Szabo, P., and Egbers, C.: Heat transport in turbulent electro-hydrodynamics, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3979,, 2021.

Recent developments in GFD: Fundamentals
Michael Kurgansky

The linear and non-linear inertial stability of the Kolmogorov flow in a rotating viscous fluid of uniform density is investigated. A necessary condition for instability is the violation of the criterion of non-viscous inertial stability, and the sufficient condition of instability is formulated in terms of the Reynolds criterion. The existence of stable secondary stationary regimes in the problem is shown, developing in a context of loss of stability of the main flow and having the shape of rolls (cloud streets in the atmosphere) oriented along it. Stable density stratification is taken into account when the direction of gravity coincides with the direction of rotation of the fluid. In this case, the necessary condition for the inertial instability of the main flow remains the same, but the critical Reynolds number for the instability depends on two additional dimensionless parameters that appear in the problem: the stratification parameter and the Prandtl number. The case of Prandtl numbers less than or equal to unity has been studied in greater detail, when there is a secondary stationary regime, which can be unstable - in contrast to the case of a fluid that is uniform in density - and density stratification is a destabilizing factor.

How to cite: Kurgansky, M.: On the inertial instability of the Kolmogorov flow in a rotating stratified fluid, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-543,, 2021.

Leo Maas and Rudolf Kloosterziel

Conservation laws relate the local  time-rate-of-change of the spatial integral of a density function to the divergence of its  flux through the boundaries of the integration domain. These provide integral constraints on the spatio-temporal development  of a field. Here we show  that  a new type of conserved quantity exists, that does not require integration over a particular domain but which holds locally,  at any point in the field.  This is derived for the pseudo-energy density of  nondivergent Rossby waves where  local invariance is obtained for (1) a single plane wave, and (2) waves produced by an impulsive point-source of vorticity. 

The definition of pseudo-energy used here  consists of a conventional kinetic part, as well as an unconventional pseudo-potential part, proposed by  Buchwald (1973).  The anisotropic nature of the nondivergent energy flux that appears in response to the point source further clarifies the role of the beta plane in the  observed western intensification of ocean currents. 

How to cite: Maas, L. and Kloosterziel, R.: Rossby wave energy: a local Eulerian isotropic invariant, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4175,, 2021.

Rupert Klein, Lisa Schielicke, Stephan Pfahl, and Boualem Khouider

Quasi-geostrophic (QG) theory describes the dynamics of synoptic scale flows in the trophosphere that are balanced with respect to both acoustic and internal gravity waves. Within this framework, effects of (turbulent) friction near the ground are usually represented by invoking Ekman Layer theory. The troposphere covers roughly the lowest ten kilometers of the atmosphere while Ekman layer heights are typically just a few hundred meters. However, this two-layer asymptotic theory does not explicitly account for substantial changes of the potential temperature stratification due to diabatic heating associated with cloud formation or with radiative or turbulent heat fluxes, which, in the middle latitudes, can be particularly important in roughly the lowest three kilometers. To alleviate this constraint, this work extends the classical QG plus Ekman layer model by introducing an intermediate, dynamically and thermodynamically active layer, called the "Diabatic Layer" here. The flow in this layer is also in acoustic, hydrostatic, and geostrophic balance but, in contrast to QG flow, variations of potential temperature are not restricted to small deviations from a stable and time independent background stratification. Instead, within this layer, diabatic processes are allowed to affect the leading-order stratification. As a consequence, the Diabatic Layer modifies the pressure field at the top of the Ekman layer, and with it the intensity of Ekman pumping seen by the quasi-geostrophic bulk flow. This leads to a new model for the coupled dynamics of the bulk troposphere, the diabatic layer, and the Ekman layer when strong diabatic processes substantially change the stratification in the lower part of the atmosphere. 

How to cite: Klein, R., Schielicke, L., Pfahl, S., and Khouider, B.: Dynamics of a Diabatic Layer in the quasi-geostrophic framework, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7377,, 2021.

Nicolas Grisouard and Varvara E Zemskova

We report on an instability arising in sub-surface, laterally sheared geostrophic flows. When the lateral shear of a horizontal flow in geostrophic balance has a sign opposite to the Coriolis parameter and exceeds it in magnitude, embedded perturbations are subjected to inertial instability, albeit modified by viscosity. When the perturbation arises from the surface of the fluid, the initial response is akin to a Stokes problem, with an initial flow aligned with the initial perturbation. The perturbation then grows quasi-inertially, rotation deflecting the velocity vector, which adopts a well-defined angle with the mean flow, and viscous stresses, transferring horizontal momentum downward. The combination of rotational and viscous effects in the dynamics of inertial instability prompts us to call this process “Ekman-inertial instability.” While the perturbation initially grows super-inertially, the growth rate then becomes sub-inertial, eventually tending back to the inertial value. The same process repeats downward as time progresses. Ekman-inertial transport aligns with the asymptotic orientation of the flow and grows exactly inertially with time once the initial disturbance has passed. Because of the strongly super-inertial initial growth rate, this instability might compete favourably against other instabilities arising in ocean fronts.

How to cite: Grisouard, N. and Zemskova, V. E.: Ekman-inertial instability, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10003,, 2021.

Wim Verkley and Camiel Severijns

Burgers and Onsager were pioneers in using statistical mechanics in the theory of turbulent fluid motion. Their approach was, however, rather different. Whereas Onsager stayed close to the energy conserving Hamiltonian systems of classical mechanics, Burgers explicitly exploited the fact that turbulent motion is forced and dissipative. The basic assumption of Burgers' approach is that forcing and dissipation balance on average, an assumption that leads to interesting conclusions concerning the statistics of turbulent flow but also to a few problems. A compilation and assessment of his work can be found in [1].

We have taken up the thread of Burgers' approach and rephrased it in terms of Jaynes' principle of maximum entropy. The principle of maximum entropy yields a  statistical description in terms of a probability density function that is as noncommittal as possible while reproducing any given expectation values. In the spirit of Burgers, these expectation values are the average energy as well as the average of the first and higher order time-derivatives of the energy (or other global quantities). In [2] the method was applied to a system devised by Lorenz . By using constraints on the average energy and its first and second order time-derivatives a satisfying description was produced of the system's statistics, including covariances between the different variables. 

Burgers' approach can also be applied to the parametrization problem, i.e., the problem of how to deal statistically with scales of motion that cannot be resolved explicitly. Quite recently we showed this for two-dimensional turbulence on a doubly periodic flow domain, a system that is relevant as a first-order approximation of large-scale balanced flow in the atmosphere and oceans. Using a spectral description of the system it is straightforward to separate between resolved and unresolved scales and by using a reference model with high resolution it is possible to study how well a parametrization performs by implementing it in the same model with a lower resolution. Based on two studies [3, 4] we will show how well the principle of maximum entropy works in tackling the problem of unresolved turbulent scales.  

[1] F.T.M. Nieuwstadt and J.A. Steketee, Eds., 1995: Selected Papers of J.M. Burgers. Kluwer Academic, 650 pp. 

[2] W.T.M. Verkley and C.A. Severijns, 2014: The maximum entropy principle applied to a dynamical system proposed by Lorenz. Eur. Phys. J. B, 87:7, (open access).  

[3] W.T.M. Verkley, P.C. Kalverla and C.A. Severijns, 2016: A maximum entropy approach to the parametrization of subgrid processes in two-dimensional flow. Quarterly Journal of the Royal Meteorological Society, 142, 2273-2283,

[4] W.T.M. Verkley, C.A. Severijns and B.A. Zwaal, 2019: A maximum entropy approach to the interaction between small and large scales in two-dimensional turbulence. Quarterly Journal of the Royal Meteorological Society, 145, 2221-2236,

How to cite: Verkley, W. and Severijns, C.: Describing the statistics of turbulent flow by using the principle of maximum entropy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12129,, 2021.

Yair De-Leon, Chaim I. Garfinkel, and Nathan Paldor

A linear wave theory of the Rotating Shallow Water Equations (RSWE) is developed in a channel on either the mid-latitude f-plane/β-plane or on the equatorial β-plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. We show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the β–effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin-like waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean-flow” phase speeds does not account for the difference in phase speeds, and the meridional structure does not often oscillate across the channel but is trapped near one the channel's boundaries in mid latitudes or behaves as Hermite function in the case of an equatorial channel. The phase speed of Kelvin-like waves is modified by the presence of a mean flow compared to the classical gravity wave speed but their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wavenumber, and the convexity of the dispersion curves also changes with the zonal wavenumber. In some cases, the Kelvin-like dispersion curve crosses those of Poincaré modes, but it is not an evidence for the existence of instability since the Kelvin waves are not part of the solutions of an eigenvalue problem. 

