Internal waves are crucial contributors to the transport of sediment, heat, and nutrients in coastal areas. While internal waves have been extensively studied using point measurements, their spatial variability is less well understood. Here, we present a unique set of high-resolution infrared imagery collected from a helicopter, hovering over very energetic shoaling and breaking internal waves. We compute surface velocities by tracking the evolution of thermal structures at the ocean surface and find horizontal velocity gradients with magnitudes that are more than 100 times the Coriolis frequency. Under the assumption of no vertical shear we determine vertical velocities from the obtained horizontal divergence estimates and identify areas of the wave undergoing breaking. The spatial variability of the internal wave occurs on scales from a few to a few hundred meters. These results highlight the need to collect spatio-temporal observations of the evolution of internal waves in coastal areas.

How to cite: Vrecica, T., Pizzo, N., and Lenain, L.: Airborne observations of shoaling and breaking internal waves, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-132, https://doi.org/10.5194/egusphere-egu23-132, 2023.

While most theoretical work on internal waves idealizes the stratification, geophysical stratifications are typically much more complicated.  We build on recent work on nearly linear stratifications by adopting perturbations that take the form of a localized patch of mixing. We present a data-centric framework that seeks to identify which locations and widths of a mixing patch yield the largest effect on the structure of exact waves (computed via the Dubreil-Jacotin-Long equation), linear waves (computed via the longwave Taylor-Goldstein equation), and evolving nonlinear waves (via time-dependent simulations using the incompressible Navier-Stokes equations). We find that the vertical structure functions of linear waves are most sensitive to perturbations below (above) the pycnocline when the pycnocline is above (below) mid-depth; furthermore, as the pycnocline approaches mid-depth, the depth of the perturbation layer with the greatest impact approaches the depth of the pycnocline. In contrast, the centre streamwise velocity profile of a DJL wave is perturbed most by layers above (below) the pycnocline when the pycnocline is above (below) mid-depth. Finally, we present the results of simulations of evolving nonlinear waves, where we compare pairs of cases with and without a perturbation layer. Despite the presence of an initial patch of unstable fluid, the perturbation layer is sustained during the simulation; nevertheless, slight Rayleigh-Taylor instabilities are observed within and about the perturbation layer. Modulations in the horizontal velocity field about the leading solitary wave are compared with the results of the linear and DJL analyses.

How to cite: Castro-Folker, N. and Stastna, M.: The sensitivity of internal solitary waves to localized patches of mixing, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3642, https://doi.org/10.5194/egusphere-egu23-3642, 2023.

The Bay of Biscay (Bob) is a hot spot for the generation of internal tides and nonlinear internal waves (NLIW). However, no studies have focused on internal waves on the continental shelf of the Bob. Here, we present 22 days of collocated temperature, velocity and backscatter profiles within a water depth H of 65 m. The background stratification evolved from two pycnoclines, with the strongest one near the sea bed, to a continuous profile due to wind-driven upwelling.

Under the double pycnocline situation, we observed trains of elevation emerging from each internal tidal front with amplitude reaching up to H/4 and propagating at speeds between 0.1 and 0.35 m/s. Sporadically depression waves were measured within the train and can propagate substantially faster (between 0.36 and 0.54 m/s). With the continuous stratification, the trains of NLIWs of elevation and containing opposite polarities were no longer observed.

These observations suggest that depression waves can cross the train of elevation waves. Resulting interactions could have significant impacts on sediment dynamics over the shelf. The double pycnocline regime and the impact of the stratification modification due to wind will be investigated numerically in future work.

How to cite: Moncuquet, A., Jones, N., Bordois, L., Zulberti, A., Dufois, F., Grasso, F., and Lazure, P.: In situ observation of mode 1 nonlinear internal waves of opposite polarity in a changing environment, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13078, https://doi.org/10.5194/egusphere-egu23-13078, 2023.

