NP6.4

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, https://doi.org/10.5194/egusphere-egu21-3836, 2021.

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, https://doi.org/10.5194/egusphere-egu21-8093, 2021.

We derive the energy transfer rate ε from the 3^rd order relative (longitudinal)  velocity structure function <Δu_l³>=(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 <Δu_l³> for inertial scales (above the injection scale) and slope 2 for  the 2^nd order structure function <Δu_l²> 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^-α 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(Δu_ls) of relative longitudinal velocity Δu_l  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, https://doi.org/10.5194/egusphere-egu21-10184, 2021.

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, https://doi.org/10.5194/egusphere-egu21-11054, 2021.

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, https://doi.org/10.5194/egusphere-egu21-13453, 2021.

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, https://doi.org/10.5194/egusphere-egu21-7745, 2021.

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, https://doi.org/10.5194/egusphere-egu21-9511, 2021.

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, https://doi.org/10.5194/egusphere-egu21-543, 2021.

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, https://doi.org/10.5194/egusphere-egu21-4175, 2021.

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, https://doi.org/10.5194/egusphere-egu21-7377, 2021.

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, https://doi.org/10.1140/epjb/e2013-40681-2 (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, https://doi.org/10.1002/qj.2817

[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, https://doi.org/10.1002/qj.3554

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, https://doi.org/10.5194/egusphere-egu21-12129, 2021.

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, https://doi.org/10.5194/egusphere-egu21-14125, 2021.

How to cite: Sibgatullin, I., Elistratov, S., and Ermanyuk, E.: Turbulent wave attractors in large-aspect ratio domains., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14557, https://doi.org/10.5194/egusphere-egu21-14557, 2021.

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, https://doi.org/10.5194/egusphere-egu21-10437, 2021.

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.

Acknowledgements

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, https://doi.org/10.5194/egusphere-egu21-11302, 2021.

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: https://doi.org/10.1002/essoar.10504620.1]. 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, https://doi.org/10.5194/egusphere-egu21-14407, 2021.

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 ω_F=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, https://doi.org/10.5194/egusphere-egu21-10904, 2021.

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, https://doi.org/10.5194/egusphere-egu21-1252, 2021.

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).

References:

[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, https://doi.org/10.5194/egusphere-egu21-10311, 2021.

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, https://doi.org/10.5194/egusphere-egu21-609, 2021.

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, https://doi.org/10.5194/egusphere-egu21-588, 2021.

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, https://doi.org/10.5194/egusphere-egu21-8332, 2021.

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: https://wisc.climate.copernicus.eu/ 

^ C-band High and Extreme-Force Speeds: https://www.eumetsat.int/chefs

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, https://doi.org/10.5194/egusphere-egu21-11075, 2021.

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, https://doi.org/10.5194/egusphere-egu21-9086, 2021.

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, https://doi.org/10.5194/egusphere-egu21-10034, 2021.

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, https://doi.org/10.5194/egusphere-egu21-9084, 2021.

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, https://doi.org/10.5194/egusphere-egu21-13543, 2021.

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, https://doi.org/10.5194/egusphere-egu21-2003, 2021.

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, https://doi.org/10.5194/egusphere-egu21-12033, 2021.

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, https://doi.org/10.5194/egusphere-egu21-3568, 2021.

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, https://doi.org/10.5194/egusphere-egu21-13107, 2021.