How to cite: De-Leon, Y., Garfinkel, C. I., and Paldor, N.: Planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin waves on the f-plane and β-plane in the presence of a uniform zonal flow, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13427,, 2021.

Otto Chkhetiani, Alexey Gledzer, Evgeny Gledzer, Maxim Kalashnik, and Alexey Khapaev

The idea of the multiplicity of equilibrium states of the atmospheric circulation in geophysical hydrodynamics goes back to Charne and DeVore 1979, where, for a model with a small number of variables, solutions with significantly different values of the zonal and wave velocity components were obtained (see also Laurie, Bouchet 2015, Herbert et al. 2020). The results of similar studies for low-parameter approximations were given by Kallen 1980, Gluhovsky 2001, Koo, Ghil 2002 ... The circulation modes differed in the magnitude of the zonal component of the flow. At weak transport, the role of almost stationary atmospheric eddies is enhanced, which corresponds to circulation blocking modes. Laboratory confirmation of the effect was obtained from Weeks et al. 1997, Tian et al. 2001.

In the same years, in the experiments of A.M. Obukhov and coworkers, modes with differently directed axes of large-scale fluid rotation were observed in closed vessels at the same value of external generation - Obukhov et al. 1976, Gledzer et al. 1981.

In the present study, supported by Russian Science Foundation (Project 19-17-00248), the above types of multi-mode are considered based on laboratory and numerical experiments in circular rotating channels. It is known that the permanent magnet location configurations (source-sinks) could create an almost stationary vortex distribution pattern Gledzer et al. 2013,2014. The transition between different states is provided by a change in the value of the main parameter of electric current generation with subsequent restoration of its initial value.

The experimental results presented below are obtained for a rotating annular channel (rotation periods up to 1 minute) filled with an electrically conductive 10% copper sulfate solution. The bottoms of circular channels with inner and outer radii of 1) 5.5 cm and 18 cm  2) 5 cm and 36 cm have an axisymmetric conical shape with a height of 1 cm.

Depending on channel rotation periods or source configurations, it is possible: 1) Initial and final modes differ quantitatively in the number of generated vortices. 2) The number of vortex formations does not change, but differ in their spatial localization. 3) After changing and restoring the value of the defining parameter, the flow returns to the mode which is practically the same as the initial one.

Numerical experiments with the shallow water model confirmed the results obtained in laboratory experiments on the possibility of transition to new modes when the parameter determining the external force is changed for some time. For the source-sink method, a change in the number of large vortices (cyclones) is observed. At MHD generation it is possible to detect a change in the finite spatial position of vortices with preservation of their number.

Experiments support the conclusion that different modes of barotropic dynamics may exist. And it is unlikely to be associated with any low-parameter approximation of the velocity field in the model.

In our and earlier experiments and models, multi-mode is a property of dynamics in general. The mechanism of multi-mode may be an alternative to the traditional scenario of transition to other modes when external conditions change.

How to cite: Chkhetiani, O., Gledzer, A., Gledzer, E., Kalashnik, M., and Khapaev, A.: Multi-mode states in quasi-two-dimensional rotating flows, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14125,, 2021.

Christina Tsai and Kuang-Ting Wu

It is demonstrated that turbulent boundary layers are populated by a hierarchy of recurrent structures, normally referred to as the coherent structures. Thus, it is desirable to gain a better understanding of the spatial-temporal characteristics of coherent structures and their impact on fluid particles. Furthermore, the ejection and sweep events play an important role in turbulent statistics. Therefore, this study focuses on the characterizations of flow particles under the influence of the above-mentioned two structures.

With regard to the geometry of turbulent structures, Meinhart & Adrian (1995) first highlighted the existence of large and irregularly shaped regions of uniform streamwise momentum zone (hereafter referred to as a uniform momentum zone, or UMZs), regions of relatively similar streamwise velocity with coherence in the streamwise and wall-normal directions.  Subsequently, de Silva et al. (2017) provided a detection criterion that had previously been utilized to locate the uniform momentum zones (UMZ) and demonstrated the application of this criterion to estimate the spatial locations of the edges that demarcates UMZs.
In this study, detection of the existence of UMZs is a pre-process of identifying the coherent structures. After the edges of UMZs are determined, the identification procedure of ejection and sweep events from turbulent flow DNS data should be defined. As such, an integrated criterion of distinguishing ejection and sweep events is proposed. Based on the integrated criterion, the statistical characterizations of coherent structures from available turbulent flow data such as event durations, event maximum heights, and wall-normal and streamwise lengths can be presented.

How to cite: Tsai, C. and Wu, K.-T.: Characterization of Geometrical and Temporal Properties of Large-scale Motions in Turbulent Flows, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14221,, 2021.

Turbulent wave attractors in large-aspect ratio domains.
Ilias Sibgatullin, Stepan Elistratov, and Eugeny Ermanyuk
Chairpersons: Yuliya Troitskaya, Victor Shrira, Daria Gladskikh
Wave turbulence
Sergei Annenkov, Victor Shrira, Leonel Romero, Ken Melville, Eva Le Merle, and Danièle Hauser

Transformation of spectral shape during wind wave development and the transition from the spectrum of developing waves to the spectrum of fully developed waves are well documented in measurements, but have so far escaped all modelling, as well as theoretical explanation. Numerical models of long-term wind wave evolution are based on the Hasselmann kinetic equation (KE). The KE predicts strict self-similarity beyond the initial several thousand characteristic periods of wave development, and therefore cannot describe the subsequent change of spectral shape. Instead, it predicts that the self-similar spectral shape, with a steep front and an enhanced peak, holds at arbitrary fetch, notwithstanding the experimental evidence that mature waves are characterised by the much wider Pierson-Moskowitz spectral shape.

To resolve the contradiction, we perform long-term modelling of wind wave evolution by direct numerical simulation (DNS), based on the Zakharov equation. We model a particular class of situations when the wave field at hand is generated by a strong quasi-stationary offshore wind jet, which is caused by pressure differences and accelerates passing through a valley into the sea. Examples of such phenomena are the Tehuano event off the Pacific coast of Mexico, and the Mistral in the northern Mediterranean. Modelling results are compared with the airborne observations of waves generated by these winds, collected during GOTEX and HYMEX experiments respectively. In parallel we also perform numerical simulations with the Hasselmann kinetic equation and the generalised kinetic equation. For modelling of waves off the Mexican coast, wind data are taken from measurements during the GOTEX experiment, and the initial conditions from the measured spectrum at the moment when wind waves prevail over swell after a short initial part of the evolution. Waves in the Mediterranean Sea are modelled with constant wind forcing and zero initial condition.

We show that the evolution of integral characteristics, e.g. significant wave height and wave steepness, is reproduced reasonably well by all modelling approaches. However, the spectral shape of developed waves demonstrates a large discrepancy between, on the one hand, the measured spectra and the DNS modelling and, on the other hand, spectra modelled by both kinetic equations. At the intermediate and advanced stage of development, both measured spectra and the DNS spectra tend to Pierson-Moskowitz spectral shape, while the modelling based on the kinetic equations invariably predicts spectra with a higher, more pronounced peak. In terms of the parameter of spectral peakedness, a commonly convenient measure of spectral shape, there is a large (of order one) discrepancy.

We propose a theoretical explanation of the discrepancy as being due to the neglect of non-gaussianity in the derivation of the kinetic equations, and provide a numerical confirmation of this hypothesis.

How to cite: Annenkov, S., Shrira, V., Romero, L., Melville, K., Le Merle, E., and Hauser, D.: Wave development and transformation under strong offshore winds: modelling by DNS and kinetic equations and comparison with airborne measurements, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10437,, 2021.

Dmitry Kozlov and Yuliya Troitskaya

The present work is a theoretical study of the hydrodynamic instability of the water-air interface, the development of which may result in the “bag breakup” fragmentation. This phenomenon begins with the appearance of a small-scale elevation of the water surface, which increases and turns into a small liquid “sail” or “bag”, limited by a thicker rim, and finally bursts into splashes. According to the results of laboratory experiments [1]–[3], the “bag breakup” fragmentation is the most effective droplet generation mechanism at hurricane wind speeds.