Energy dissipation due to the breaking of surface waves remains an important open topic in both the open ocean and in coastal waters. Here we will discuss similarities between the deep- and shallow-water regimes. To do this, we first present data from direct numerical simulations of shoaling and breaking solitary waves in bathymetric depth transition. In an abrupt depth transition, we investigate the influence of the severity of the depth transition on whether the incident wave will break, finding good agreement with experimental data of Losada et al. (1988). We next investigate the energy dissipation rate in a gradual, linear depth transition. The resulting dataset is compared with an array of existing physics-based scaling arguments, and finds especially good agreement with an inertial model of Mostert & Deike (2020). We then discuss possible scaling approaches for understanding breaker dissipation in shallow water and draw comparisons with deep-water data and models. We will conclude with some insights towards a potential universal breaking parametrisation.

How to cite: Mostert, W., Boswell, H., and Yan, G.: Breaking threshold and energy dissipation in solitary waves in a depth transition, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-15066, https://doi.org/10.5194/egusphere-egu23-15066, 2023.

We report on results from laboratory experiments performed in a quasi-two-layer system of cold and warm water in a rectangular laboratory tank. Warm front propagation is initiated by removing a vertical barrier from between the two prepared sections of the tank containing cold and warm water filled up to the same level. The warm front propagation in the vicinity of the free water surface is monitored using a high precision infrared camera from above, and with dye visualisation from the side simultaneously. After the warm front reaches the sidewall of the tank, its "head" is reflected, and hence an internal bore emerges along the interface separating the two layers. Following further reflections the bore splits to a train of internal solitary waves, resembling the solutions of the KdV equation. We find that, interestingly, although the waves propagate along the internal interface, certain surface signatures of the bore and wave dynamics can be detected from the water surface temperature fields due to secondary convective flows. This result may have certain applicability for the detection of internal waves using infrared sea-surface temperature data from satellites.

How to cite: Vincze, M. and Kiss, Z. Á.: Laboratory experiments on internal solitary wave reflections and their detectability via water surface infrared thermography, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-14424, https://doi.org/10.5194/egusphere-egu23-14424, 2023.

Tidal bores are natural phenomena observed in at least 450 river estuaries all around the world from Europe to America and Asia. Tidal bores manifest as a series of waves propagating over long distances upstream in the estuarine zone of a river. Bores can be studied experimentally using sloshing water tanks where sloshing itself is a process with many applications, not only relevant for environmental flows. In a remarkable paper, Cox and Mortell (1986) showed that for an oscillating water tank, the evolution of small-amplitude, long-wavelength, resonantly forced waves follow a forced Korteweg-de Vries (fKdV) equation. The solutions of this model agree well with experimental results by Chester and Bones (1968). At first glance this is surprising since their experimental setup is in conflict with a number of assumptions made for deriving the fKdV equation. It is hence worth to repeat the experiment by Chester and Bones but using a long narrow channel setup.

We use a long circular channel and repeat the experiments by Chester and Bones. We compare the results with solutions from the fKdV equation but also with the one from a full nonlinear model solving the Navier-Stokes equations. Under resonance conditions, depending on the parameters, we find a range of nonlinear localized wave types from single and multiple solitons to undular bores. As shown by Cox and Mortell, when the fluid is considered to be inviscid a kind of Fermi-Pasta-Ulam recurrence is observed for the fKdV model. Stationarity is reached by including a weak damping to the fKdV equation. 

References
A.A. Cox, M.P. Mortell 1986. J. Fluid Mech. 162, pp. 99-116.
W. Chester and J.A. Bones 1968. Proc. Roy. Soc. A, 306, 23 (Part II).

How to cite: Harlander, U., Schön, F.-T., Borcia, I. D., Richter, S., Borcia, R., and Bestehorn, M.: Resonant water-waves in a circular channel: forced KdV solutions, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-15036, https://doi.org/10.5194/egusphere-egu23-15036, 2023.

Emulsions are a major class of multiphase flows, crucial in industrial process (e.g. food and drug production) and ubiquitous in environmental flows (e.g. oil spilling in maritime environment). Already at volume fractions of few precents, the dispersed phase interacts with pre-existing turbulence created at large scale, yet the interaction between phases and the turbulent energy transport across scales is not yet fully understood.

In this work, we use Direct Numerical Simulation to study emulsions in homogeneous and isotropic turbulence, where the Volume of Fluid (VoF) method is used to represent the complex features of the liquid-liquid interface.

We consider a mixture of two matching-density phases, where we vary volume fraction, viscosity ratio and large-scale Weber number aiming at understanding the turbulence modulation and the observed droplet size distributions.  The analysis, based on the spectral scale-by-scale analysis, reveals that energy is consistently transported from large to small scales by the interface, and no inverse cascade is observed. We find that the total surface is directly proportional to the amount of energy transported, and that the energy transfer in the inertial range provides information about the droplet dynamics. We observe the -10/3 and -3/2 scaling on droplet size distributions, suggesting that the dimensional arguments which led to their derivation are verified in HIT conditions and denser conditions. Finally, we discuss the highly intermittent behaviour of the multiphase flow, which can be directly related to the polydisperse nature of the flow.

The study provides some significant observations towards a more comprehensive understanding of multiphase turbulence, opening new questions for future studies. 

How to cite: Chibbaro, S., Crialesi-Esposito, M., and Brandt, L.: Droplet dynamics in homogeneous and isotropic turbulence, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-5790, https://doi.org/10.5194/egusphere-egu23-5790, 2023.

The Canary Islands region is located in the North-East Atlantic Ocean, next to the African coast. It is situated within the equatorward travelling Canary Current.

This area has a high mesoscale activity. Some important features of this area are the African Upwelling System, the filaments originated by the upwelling, and long-lived cyclonic and anticyclonic mesoscale eddies. The generation of these mesoscale eddies, by the perturbation of the Canary Current caused by the islands, has been largely studied.

The aim of this work is to use a novel Hybridisable Discontinuous Galerkin (HDG) oceanic model, based on Finite Elements, in addition to real in situ and satellite data, in order to study different generation mechanisms and the evolution of the mesoscale eddies south of the Canary Islands.

How to cite: Hernández García, I., Oliver Serra, A., and Machín Jiménez, F.: Use of HDG oceanic models to study eddy formation in coastal upwelling areas, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-6336, https://doi.org/10.5194/egusphere-egu23-6336, 2023.

During the austral midsummer near the South Shetland Islands, an interdisciplinary cruise (COUPLING) was carried out in January 2010 (Sangrà et al, 2014). For this study we selected one transect of 12 stations across the Central Bransfield Strait with vertical profiles of Conductivity, Temperature and Depth (CTD) and Acoustic Doppler Current Profiler (ADCP). Vertical profiles of microstructure turbulence were measured at stations of the transect located in specific dynamic features (two fronts: Bransfield Front and Peninsula Front; and an anticyclonic eddy) from a free-fall turbulence profiler. Using CTD and ADCP data, we computed the Thorpe scales, gradient Richardson numbers and density ratios that were compared with microstructure data.

We found that the most active turbulent layer was observed within the upper mixed layer (UML) of the anticyclonic eddy between stations 3 and 6 of the transect. However, intense inversions below the UML were found at the axis of the Peninsula Front (station 9). In the region of the Bransfield Front, it is noteworthy that there were obtained relative high values of kinetic energy dissipation rate (ε) with mixing processes due to vertical shear instabilities and double diffusion.  With this work, we have a deeper understanding of the mixing processes in the Bransfield Strait, which will allow a better estimation of the vertical fluxes of heat, salt and nutrients for this region.

Key words:

Bransfield Strait, Diapycnal Mixing, Microstructure Turbulence.