We propose a hypothesis that the formation of the initial elevations of the water surface, which undergoes fragmentation, is caused by the hydrodynamic instability of disturbances of the wind drift current in the water. A weakly nonlinear stage of instability in the form of a resonant three-wave interaction has been studied. It has been discovered that the nonlinear resonant interaction of a triad of wind drift perturbations, of which one wave is directed along the flow, and the other two are directed at an angle to the flow, leads to an explosive increase of amplitudes as it was in [4]. Within the framework of the piecewise-continuous model of the drift current profile, the characteristic time and spatial scales of disturbances have been found and it has been shown that their characteristic dependences on the air friction velocity are consistent with the previously obtained experimental data.


This work was supported by RFBR projects (19-35-90053, 19-05-00249) and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.


How to cite: Kozlov, D. and Troitskaya, Y.: Explosive interaction of gravity-capillary triads as the initial stage of “bag-breakup” droplet generation mechanism at high winds , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11302,, 2021.

Maria Yurovskaya, Vladimir Kudryavtrsev, and Bertrand Chapron

Wave fields generated by tropical cyclones (TC) are of strong interest for marine engineering, navigation safety, determination of coastal sea levels and coastal erosion. Considerable efforts have been made to improve knowledge about the surface waves in TC, both from measurements and numerical experiments. Full sophisticated spectral wave models certainly have the capability to provide detailed wave information, but they require large computer power, precise well-resolved surface winds and/or needs to consider large ensembles of solutions. In this context, more simplified but robust solutions are demanded.

This work is based on 2D-parametric model of waves evolution forced by wind field varying in space and time, non-linear wave interactions and wave breaking dissipation [submitted to J. Geoph. Res., see also preprint DOI:]. Numerical solutions of model provide efficient visualization on how waves develop under TC and leave it as swell. Superposition of wave-rays exhibits coherent spatial patterns of wave parameters depending on TC characteristics, - maximal wind speed (um), radius (Rm), and translation velocity (V).

In this presentation we demonstrate how solutions of 2D-parametric model can be described analytically through self-similar functionsusing proper scaling involving the main TC parameters: um, Rm, and V. These self-similar solutions can be treated as TC-wave Geophysical Model Function (TC-wave GMF), to help analytically derive azimuthal-radial distributions of the primary wave system parameters (SWH, wavelength, direction) under TC characterized by arbitrary sets of um, Rm and V conditions. Self-similar solutions describe the main properties of wave field under TC, in particular: right-to-left half asymmetry of wave field under TC; strong dependence of wave energy and wavelength on V, um and Rm caused by group velocity resonance; division of TCs on “slow” and “fast” when TC-induced waves outrun TC and form wake of swell trailing TC.

Comparisons between self-similar solutions and measurements of TC-generated waves reported in the literature, demonstrate excellent agreement to warrant their use for research and practical applications.

The core support for this work was provided by the Russian Science Foundation through the Project №21-47-00038 at RSHU. The support of the Ministry of Science and Education of the Russian Federation under State Assignment No. 0555-2021-0004 at MHI RAS, and State Assignment No. 0736-2020-0005 at RSHU are gratefully acknowledged.

How to cite: Yurovskaya, M., Kudryavtrsev, V., and Chapron, B.: On self-similarity of waves in tropical cyclones, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14407,, 2021.

Costanza Rodda, Clement Savaro, Antoine Campagne, Miguel Calpe Linares, Pierre Augier, Joël Sommeria, Thomas Valran, Samuel Viboud, and Nicolas Mordant

Atmospheric and oceanic energy spectra are characterized by global scaling laws, suggesting a common mechanism driving the energy route to dissipation. Although several possible theories have been proposed, it is not clear yet what the phenomena contributing the most to the energy at the different spatial scales are. One possible scenario is that internal gravity waves, which can be ubiquitously found in the atmosphere and the ocean and play a fundamental role in the energy transfer, cause the observed spectral slopes at the mesoscales in the atmosphere and submesoscales in the oceans. In the context of this open field of investigation, we present an experimental study where internal gravity waves are forced at a given frequency by the oscillating walls of a large pentagonal-shaped domain filled with a stably stratified fluid. The setup is built inside the 13-meters-diameter tank at the Coriolis facility in Grenoble, where geophysical regimes (with high Reynolds number and low Froude) can be achieved and rotation can also be added. The purpose of our investigation is to determine whether it is possible to induce a wave turbulence cascade by forcing internal waves at the large scales. Following a previous study1, where instead of the pentagonal a square domain was utilized, we obtained the velocity field employing time-resolved particle image velocimetry and then calculated the energy spectra. The previous study inside a square domain showed some evidence of a cascade, but it was strongly affected by 2D modes that sharpened the spectrum. Therefore, we changed the domain shape to a pentagon to reduce this finite-size effect. When the waves are forced at frequency ωF=0.4 N, our data shows that the spectra follow the scaling law ω-2 at frequencies larger than the forcing frequency and extending beyond N. The experimental spectra strikingly resemble the characteristic Garret-Munk spectrum measured in the ocean. As the interaction of weakly non-linear waves dominates the dynamics at frequencies smaller than the buoyancy frequency N, we can conclude that the experimental spectra are generated by weak internal wave turbulence driving the turbulent cascade at the high-frequency end of the spectrum. 


1 "Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility", C. Savaro, A. Campagne, M. Calpe Linares, P. Augier, J. Sommeria, T. Valran, S. Viboud, and N. Mordant, PRF 2020

How to cite: Rodda, C., Savaro, C., Campagne, A., Calpe Linares, M., Augier, P., Sommeria, J., Valran, T., Viboud, S., and Mordant, N.: Can laboratory experiments reach regimes relevant for the oceanic dynamics?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10904,, 2021.

Vincent Böning

Turbulent convection is generally believed to occur on the Sun on three different characteristic length scales. These are the smaller granulation scale, the intermediate supergranulation scale, and the potentially existing giant cell scale. While granulation is mostly understood, there are several competing theories for the emergence of supergranules as a characteristic length scale and coherent phenomenon. While the prevailing approaches assume a convective origin of supergranulation, others follow the path of a potential wave-like behaviour of these features, because the power spectrum of supergranulation seemingly follows a dispersion relation. Since supergranulation shows an asymmetry in up and downflows, it is clear that non-linear affects must play a role in its evolution, which create a characteristic observed skewness in the divergence of the horizontal motions at the solar surface. Supergranulation may thus as well be a non-linear wave or an example of wave turbulence. While the power spectrum of supergranulation is reasonably constrained by observations, we here present an observational characterization of the non-linearities involved in creating supergranules. We characterize the spatial pattern of solar supergranulation using a third-order correlation in Fourier space, the bispectrum. We find that the strongest non-linearity is present when the three coupling wave vectors are all at the supergranular scale. These are the same wave vectors that are present in regular hexagons, which have been used in analytical studies of solar convection. At these Fourier components, the bispectrum is positive, consistent with the positive skewness in the data and consistent with supergranules preferentially consisting of outflows surrounded by a network of inflows. We use the bispectral estimates to generate synthetic divergence maps that are very similar to the data. Using this method, we estimate the fraction of the variance in the divergence maps from the nonlinear component to be of the order of 4–6%. We conclude by discussing the implications of our study on the question whether supergranulation is rather a convective feature or an example of wave turbulence.

How to cite: Böning, V.: Characterizing solar supergranulation using the bispectrum: Convection or wave turbulence?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16348,, 2021.

Benjamin K. Smeltzer and Simen Å. Ellingsen

Turbulence is ubiquitous in the topmost skin of the ocean, where it interacts with surface waves. Rapid distortion theory predicts that wave motion will increase turbulent energy, leading to a dissipation of waves [1]. Waves are believed to contribute significantly to the turbulence in the ocean mixed layer, yet field measurements are unable to validate or distinguish between models and theories [2].

In this work we study the modification of turbulence by surface waves using experimental measurements of turbulent flows in the presence of waves, in a laboratory set-up acting as a small-scale model of the water side of the ocean surface layer. Turbulent Langmuir numbers comparable to those in the ocean are achieved, ensuring scalability. Particle image velocimetry (PIV) measurements were performed in a large water channel wherein mechanically generated waves may propagate on a current. An active grid at the inlet allowed the turbulence intensity and mean flow to be tailored independently. The flow field was measured in the streamwise-vertical plane for various flow cases and waves of varying steepness and frequency. The turbulence characteristics are compared to cases without waves to study the impact of the waves on the turbulence and the results are discussed considering predictions from rapid distortion theory.


[1] Teixeira M. and S. Belcher 2002 “On the distortion of turbulence by a progressive surface wave” Journal of Fluid Mechanics  458 229-267.

[2] D’Asaro E.A. 2014 “Turbulence in the upper-ocean mixed layer” Annual Reivew of Marine Sciences 101-115.

How to cite: Smeltzer, B. K. and Ellingsen, S. Å.: Experimental study of Wave-turbulence interaction, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15811,, 2021.

Non-linear waves and wave-current interaction
Wu-ting Tsai and Guan-hung Lu

The energetic, coherent vortical motions in the aqueous surface layer beneath the wind waves dominate the liquid-phase controlled transport processes across the air-water interface. Through interacting with the interface, these coherent vortices manifest themselves by forming quasi-streamwise, high-speed streaks on the wind waves. The density of these streamwise streaks, which can be quantified by the transverse spacing of streaks, thus characterizes the interfacial transfer contributed by the coherent vortices. The formation of surface streaming on the wind waves is geometrically similar to the low-speed streaks observed in the turbulent wall layers. It is generally accepted that the mean spanwise spacing between these low-speed streaks, when scaled by the viscous length, would exhibit a universal value of 100. Observations in wind-wave flumes, however, show that the transverse scale between high-speed streaming on nonbreaking wind waves is narrower than that between low-speed streaks next to no-slip wall. Comparative numerical simulations of shear flow bounded by flat and wavy surfaces are conducted to explain the variation. Analysis of the vorticity transport in the simulated flows bounded by a wavy surface reveals that the presence of surface waves enhances the production of streamwise enstrophy and, consequently, intensifies the generation of quasi-streamwise vortices that form the elongated streaks.
This work is supported by the Taiwan Ministry of Science and Technology (107-2611-M-002 -014 -MY3 and 110-2923-M-002 -014 -MY3).

How to cite: Tsai, W. and Lu, G.: Surface streaming on nonbreaking wind waves, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13965,, 2021.

Alexander Dosaev, Maria Shishina, and Yuliya Troitskaya

Waves on deep water with constant vorticity propagating in the direction of the shear are known to be weakly dispersive in the long wave limit. Weakly-nonlinear evolution of such waves can be described by the Benjamin-Ono equation, which is integrable and has stable soliton solutions. In the present study we investigate behaviour of finite-amplitude counterparts of Benjamin-Ono solitons by modelling their dynamics within exact equations of motion (Euler equations). Due to the solitons having a near-Lorentzian shape with slowly decaying tails, we need to approach them by examining periodic waves, whose crests, indeed, become more and more localised as the period increases. We perform a parameter space study and analyse how stability of very long waves depends on their amplitude and period. We show that large-amplitude solitary waves are unstable.
This research was supported by RFBR (grant No. 16-05-00839) and by the President of Russian Federation (grant No. MK-2041.2017.5). Numerical experiments were supported by RSF grant No. 14-17-00667, data processing was supported by RSF grant No. 15-17-20009.

How to cite: Dosaev, A., Shishina, M., and Troitskaya, Y.: Stability of solitary waves on deep water with constant vorticity, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10197,, 2021.

Rizwan Qayyum, Lorenzo Melito, Maurizio Brocchini, Joseph Calantoni, and Alex Sheremet

An array of oceanographic instruments deployed on an approx. 1.2-km long transect on the Senigallia Adriatic shelf fronting Misa River mouth captured persistent (approx. 2 days), low-frequency oscillations of sea level and cross-shore velocity, following the strong Bora event of Jan, 24-25th, 2014 (the field experiment is described in Brocchini et al., 2017). The Bora storm generated remarkably energetic waves, with 10-s peak period and 3-m significant height.  Following the storm, pressure and velocity records show  20 to 120 min oscillations, with amplitudes in the order of 10-20 cm/s, and  2-10 cm. Pressure  oscillations were in phase across the entire 1.2-km transect. Pressure and cross-shore velocity spectra show well-defined, distinct peaks at frequencies close to multiples of 0.01 1/min, which suggests a seiche process. The  velocity spectrum decays fast at frequencies < 0.03 1/min, while the pressure spectrum exhibits additional peaks at 0.01 and 0.02 1/ min, a behavior consistent with the neighbourhood of the shoreline antinode of a cross-shore standing wave.

Although the oscillations follow, and are obviously related to, a strong Bora event, the forcing mechanism and their large scale structure and dynamics are not well understood (details of Bora events themselves have only recently been clarified; Grisogono and Belusic, 2008). Due to its basin shape and topography, the Adriatic may exhibit both longitudinal and transversal seiches. Longitudinal seiches are typically associated with intense winds out of SE, large frontal systems, or with cyclonic activity, with a dominant 22-hour fundamental mode that persists for days. The much shorter period of the observed oscillations observed suggests seiche modes that are dominantly transversal.

Here, we use theoretical and numerical models to investigate the spatio-temporal structure and the generation mechanism of these oscillations. The generation mechanism could be a combination of stress fluctuations in the Bora wind, and convection cells associated with unstable atmospheric stratification in the wake of the Bora event. As narrow jets,  Bora winds exhibit significant instability and velocity fluctuations  (10-min oscillations between 15 and 25 m/s; Grisogono and Belusic 2008). Convection cells forming in an unstable atmospheric stratification in the wake of a cold-front passage over the North sea were shown to be the forcing of ocean surface oscillations on a similar scale observed at Port of Rotterdamwere, the Netherlands (DeJong and Battjes, 2004).

The study highlights aspects of the relation between Bora events and transversal seiches that are not well documented and poorly understood, but relevant in relation with other air-sea interaction processes that have a significant shoreline impact, such as wave activity, meteotsunamis, and flooding induced by storm surges.

How to cite: Qayyum, R., Melito, L., Brocchini, M., Calantoni, J., and Sheremet, A.: The role of Bora winds in generating short-period O(30 min) seiches in the Adriatic sea, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1252,, 2021.

Ion Dan Borcia, Sebastian Richter, Wenchao Xu, Rodica Borcia, Uwe Harlander, and Michael Bestehorn

Nonlinear surface waves in the form of tidal bores can have a profound impact on the flow in rivers and estauries. The waves can also be studied experimentally in a specially designed periodic channel at BTU Cottbus-Senftenberg [1],[2]. We hence analyze these surface waves in this narrow circular channel partially filled with water and compare the data with numerical simulations. The flow in the channel is blocked by a barrier and the channel oscillates in azimuthal direction with variable frequency,  maintaining the same maximum velocity. The response in terms of wave shape, maximum amplitude and root mean square of the surface deviations are numerically investigated and compared with experiments. Note that for the experimental setup a number of maximum eight ultrasound sensors can provide the local height evolution. Due to the oscillations, the barrier produces wave trains or hydraulic jumps which then propagate inside the channel. Reflections, damping and collisions take place. Some frequencies are  favourised and in the first approximation can also be calculated using a shallow water model. How will be seen, only the odd multiples of the basic frequency produce high answers (resonances).

[1] I.D. Borcia, R. Borcia, Wenchao Xu, M. Bestehorn, S. Richter, and U. Harlander. Undular bores in a large circular channel. European Journal of Mechanics - B/Fluids, 79, 67-73, 2020.

[2] I.D. Borcia, R. Borcia, S. Richter, Wenchao Xu, M. Bestehorn, and U. Harlander. Horizontal Faraday instability in a circular channel. Proceedings in Applied Mathematics and Mechanics (PAMM), 19, , 2019.

How to cite: Borcia, I. D., Richter, S., Xu, W., Borcia, R., Harlander, U., and Bestehorn, M.: Water wave resonance in a circular oscillating channel, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8743,, 2021.

Grigory Zasko, Andrey Glazunov, Evgeny Mortikov, Yuri Nechepurenko, and Pavel Perezhogin

In this report, we will try to explain the emergence of large-scale organized structures in stably stratified turbulent flows using optimal disturbances of the mean turbulent flow. These structures have been recently obtained in numerical simulations of turbulent stably stratified flows [1] (Ekman layer, LES) and [2] (plane Couette flow, DNS and LES) and indirectly confirmed by field measurements in the stable boundary layer of the atmosphere [1, 2]. In instantaneous temperature fields they manifest themselves as irregular inclined thin layers with large gradients (fronts), spaced from each other by distances comparable to the height of the entire turbulent layer, and separated by regions with weak stratification.

Optimal disturbances of a stably stratified turbulent plane Couette flow are investigated in a wide range of Reynolds and Richardson numbers. These disturbances were computed based on a simplified linearized system of equations in which turbulent Reynolds stresses and heat fluxes were approximated by isotropic viscosity and diffusion with coefficients obtained from DNS results. It was shown [3] that the spatial scales and configurations of the inclined structures extracted from DNS data coincide with the ones obtained from optimal disturbances of the mean turbulent flow.