References:

Sangrà, P., C. García-Muñoz, C.M. García, A. Marrero-Díaz, C. Sobrino, B. Mouriño-Carballido, B. Aguiar-González, C. Henríquez-Pastene, A. Rodríguez-Santana, L. M. Lubián, M. Hernández-Arencibia, S. Hernández-León, E. Vázquez, S.N. Estrada-Allis (2014). Coupling between upper ocean layer variability and size-fractionated phytoplankton in a non-nutrient-limited environment. Marine Ecology Progress Series, 499, 35-46.

How to cite: Rodríguez-Santana, Á., Aguiar-González, B., Marrero-Díaz, Á., Valencia, L. P., and Machín, F.: Diapycnal Mixing in the Bransfield Strait, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-9614, https://doi.org/10.5194/egusphere-egu23-9614, 2023.

The Gulf Stream plays an important role in the meridional overturning circulation in the North Atlantic, one of the primary mechanism by which the warm, salty water can move from low to high latitudes. It also provides closure to the North Atlantic subtropical gyre circulation as a western boundary current and makes Western European countries much warmer by transporting warm water across the ocean.

Observational data of the Gulf Stream (along the Oleander line, between New Jersey and Bermuda) has found that its stream-wise velocity skews to the right with increasing depth. This has motivated our development of an idealized model of a laterally skewed Gulf Stream jet that is surface trapped overlying a flat bottom. The nonlinear evolution of this unstable asymmetric jet is investigated using the Oceananigans.jl library for multiple values of a skewness parameter. The results show that the maximum growth rate has a nonlinear dependency on the skewness parameter, though weak and strong skew tend to be stabilizing and destabilizing, respectively. 

How to cite: Poulin, F.: The stability of an asymmetric slice of the Gulf Stream, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-10130, https://doi.org/10.5194/egusphere-egu23-10130, 2023.

Ocean currents have been observed to impact the spatial distribution of significant wave height (hereafter "Hs") of surface gravity waves profoundly, with implications for air-sea fluxes, extreme waves, and error budget in satellite observations. In this work, we derive analytic formulas that relate Hs to current velocities under the weak-current approximation, cross-validate the results with WAVEWATCH III, and find implications potentially useful for observational and modelling studies. 

First, we show that when swell-like surface waves interact with a localized current, caustics, where rays cross in real space, do not lead to singularities in Hs if the wave energy spectra have a realistic directional spread in wavenumber space. This has implications for understanding the origin of freak waves, where caustics have been postulated as a possible source. Then, we consider another regime where weak turbulent flows are considered. Analytic formulas are found that deterministically link the patterns of Hs to currents. The formulas' statistical counterparts are applied to study how the spectral slopes, amplitudes and directionality of Hs are related to currents. Our results demonstrate that the variations of Hs are controlled by the rotational component of the currents, suggesting the potential of using information from surface wave to infer current properties in real observations, or vice versa.

How to cite: Wang, H., Villas Bôas, B., Vanneste, J., and Young, W.: Imprint of ocean currents on signicant wave height, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-16032, https://doi.org/10.5194/egusphere-egu23-16032, 2023.

We present experimental results from large-scale laboratory experiments of rotating downslope gravity currents intruding into a two-layer stratified ambient performed in the Coriolis Rotating Platform in Grenoble. By means of PIV velocity and conductivity data for the density measurement, we show that mixing occurs mostly on the slope area during the descent rather than once the current has penetrated the stratified ambient, where the Richardson number remains above the stability threshold of 1/4. Looking at the time evolution of the vertical density profile in the stratified receiving ambient, two distinct mixing regimes can be identified, the first issued by laminar transport through Ekman dynamics, the second by turbulent transport due to intermittent cascading events. Vertical density gradients reveal a linear piece-wise dependence on the density anomaly, highlighting an advection-diffusion process as proposed by the theoretical model of Munk & Wunsch (1998). If the gravity current flow is laminar on the slope, the structure shows a linear variation of the density with depth ; For the turbulent transport regime characterized by intermittent cascades, an exponential shape is rather observed. The shape of the density structure allows to estimate bulk mixing coefficients and entrainment velocities at the top and the bottom of the intruding gravity current, which can be further compared to oceanographic observational data.