Critical value of the stability parameter is found starting from which the optimal disturbances resemble inclined structures. The physical mechanisms that determine the evolution, energetics and spatial configuration of these optimal disturbances are discussed. The effects due to the presence of stable stratification are highlighted.

Numerical experiments with optimal disturbances were supported by the RSF (grant No. 17-71-20149). Direct numerical simulation of stratified turbulent Couette flow was supported by the RFBR (grant No. 20-05-00776).


[1] P.P. Sullivan, J.C. Weil, E.G. Patton, H.J. Jonker, D.V. Mironov. Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundary layer // J. Atmos. Sci., 2016, V. 73, P. 1815-1840.

[2] A.V. Glazunov, E.V. Mortikov, K.V. Barskov, E.V. Kadantsev, S.S. Zilitinkevich. Layered structure of stably stratified turbulent shear flows // Izv. Atmos. Ocean. Phys., 2019, V. 55, P. 312–323.

[3] G.V. Zasko, A.V. Glazunov, E.V. Mortikov, Yu.M. Nechepurenko. Large-scale structures in stratified turbulent Couette flow and optimal disturbances // Russ. J. Num. Anal. Math. Model., 2010, V. 35, P. 35–53.

How to cite: Zasko, G., Glazunov, A., Mortikov, E., Nechepurenko, Y., and Perezhogin, P.: Optimal energy growth in stably stratified turbulent Couette flow, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10311,, 2021.

Alex Sheremet, Yulia. I. Troitskaya, Irina Soustova, and Victor I. Shrira

Edge waves (EW) are surface gravity waves topographically trapped near the highly reflective ocean shorelines. Over mildily sloping beaches, the high-reflectivity condition is only satisfied for infragravity waves (IGW, periods of a few minutes). Initially believed to drive alongshore-periodic shoreline features, EW have been shown to be important also for a variety of coastal ocean processes such as nonlinear shoaling of wind waves, coastal flooding, ice-shelf break up in polar oceans, and others.  As IGW, on mildly sloping beaches EW are outside the wind-wave frequency range, which seems to exclude direct wind forcing as generating mechanism. It is generally agreed that IGW ove mildly sloping beaches are generated by nonlinear swell interaction.

Wave-wave interactions can excite both alongshore progressive and standing EW, but EW directional symmetry should match swell directionalty. This simple rule is confirmed also by observations. Exceptions to thius rule are intriguing: if directionally-asymmetric edge waves fields that do not match the swell direction, occur, the implication is that wave-wave interactions are not the dominant IGW/EW generation mechanism. Direct wind forcing would then be the only conceivable candidate. The high correlation of swell and IG wave directionality, however, suggests that such occurrences must be rare, possibly associated with peculiar coastal weather conditions. 

We investigate data produced by the most comprehensive effort to date to study EW - the nearshore array deployed by Elgar, Herbers, O'Reilly and Guza during the SandyDuck'97 experiment - which recorded pressure and velocity continuously at 2 Hz from August to December 1997, at sensors distributed on six alongshore lines between approximately the 1-m and 6-m isobaths near the Duck NC pier. Estimates directional IGW/EW match well swell directionality. However, a few events exhibit strong IG/EW directional asymmetry matching wind direction, with nearly shorenormal offshore swells. In most of these cases, IGW propagate against the nearshore current. These events are consistent with a mechanism for direct generation of IGW/EW by wind. It is not clear whether their scarcity is due to intrinsic properties of the wind generation mechanism, or to the rather low-energy conditions of the SandyDuck'97 experiment. In general, both nonlinear wave-wave interactions and wind generation should be taken into account, and we expect the wind generation mechanism to play an increasingly important role in storms, for example, for modeling wave surges. An investigation into modeling EW generation by wind will be reported elsewhere. 


How to cite: Sheremet, A., Troitskaya, Y. I., Soustova, I., and Shrira, V. I.: An investigation into edge-wave generation by wind, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-609,, 2021.

Sebastian Essink, Ren-Chieh Lien, and Eric Kunze

Storm-generated near-inertial waves are a significant source for deep-ocean mixing. However, their energy pathways beyond wind generation and equatorward propagation as low modes are still elusive. Previous studies suggest that the bulk of inertial wind power is lost in the nearfield of storm forcing, but there is little observational evidence to confirm this.

Finescale horizontal velocity, temperature, salinity and microscale temperature profiles to 500-m depth were collected in the Kuroshio-Oyashio Confluence east of Japan during the storm-seasons of 2016 and 2017 with chi-augmented EM-APEX floats. Temporal sampling was at 1-h resolution during storms, sufficient to resolve near-inertial motions. Turbulent dissipation rates  and diapycnal diffusivities K were inferred from microscale temperature-gradient spectra.  Several floats were trapped near the velocity maximum of anticyclonic eddies.  Mesoscale eddies are known to trap and amplify near-inertial waves and to modulate near-inertial wave distribution and dissipation.

Near-inertial energy-fluxes within the eddy are mostly inward and downward. Signatures of a critical layer, e.g., increasing vertical wavenumbers, shear, and turbulence are present at the depth where the eddy vorticity approaches the surface value, and strong vertical mean shears and vorticity-gradients occur. Turbulence is reduced by a factor of 10 above 180-m depth, despite elevated near-inertial energy, and enhanced between 200 and 255 m. Three mechanisms for the generation of enhanced turbulence are hypothesized: i) local and remotely forced near-inertial waves superimposing to create shear-unstable layers, ii) kinematic superposition of eddy and near-inertial shear that generates patches of turbulence at inertial periods, iii) a near-inertial critical layer due to dynamic wave/mean interaction. Ray tracing simulations will be performed to examine whether vertical vorticity gradients and/or Doppler shifting are responsible for the presence of a critical layer.

How to cite: Essink, S., Lien, R.-C., and Kunze, E.: Near-inertial wave modulated turbulence in a Kuroshio anticyclonic eddy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15502,, 2021.

Victor Shrira and Rema Almelah

The work examines the Ekman current  response to a steady
wind within the Stokes-Ekman paradigm. Under constant wind
in the classical Ekman model there is a single attractor
corresponding to the Ekman (1905)steady solution. It is
known that the account of wind waves  strongly affects the
Ekman current dynamics via the Stokes drift, which is
described by the Stokes-Ekman  model. Waves continue to
evolve even under constant wind, which makes  steady
solutions of the Stokes-Ekman equation impossible. Since
the dynamics of the Ekman response in the presence of
evolving wave field have not been considered,  the basic
questions on how  the Ekman current evolves and,
especially, whether it grows or decays at large times,
remain open.

Here by employing the known self-similar laws of wave
field evolution and  solving analytically the
the Stokes-Ekman equation we  find and analyse
evolution of the Ekman current. We show that the system has
a single time dependent attractor which can be described
asymptotically. The large time asymptotics of the Ekman
current is found to be determined by the regime of wave
field evolution:  for the regimes typical of young waves
 the Ekman current grows with time to infinity, in contrast, for
`old waves'  the Ekman current asymptotically decays.


How to cite: Shrira, V. and Almelah, R.: What happens with the Ekman current under constant wind?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-588,, 2021.

Irina Soustova, Yuliya Troitskaya, and Daria Gladskikh

A parameterization of the Prandtl number as a function of the gradient Richardson number is proposed in order to correctly take into account stratification when calculating the thermohydrodynamic regime of inland water bodies. This parameterization allows the existence of turbulence at any values ​​of the Richardson number.

The proposed function is used to calculate the turbulent thermal conductivity coefficient in a k-epsilon mixing scheme. Modification is implemented in the three-dimensional hydrostatic model developed at the Research Computing Center of Moscow State University.

It is demonstrated that the proposed modification (in contrast to the standard scheme with a constant Prandtl number) leads to smoothing all sharp changes in vertical distributions of turbulent mixing parameters (turbulent kinetic energy, temperature and thickness of the shock layer) and imposes a Richardson number-dependent relation on the empirical constants of k-epsilon turbulent mixing scheme.

The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5) and by the RFBR (19-05-00249, 20-05-00776). 

How to cite: Soustova, I., Troitskaya, Y., and Gladskikh, D.: Modification of the k-epsilon scheme and its application for describing turbulence in inland water bodies, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8332,, 2021.