How to cite: Rétif, S., Negretti, M.-E., Wirth, A., and Tassigny, A.: Laminar transport and turbulent cascades in downslope rotating gravity currents., EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-2594, https://doi.org/10.5194/egusphere-egu23-2594, 2023.

Realistic currents in seas and oceans are almost always changing in depth thus indicating on the presence of shear in the mean ambient flow. However, analysis methodologies interpreting directional wave data gathered by in-situ measurement devices such as: buoys, pressure gauges and Acoustic Doppler Current Profilers (ADCPs) utilize potential irrotational flow theory which cannot account for the rotational shearing currents. The effects of shearing currents on the wave direction estimations were studied on synthetic ADCP data of waves propagating in a predetermined spread. The synthetic data was generated employing the Rayleigh Boundary Value Problem (BVP) and a selected ambient current profile. The potential data processing led to significant errors in wave directional spread estimation for common shearing currents (~10°  in mean wave direction for the presented example). This finding is of great importance, as it addresses the influence of an ambient current profile on wave propagation direction. The obtained results suggest that there is an uncertainty with the confidence of any wave directional spread ever presented by in-situ wave measurement devices.

A new methodology was developed for estimating directional wave spectra based on rotational flow physics by acquiring new terms emanate from wave-shearing current interaction governing equations. This included a derivation of new numerical transfer functions for the fluid’s physical properties based on the Rayleigh BVP. Then, by applying classical cross- and auto-spectral analysis on time-series data sets, the directional spread function was numerically reconstructed. The newly derived data processing methodology was applied to the same synthetic ADCP data sets. It was found to be capable of reconstructing the spread with great accuracy (0.4° in mean wave direction for the presented example). In addition, to modeling and synthetic data, field measurement data from several campaigns were also analyzed showing the importance of accounting for the vertical shear. This makes it a prominent methodology for estimating directional wave spectra in realistic oceanic conditions.

How to cite: Toledo, Y., Soffer, R., and Kit, E.: New method of directional spectrum estimation accounting for ambient shearing currents, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4236, https://doi.org/10.5194/egusphere-egu23-4236, 2023.

It is known that the wave action propagated in spectral wave models is a small steepness approximation of the observable wave action. For relevant steepness, we need higher order corrections to get a proper representation of the sea states [Janssen, 2009]. For the same reasons, other diagnostic variables should be corrected. Based on the fifth order Stokes solution obtained by Fenton [1985], Jonsson and Arneborg [1995] showed the importance of higher order corrections for determining the energy properties of long crested waves.

Proceeding from Longuet-Higgins and Stewart [1960], assuming a mean stream velocity, we see that how, using Krasitskii [1994] canonical transformations, we can derive general 2D weakly non linear corrections to the rate of transfer of energy across a surface fixed in space. For a monochromatic wave, the resulting equations are compared with truncated expressions given by Jonsson and Arneborg [1995], confirming that second order contributions (in terms of wave energy) can be relevant, depending on steepness and relative water depth.
After applying a proper statistical closure, the derived equations can be used to correct the wave energy properties of wave models spectra, for example to refine the informations transferred to a coupled circulation model.

John D. Fenton. A Fifth-Order Stokes Theory for Steady Waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 111(2):216–234, 1985. ISSN 0733-950X.
Peter a. E. M. Janssen. On some consequences of the canonical transformation in the Hamiltonian theory of water waves. J. Fluid Mech., 637(November):1–44, 2009. ISSN 1469-7645.
Ivar G. Jonsson and Lars Arneborg. Energy properties and shoaling of higher-order stokes waves on a current. Ocean Engineering, 22(8):819–857, 1995. ISSN 00298018.
Vladimir P. Krasitskii. On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech., 272(-1):1–20, 1994. ISSN 0022-1120.
M. S. Longuet-Higgins and R W Stewart. Changes in the form of short gravity waves on long waves and tidal currents. Journal of Fluid Mechanics, 8(04): 565–583, 1960.