Lunch break
Chairpersons: Yuliya Troitskaya, Wu-ting Tsai, Vladimir Kudryavtsev
Remote sensing
Ad Stoffelen, Gert-Jan Marseille, Weicheng Ni, Alexis Mouche, Federica Polverari, Marcos Portabella, Wenming Lin, Joe Sapp, Paul Chang, and Zorana Jelenak

How strong does the wind blows in a hurricane proves a question that is difficult to answer, but has far-reaching consequences for satellite meteorology, weather forecasting and hurricane advisories. Moreover, huge year-to-year variability in extremes challenges evidence for changing hurricane climatology in a changing climate. Tropical circulation conditions, such as El Nino and the Madden Julian Oscillation, are associated with the large year-to-year variability and their link to climate change is poorly understood, though of great societal interest. Since hurricanes are sparsely sampled, satellite instruments are in principle very useful to monitor climate change. However, their stability over time in quality and quantity (sampling) needs to be guaranteed. Moreover, to use the longest possible satellite record, satellite instrument intercalibration of the extremes is needed [6]. This applies for a single instrument using a single processor version (calibration, Quality Control, Geophysical Model Function, retrieval) for change detection over a decade typically and the use of overlapping single-instrument/single-processor series for climate analyses. Currently, systematic inconsistencies in the extremes exist, as illustrated within the European Union (EU) Copernicus Climate Change Windstorm Information Service (C3S WISC*) and European organisation for the exploitatrion of Meteorological Satellites (EUMETSAT) C-band High and Extreme-Force Speeds (CHEFS^) projects. Besides for the scatterometers ERS, QuikScat, ASCAT and OSCAT, these instrument series may be extended to passive microwave wind instruments from 1979, if proven reliable at the extremes?

In the EUMETSAT CHEFS project, KNMI, ICM and IFREMER worked with international colleagues to improve the detection of hurricane-force winds. To calibrate the diverse available satellite, airplane and model winds, in-situ wind speed references are needed. Unfortunately, these prove rather inconsistent in the wind speed range of 15 to 25 m/s, casting doubt on the higher winds too. However, dropsondes are used as reference operationally at high and extreme winds in nowcasting and in the European Space Agency (ESA) project MAXSS satellite intercalibration is further investigated based on dropsondes to serve this community. However, from a scientific point of view, we should perhaps put more confidence in the moored buoy references? This would favor accuracy in drag parameterizations and physical modelling and observation of the extremes. This dilemma will be presented to initiate a discussion with the international community gathered at EGU ’21.

* Windstorm Information Service: 

^ C-band High and Extreme-Force Speeds:

How to cite: Stoffelen, A., Marseille, G.-J., Ni, W., Mouche, A., Polverari, F., Portabella, M., Lin, W., Sapp, J., Chang, P., and Jelenak, Z.: Hurricane ocean wind speeds, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11075,, 2021.

Evgeny Poplavsky, Nikita Rusakov, Olga Ermakova, Daniil Sergeev, Yuliya Troitskaya, and Galina Balandina

The work is concerned with the development of a method for the retrieval of tropical cyclones boundary atmospheric layer parameters, namely the wind friction velocity and wind speed at meteorological height. For the analysis, we used the results of field measurements of wind speed profiles from dropwindsondes launched from National Oceanic and Atmospheric Administration (NOAA) aircraft and collocated data from the Stepped-Frequency Microwave Radiometer (SFMR) located onboard of the same aircraft.

The results of radiometric measurements were used to obtain the emissivity values, which were compared with the field data obtained from the falling dropwindsondes. Using the algorithm taking into account the self-similarity of the velocity defect profile (Ermakova et al., 2019), the parameters of the atmospheric boundary layer were determined from the data measured by dropwindsondes. This algorithm gives an opportunity to obtain the wind speed value at meteorological height and wind friction velocity from the averaged data in the wake part of the profiles of the marine atmospheric boundary layer.

A comparison of the wind speed U10 dependencies, retrieved from the SFMR data and measurements from dropwindsondes, with the similar dependencies obtained in (Uhlhorn et al., 2007), was made, and their satisfactory agreement was demonstrated. This work was supported by the RFBR projects No. 19-05-00249, 19-05-00366.

How to cite: Poplavsky, E., Rusakov, N., Ermakova, O., Sergeev, D., Troitskaya, Y., and Balandina, G.: Development for wind friction velocity retrieval algorithm based on the SFMR and NOAA dropwindsondes measurements in hurricane conditions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9086,, 2021.

Adrian Callaghan

Breaking waves are an important physical feature of the ocean surface and play a fundamental role in many air-sea interaction processes. Sufficiently energetic breaking waves can entrain enough air that they appear as whitecaps on the ocean surface and these are the focus of this work. Phillips (1985) presents a statistical description of the length of breaking wave crest per unit area within a breaking speed interval Λ(c), often referred to as the “lambda distribution”. Many field studies have measured Λ(c) using digital image remote sensing of the ocean surface, corroborating the theoretical work of Phillips. In conjunction with the so-called breaking strength parameter, b, defined by Duncan (1981), the fifth moment of Λ(c) has been used to quantify the energy dissipation rate of the surface breaking wave field. Within the Duncan framework, many numerical and experimental laboratory studies have shown that b is not constant but depends on the spectral and physical slope of the breaking waves, and it can vary by several orders of magnitude.

Significant effort has been made to estimate the average value of the breaking strength parameter for populations of breaking waves observed in the field, <b>. This can be achieved with measurements of Λ(c), an estimate of the wind to wave energy flux and assumptions of a stationary wave field. While several recent field studies have estimated <b> to be O(1 X 10-3), independent estimates of <b> derived from averaging values of b estimated for individual whitecaps in a given sea state have not yet been reported.

Here digital images of the sea surface are analysed and the volume-time-integral (VTI) method presented in Callaghan et al (2016) is used to estimate b on a whitecap-by-whitecap basis. The VTI method uses the time-evolving surface foam area of a whitecap together with a laboratory-determined average turbulence intensity inside a breaking wave crest, to estimate the total energy dissipated by an individual whitecap. This total energy loss can then be used to calculate the average energy dissipation rate of an individual whitecap, from which b can be estimated.

The dataset presented here consists of approximately 500 whitecaps and the range of b values estimated is distributed between 1 X 10-4 to 1 X 10-2, with average values lying close to 1-2 X 10-3. This range of b values agrees well with laboratory results amassed over decades of experimental research. Furthermore, the average values of 1-2 X 10-3 agree very well with two recent <b> values reported in Zappa et al. (2016) and Korinenko et al. (2020). These results suggest that the VTI method can be a useful tool to remotely estimate the energy dissipation, and its rate, of individual whitecaps in the field using above-water digital image remote sensing.

How to cite: Callaghan, A.: Remote sensing of energy dissipation by individual oceanic whitecaps using above-water digital imagery, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10034,, 2021.

Nikita Rusakov, Georgy Baidakov, Evgeny Poplavsky, Yuliya Troitskaya, and Maksim Vdovin

The work is concerned with the study of the breaking surface wave effect on the intensity and spectral characteristics of a scattered radar signal in laboratory conditions.

The experiments were carried out on the reconstructed TSWiWaT wind wave flume of the IAP RAS. The channel is 12 m long, the channel cross-section varies from 0.7 x 0.7 m at the entrance to 0.7 x 0.9 m in the working section at a distance of 9 m. The airflow speed on the axis is 3-35 m/s, which corresponds to the values of the wind speed U10 of 11-50 m/s.

The wave characteristics in the flume were measured by an array of three wave gauges positioned in the corners of an equal-side triangle with 2.5 cm side, the data sampling rate was 200 Hz. Such a system gives the opportunity to retrieve 3D frequency-wave number spectra of surface waves.

The airflow parameters were measured using the profiling method. The velocity profiles were measured in the working section using an S-shaped Pitot tube. Microwave measurements were carried out using an X-band coherent Doppler scatterometer with a wavelength of 3.2 cm with sequential reception of linear polarizations.  The absolute value of the radar cross-section (RCS) on the wavy water surface was determined by comparing the scattered signal with the signal reflected from the calibrator with a known value of the RCS - a metal ball with a diameter of 6 cm. The dimensions of the observation cross-section were 40 cm x 40 cm, the incidence angles were 30°, 40°, 50° for the upwind direction, the distance to the target was 3.15 m.

Two series of experiments were carried out. In the first case, wind waves on the surface of pure deep water, developing under the action of a fan generated wind, were studied. In the second case, a train of three waves was generated at the beginning of the channel, with the fan turned on, in order to simulate shallow water an inclined plate was placed under water in front of the measurement area. As a result, the breaking waves occurred at a fixed point and at weaker winds compared to the first case.

As a result, an increase in the scattered signal intensity during artificial wave breaking in the case of weak winds was noted. For strong winds, the effect turned out to be insignificant, despite the increased amplitude of the waves under study. The Doppler spectra analysis is also presented.

This work was supported by the RFBR projects No. 19-05-00249, 19-05-00366.  

How to cite: Rusakov, N., Baidakov, G., Poplavsky, E., Troitskaya, Y., and Vdovin, M.: Investigation of X-band backscattering from wave breaking in a laboratory experiment, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9084,, 2021.

Hurricanes and complex phenomena at the air-sea interface
Sydney Sroka and Kerry Emanuel

Since air-sea enthalpy and momentum fluxes control a tropical cyclone’s intensification rate, increasing the accuracy of the associated bulk parameterizations is crucially important for improving forecast skill. Despite the powerful influence that sea spray has on air-sea enthalpy and momentum fluxes, most state-of-the-art tropical cyclone forecast models do not incorporate the microphysics of sea spray evaporation into their boundary layer flux schemes. We present the results from direct numerical simulations of the evaporating sea surface subject to a strong wind forcing to help evaluate the parameterizations of bulk exchange coefficients of momentum and enthalpy. By developing microphysics-based bulk parameterizations, the influence that sea spray exerts on tropical cyclone intensification can be more accurately simulated and intensity forecasts could be improved.

How to cite: Sroka, S. and Emanuel, K.: Numerical Simulations of the Evaporating Sea Surface Under Extreme Winds, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13543,, 2021.

Jialin Zhang, Wenqing Zhang, Haofeng Xia, and Changlong Guan

Sea spray has important influence on the evolution of tropical cyclone. The influence of sea spray in the numerical simulation and prediction of tropical cyclones is not ignorable. In order to explore the kinetic and thermodynamic effects of sea spray on tropical cyclone, the drag coefficient CD and the enthalpy transfer coefficient CK with sea spray’s effects were included in the coupled ocean-atmosphere-wave-sediment transport modeling system (COAWST). The numerical results show that, the effect of sea spray can effectively improve the simulation results of tropical cyclone path. When only the kinetic effect of sea spray is considered, the momentum flux at the surface of sea is little affected, and the upward sensible heat flux and latent heat flux are slightly increased. When kinetic and thermodynamic effects of sea spray is considered at the same time, the momentum flux is slightly increased, the upward sensible heat flux is increased, and the latent heat flux is significantly increased, the intensity of tropical cyclone is significantly enhanced, mainly due to the thermodynamic effect . Considering the kinetic and thermodynamic effects of sea spray at the same time is more effective than considering the kinetic effects of sea spray in improving the intensity simulation of tropical cyclone.

How to cite: Zhang, J., Zhang, W., Xia, H., and Guan, C.: Numerical simulation study of sea spray’s effect on tropical cyclone——a case study of typhoon “Megi”, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7191,, 2021.

Konstantinos Chasapis, Eugeny Buldakov, and Helen Czerski

The bubbles generated by breaking waves in the open ocean are an important feature of the ocean surface. They affect optical and acoustical properties of the top few meters of the ocean, influence surfactant scavenging, aerosol production and air-sea gas transfer. Short-lived larger bubbles which re-surface and burst dominate the transfer of less soluble gases such as carbon dioxide. A single wave crest approaching breaking deforms rapidly and in a storm sea the most common breaker is the spilling type. Detailed observations in space and time connecting the shape of the spilling breaker to subsequent bubble populations are limited, and the effect on the bubble penetration depth and residence time underwater is particularly important. In this study, we carried out a series of experiments to track the formation and evolution of large bubbles for different local crest geometries.

A breaking wave in a wave flume was generated with dispersive focusing of a wave group. The group has a pre-defined amplitude spectrum. Running experiments with different phase shifts of the same amplitude spectrum showed that when a peak-focussed wave (zero phase shift) breaks, then wave groups with other added phase shifts break as well. To investigate possible differences in the deformation of those breakers a laser imaging technique was used. An algorithm identified the 2D shape of the breaker in successive images. It also separated the crests from bulges based on geometric criteria. We showed that, despite wave groups having same spectra, the extracted bulges differed locally in shape, volume and velocity for each phase shift at the location of breaking. Therefore, breakers ranging from the more traditional spilling type, which has a bulge that collapses on the front face of the wave, to the micro-plunging type, which has a pronounced overturning tip, were observed depending on the phase shift. 

The evolution of bubbles for each phase shifted bulge was captured by a high speed camera and measured by a feature extraction algorithm. We generally found that spilling bulges created fewer bubbles in total than micro-plungers. They also created fewer larger bubbles, i.e. with radius r>1 mm, at all measured flume areas. In contrast, micro-plungers that trap air within a small cavity as they break had less steep size distributions for r>1 mm. The maximum volume of air per radius showed a gradual shift from r>1 mm to r=1 mm moving away from the breaking location for all breakers. It is interesting, finally, that the maximum volume per radius did not shift to smaller radii as time passes. This is an indication that the largest bubbles, i.e. r>4 mm, rise to the surface and burst instead of splitting into smaller ones, irrespectively of the local breaker properties. 

How to cite: Chasapis, K., Buldakov, E., and Czerski, H.: Evolution of bubble statistics in intermediate water due to phase shifted breaking wave groups, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2003,, 2021.

Alexander Kandaurov, Yuliya Troitskaya, Vasiliy Kazakov, and Daniil Sergeev

Whitecap coverage were retrieved from high-speed video recordings of the water surface obtained on the unique laboratory faculty The Large Thermostratified Test Tank with wind-wave channel (cross-section from 0.7×0.7 to 0.7×0.9 m2 at the end, 12 m fetch, wind velocity up to 35 m/s, U10 up to 65 m/s). The wind wave was induced using a wave generator installed at the beginning of the channel (a submerged horizontal plate, frequency 1.042 Hz, amplitude 93 mm) working in a pulsed operation (three periods). Wave breaking was induced in working area by a submerged plate (1.2×0.7 m2, up to 12 depth, AOA -11,7°). Experiments were carried out for equivalent wind velocities U10 from 17.8 to 40.1 m/s. Wire wave gauge was used to control the shape and phase of the incident wave.

To obtain the surface area occupied by wave breaking, we used two Cygnet CY2MP-CL-SN cameras with 50 mm lenses. The cameras are installed above the channel at a height of 273 cm from the water surface, separated by 89 cm. The image scale was 302 μm/px, the size of the image obtained from each camera is 2048x1088 px2, which corresponds to 619x328 mm2 (the long side of the frame along the channel). The shooting was carried out with a frequency of 50 Hz, an exposure time of 3 ms, 250 frames were recorded for each wave train. To illuminate the image areas to the side of the measurement area, a diffuse screen was placed on the side wall, which was illuminated by powerful LED lamps to create a uniform illumination source covering the entire side wall of the section.

Using specially developed software for automatic detection of areas of wave breaking, the values of the whitecap coverage area were obtained. Automatic image processing was performed using morphological analysis in combination with manual processing of part of the frames for tweaking the algorithm parameters: for each mode, manual processing of several frames was performed, based on the results of which automatic algorithm parameters were selected to ensure that the resulting whitecap coverage corresponded. Comparison of images obtained from different angles made it possible to detect and exclude areas of glare on the surface from the whitecap coverage.

The repeatability of the created wave breakings allows carrying out independent measurements for the same conditions, for example the parameters of spray generation will give estimations of the average number of fragmentation events per unit area of the wave breaking area.

The work was supported by the RFBR grants 21-55-50005 and 20-05-00322 (conducting an experiment), President grant for young scientists МК-5503.2021.1.5 (software development) and the RSF grant No. 19-17-00209 (data processing).

How to cite: Kandaurov, A., Troitskaya, Y., Kazakov, V., and Sergeev, D.: Whitecap coverage measurements in laboratory modeling of wind-wave interaction in presence of induced wave breaking, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12033,, 2021.

Royston Fernandes, Marie-Noelle Bouin, and Jean-Luc Redelsperger

The ability to estimate flux exchanges between the sea-surface and the atmosphere has tremendous importance on weather prediction and climate simulations. These exchanges are influenced by wave processes - growth and decay, and turbulent interactions at the air-sea interface. For momentum, the ensemble of these exchanges is presented as the sea-surface drag (Cd), which increases with (10-m high) wind intensity till about 20-30 m/s, and decreases thereafter. The reason for this decrease remains less understood, mainly due to (i) our inability to explicitly measure the individual wind-wave exchanges, and (ii) the inability of existing semi-empirical parameterizations to explain the Cd behavior. To this end, we developed a physically based stress parameterization for a coupled wind-wave model, capable of reproducing both wave growth and wave breaking stresses at the air-sea interface. The advantage of such a numerical approach, over field experiments, is that it allows us to investigate the different process, under different constraining environments, in-order to disentangle the factors in play on Cd. Our coupled model enables a two-way interaction between the ocean-waves and turbulent flow. and can simulate (i) the main turbulent eddies of the air-flow, and (ii) the wind-wave interactions. After evaluating the model against published field experiments we use it to explore the impact of wave growth and wave-breaking on the Cd under strong winds. Our results demonstrate that under strong winds the air-flow gets separated from the sea-surface, a process associated with wave-breaking, resulting in the turbulent flow sensing a smoother surface as against an actually rough sea surface, thereby decreasing Cd. Finally, our model allows us to investigate the sensitivity of Cd to different influencing factors under strong winds.