How to cite: Pezzutto, P.: Weakly nonlinear wave energy flux and radiation stress, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-14457, https://doi.org/10.5194/egusphere-egu23-14457, 2023.

Due to the climate change, it is necessary to modify the energy modes of production. The mix energetic, based on renewable energies as tidal currents, is one of the solutions to decrease the energy production carbon footprint. This study focuses on hydrodynamic interactions in Alderney Race (France), which is the most energetic tidal site in Western Europe. The impact of a winter storm occurring during spring tide is assessed thanks to numerical modeling with a 3D fully-coupled wave-current model and in-situ data. Firstly, an analysis of the impacts of the storm on the wave field and the current effects on waves is performed. Then, the modifications of the current and tidal stream energy caused by waves are discussed. After a successful validation step with excellent PBIAS and R2 scores, the main finding are : i) although the current intensity is strong (around 3-4m/s), wave effectssignificantly change the vertical profile of the current, with a reduction of the PBIAS by a factor of 1.78 between simulations with and without wave effects, ii) ocean waves affect the tidal assymmetry, with a flood current whose intensity is 13% higher than for the ebb current, inducing a decrease of 30% in the tidal stream energy, iii) the flow is very sensitive to the angle between the directions of propagation of waves and current, with an acceleration or a reduction of the velocity, as observed in the presence of a 3D turbulent structure, iv) current effects on waves cause a wavenumber shift, changes in significant wave height (modulated by tide), wave direction due to refraction and an increase of the energy transfer from waves to ocean ascribed to the wave breaking. By a feedback mechanism, the modifications of the wave field by current and water level significantly alter the flow with a decrease of its velocity when waves propagate against current. This study shows that the 3D wave-current interactions need to be considered during a storm even during a spring tide event where currents are the strongest.

How to cite: Bennis, A.-C., Furgerot, L., Bailly du Bois, P., Poizot, E., Méar, Y., and Dumas, F.: Three-dimensionnal Wave-Current Interactions can significantly affect a Strong Tidal Current in a Complex Environment: Application to Alderney Race, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-16723, https://doi.org/10.5194/egusphere-egu23-16723, 2023.

How to cite: Mehlig, B., Candelier, F., Qiu, J., Zhao, L., and Voth, G.: Inertial torque on a squirmer, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-17324, https://doi.org/10.5194/egusphere-egu23-17324, 2023.

Planktonic microorganisms immersed in a fluid interact with the ambient flow, altering their trajectories. In surface gravity waves, a common goal for microswimmers is vertical migration. By modeling phytoplankton as spheroidal bodies with a certain swimming velocity, we investigate how the combination of swimmer's dynamical characteristics and fluid velocity gradients affect the motion. We investigate the case of prolate, negative buoyant swimmers. We consider also the case of gyrotactic swimmers. We find that it is possible for microswimmers to be trapped at a finite depth below the sea level. This phenomenon is due to the coupling between swimming, gyrotaxis and flow-induced reorientations. The trajectories obtained by numerical simulations, indicate that the dynamics consist of fast oscillations at the surface wavelength superposed with a slower trend at a longer timescale. This suggests using a multiple time-scale expansion to remove the fast oscillations. The presence of stable fixed points for the slow dynamics allows the trapping behaviour.

How to cite: Ventrella, F. M., De Lillo, F., Boffetta, G., Cencini, M., Thiffeault, J.-L., and Pujara, N.: Prolate microswimmer in surface gravity waves, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-6774, https://doi.org/10.5194/egusphere-egu23-6774, 2023.

How to cite: Berti, S., Tergolina, V. B., Calzavarini, E., and Mompean, G.: Light-limited dynamics of sinking phytoplankton in a convective flow model with ice-covered waters, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-1200, https://doi.org/10.5194/egusphere-egu23-1200, 2023.