How to cite: Fernandes, R., Bouin, M.-N., and Redelsperger, J.-L.: A new physically based parameterization for wind-wave stresses under strong winds, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15905,, 2021.

Xingkun Xu, Joey Voermans, Alexander Babanin, Hongyu Ma, and Changlong Guan

As one of typical elements in the air-sea boundary layer, sea spray is expected to mediate energy flux exchange in the air and ocean boundary layers, and therefore it is of crucial importance to the meteorology, oceanology, and regional climatology. In addition, the spray is also considered as one of the missing physical mechanisms in atmospheric and oceanic numerical models. Hence, it is necessary to accurately predict how much sea spray is produced at the air-sea boundary layer. Though spray has been studied for a number of decades, large uncertainties still linger. For instance, uncertainties in qualifying how much spray is produced on the sea surface reach 106 times. This is because of the rarity of spray observations in the field, especially under strong wind condition.

To give a reliable spray production model, scientists tried to employ laser-based facilities in the field to observe sea spray by interpreting infrared laser-beam intensity into sea spray volume flux over the water surface. Hence, in the current study, we collected datasets in the field measured by laser-based facilities on the North-West Shelf of the coast of Western Australia, thereafter, further analyzed, and calibrated them through a series of academic, statistical, and physical analysis to ensure the data quality. After that, assuming the existence of spray drops in the air-sea layer would attenuate the infrared laser-beam intensity, the weakening extends of laser-beam intensity is used to estimate the volume flux of sea spray above the ocean surface at winds speed ranging from light to extreme during the passage of Tropical Cyclone Olwyn (2015). It should be noted that our observations of sea spray volume flux are within the ranges of existing models and are consistent with the model proposed by Andreas (1992) in both trend and magnitude.

Using the field observations of the sea spray volume flux, a sea spray volume flux model can be constructed. Given that sea spray droplets are generated at the ocean surface through breaking waves and wind shear, the sea spray volume flux is expected to be dominated by the properties of the local wind and wave field. For physical consistency across the wide range of scales observed in the field and laboratory, non-dimensional parameters (i.e., non-dimensional wind speed and the mean wave steepness) were adopted to construct the model. Consequently, a power-law non-dimensional spray volumetric flux model is suggested based on the estimation of the spray volume flux. It should be noted that one sensitive test was conducted to substantiate the inclusion of wave breaking process, here simply included with the mean wave steepness, improves spray volume flux parameterization.

How to cite: Xu, X., Voermans, J., Babanin, A., Ma, H., and Guan, C.: The estimation of sea spray at wind speeds ranging from light to extreme, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3568,, 2021.

Alexandra Kuznetsova, Alexander Dosaev, Nikita Rusakov, Evgeny Poplavsky, and Yuliya Troitskaya

The ice cover decrease in the Arctic in the past decade has led to polar hurricanes (polar lows) occurring along the entire Northern Sea Route. Wind speeds of these hurricanes reach 35-40 m / s. Over the past 20 years, significant progress in predicting storm trajectories has been achieved, while the quality of forecasting their intensity is still poor. This is due to the fact that the intensity (maximum wind speed and minimum pressure) is determined by the interaction of the atmosphere and the ocean, and at high wind speeds it has significant uncertainty, especially for the smallest-scale processes: splashes, wave collapses and foam bubbles [1].

Numerical modeling of the polar low development was carried out within the framework of the WRF model [2] in order to develop methods for modeling such extreme events. The water area of the Barents Sea was considered, where a large number of polar hurricanes were observed. Among the identified polar hurricanes [3], a hurricane that took place on 02/05/2009 and was observed at coordinates 69º N, 40º E was chosen. Several approaches were considered to simulate the weather conditions in the studied area of the Barents Sea in the presence of a polar hurricane. The WRF model simulation with the CFSR reanalysis was carried out. The configuration of the model consisted in using, first, the well-proven technique of Large Eddy Simulation (LES) modeling of the planetary boundary layer (PBL). Secondly, the simulation was performed using the WRF add-in for the polar region, Polar WRF [4]. The comparison of the approaches is made. The mechanism of intensification of the atmospheric vortex is considered whether it is baroclinic shear, heat fluxes on the surface or outcome of latent heat during condensation.

This work was supported by a RFBR grant № 18-05-60299.


1. Troitskaya, Yu, et al. "Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds." Scientific reports7.1 (2017): 1-4.
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How to cite: Kuznetsova, A., Dosaev, A., Rusakov, N., Poplavsky, E., and Troitskaya, Y.: Methods of modeling the polar low development , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10802,, 2021.

Anna Zotova, Yuliya Troitskaya, Alexander Kandaurov, and Daniil Sergeev

Fundamental contribution to the formation of sea spray under strong winds is provided by the bag-breakup phenomenon - rupture of film in the form of parachute [1]. Breaking of water film into droplets is caused, among other factors, by processes occurring on the free edge of the film moving under action of surface tension forces. The study of these processes will help to understand how characteristics of the film and the drops appearing after its rupture are related.

Using the Basilisk software package with Volume of Fluid advection scheme for interfacial flows, numerical simulation of three-dimensional water film placed in domain filled with air was carried out. The water film was placed into domain filled with air. One of the edges of the film is free, and the second is fixed on the left boundary of the domain; along the third coordinate, the boundary conditions are periodic. At the initial moment of time, the film is defined by a sheet with variable thickness - the upper boundary has the form of a cosine. The change in the shape of the film over time was recorded. It is revealed that the inhomogeneity of the film thickness leads to the appearance of a significant curvature of the edge of the film as it moves under the action of surface tension forces.

This work was supported by the RFBR grants (20-05-00322, 21-55-50005, 21-55-52005) and RSF grant 19-17-00209.

[1] Troitskaya, Y. et al. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Sci. Rep. 7, 1614 (2017).

How to cite: Zotova, A., Troitskaya, Y., Kandaurov, A., and Sergeev, D.: Numerical simulation of water film edge dynamics, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14110,, 2021.

Oleg Druzhinin

Now it is a common knowledge that at sufficiently strong winds, sea-spray droplets interfere with  turbulent exchange processes occurring between atmosphere and hydrosphere. The results of field and laboratory experiments show that mass fraction of air-borne spume water droplets increases with the wind speed and their impact on the marine atmospheric boundary layer may become significant. The contribution of droplets to the momentum and sensible and latent heat fluxes may be crucial for our understanding of conditions favorable for the development of anomalous weather phenomena such as tropical hurricanes and polar lows. Phenomenological models and bulk algorithms are mostly based on hypothetical assumptions concerning the properties of droplet-air interaction which strongly influence the accuracy of their forecast. Lagrangian stochastic modeling also requires an adhoc knowledge of the properties of turbulent fields ‘seen’ by the droplets along their trajectories. These details of droplet-air interaction are difficult to measure in lab conditions and can be gleaned via direct numerical simulation (DNS). DNS solves primitive equations for the carrier air in the Eulerian frame and of droplets motion in a Lagrangian frame and accounts for the two-way coupling of momentum, heat and moisture between the carrier and dispersed phases, and allows us to investigate the droplet contribution to the exchange fluxes under different injection conditions and flow bulk parameters. The results obtained for different conditions show us that droplets dynamics and their contribution to the momentum and heat fluxes are controlled by many factors including droplets velocity at injection, the gravitational settling velocity, surface wave slope, bulk relative humidity and temperature of the atmospheric boundary layer as compared to the sea surface conditions.

This work is supported by the Ministry of Education and Science of the Russian Federation (Task No. 0030-2019-0020). Numerical algorithms were developed under the support of RFBR (20-05-00322, 21-55-52005, 18-05-60299). Postprocessing was performed under the support of the Russian Science Foundation (No. 19-17-00209).

How to cite: Druzhinin, O.: Direct numerical simulation of droplet-mediated exchange fluxes in the marine atmospheric boundary layer, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13107,, 2021.