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We study the evolution of a turbulent layer in a stratified ocean layer using the theory of unsteady turbulent flows in a stratified fluid developed in [1] and subsequent works. The theory starts from a kinetic equation for turbulence parameters and results in the set of equations involving the mutual transformation of the kinetic and potential energies of turbulence that is shown to significantly affect the overall dynamics of energy exchange between small-scale turbulence and mesoscopic motions and the formation of the upper mixed layer. Besides, this approach allows an account for some important but usually neglected effects such as the dependence of vertical anisotropy of turbulence on stratification. Notably, the transformation between kinetic and potential energies eliminates the restriction on the existence of turbulence at large Richardson numbers. The results are applied to the analysis of in situ data for turbulence evolution under the action of shear flows and internal waves, obtained in different regions that are significant for climate research, including the upper equatorial ocean. The fundamental role of potential energy in the formation of a turbulent flow is demonstrated.The work was supported by RSF project No. 23-27-00002.[1] Ostrovsky L.A., Troitskaya Yu.I. (1987) A model of turbulent transfer and dynamics of turbulence in a stratified shear flow. Izvestiya, Atm. and Oceanic Phys., 23(10), 767-773 (1987).

The “bag breakup” fragmentation is the dominant mechanism for spume droplet production in high winds, which substantially affects the ocean–atmosphere exchange processes. The amount of droplets ejected from the surface, as well as their typical sizes, is prescribed by the surface wind velocity and fetch. The corresponding empirical correlations were obtained only for the limited parameters of the laboratory environment. The applicability range can be extended through the construction of a theoretical model that describes the initiation of the bag-breakup fragmentation, estimates the fragmenting liquid volume prescribing the droplet sizes, and determines the dependence on the wind parameters. This paper presents such a model. First, we conducted linear stability analysis of small-scale disturbances at the water surface under a high wind; this showed that the small-scale ripples (about 1 cm) propagating against the wind in the surface wind drift following the reference frame grew fast due to the Kelvin–Helmholtz instability, when the wind friction velocity exceeded the threshold of about 1 m s−1. Given the weak dispersion, the nonlinear stage of evolution was addressed using the Riemann simple wave equation modified to describe the increasing disturbances. The analytical solution for the equation suggested the scaling of the volume of liquid undergoing the bag-breakup fragmentation and its dependence on in agreement with the laboratory data. Using the scaling, we calculated the statistics of the bag-breakup fragmentation based on the lognormal size distribution of the fragmenting objects. Significance Statement The “bag breakup” fragmentation is the dominant mechanism for generating spray in hurricane winds. The parameters of spray droplets substantially affect the exchange processes between the ocean and the atmosphere and, thereby, the development of sea storms. The rapid process of spray generation can only be studied in laboratory environments using sophisticated experimental techniques. To apply the laboratory data to field conditions, we need a theoretical model that describes the threshold for fragmentation initiation, the fragmenting liquid volume, which scales the size and number of spray droplets, their dependence on wind parameters, etc. In the present work, we suggest a simple analytical model of the bag-breakup initiation, verify it in the laboratory experiment, and suggest the statistical description of the fragmentation events.

Lagrangian stochastic models (LSM) are widely used to model the dispersion of sea spray droplets injected from the water surface into the marine atmospheric boundary layer (MABL) and for evaluation of the spray impact on the exchange fluxes between the atmosphere and the ocean. While moving through the MABL the droplets pass through the region of high gradients of air velocity, temperature and humidity occurring in the vicinity of the air-water interface. In this case, the applicability of LSMs constructed under the assumption of weakly inhomogeneous flows is questionable. In this work, we develop a Lagrangian stochastic model taking into account the strongly inhomogeneous structure of the airflow in MABL and, in particular, the anisotropy of turbulence dissipation rate. The model constants and the diffusion matrix coefficients are calibrated by comparison of the LSM prediction for the profiles of droplet concentration and the exchange fluxes of sensible and latent heat against the results of direct numerical simulation (DNS) of turbulent, droplet-laden airflow over a waved water surface.

Processes of sea spray formation play important role in the interaction of ocean and atmosphere under strong winds. Among other factors, the formation of small droplets is caused by the falling of previously generated larger drops onto the sea surface. Using the Basilisk software package [1] numerical simulation of fall of a large drop with a substantial horizontal velocity on a water surface was carried out. The problem of the following configuration was considered: a cubic domain was half filled with water, and air was in the upper half. At the initial time, at a height of h = 2 cm above the water surface, there was a drop with a diameter of 2 mm, the horizontal projection of the drop velocity was v0x = 3 m/s, the vertical projection of the drop velocity v0y = 1.25 m/s was obtained from the calculation that at a height of 10 cm above the water surface, the vertical component of the droplet velocity was equal to zero. Boundary conditions along the x coordinate were periodic. The coordinates and volume of each individual water body (including each drop) were recorded over time.This work was supported by the RFBR grant 21-55-52005 and RSF grant 21-19-00755.[1] Popinet, S. The Basilisk code: http://basilisk.fr.

A series of experiments was carried out on the Thermostratified Wind Wave Tank of IAP RAS, to study the processes of secondary generation of spray due to the fall of the droplets onto a rough surface. The general scheme of the experiments was similar to [1]. The range of equivalent wind speed from U10 is from 21 to 34 m/s. Initially, high-speed filming with shadow visualization of the rough surface from above was performed, followed by detection, marking and calculating the number of events during image processing using special programs. It has been demonstrated that the number of phenomena of falling drops into water per unit time per unit area, leading to the formation of spray, significantly exceeds the similar values for previously studied mechanisms of spray generation: liquid ligaments fragmentation type, bubbles rupture and bag-breakup fragmentation type. Further, detailed studies of this phenomenon were carried out with a higher resolution filming. Two main scenarios of this event: with the formation of a “crown” at large angles of drop incidence, and the so-called "jet" at small angles were identified by analogy with [2]. The number droplets, size and velocity distributions were obtained for different wind speeds. These results can be used to design a spray generation function due to this phenomenon.Investigations were supported by Russian Science Foundation project 21-19-00755 (carrying out experiments), Russian Foundation Basic Research project 21-55-52005 (data processing), work of A.A. Kandaurov was partially supported by the President's grant for young scientists МК-5503.2021.1.5.Troitskaya, A. Kandaurov, O. Ermakova, D. Kozlov, D. Sergeev, and S. Zilitinkevich, The ‘Bag Breakup’ Spume Droplet Generation Mechanism at High Winds. Part I: Spray Generation Function, J. Phys. Oceanogr., vol. 48, no. 9, pp. 2167–2188, 2018. V. Gielen, P. Sleutel, J. Benschop, M. Riepen, V. Voronina, C. W. Visser, D. Lohse, J. H. Snoeijer, M. Versluis, andH. Gelderblom, Oblique drop impact onto a deep liquid pool, Phys. Rev. Fluids, vol. 2, pp. 083602, 2017.

The "bag breakup" fragmentation is the dominant mechanism for generating spray in hurricane winds, which parameters substantially affect the exchange processes between the ocean and the atmosphere and, thereby, the dynamics of the development of sea storms. This fast process can only be studied in the lab using sophisticated experimental techniques based on high-speed video filming. In such circumstances, the transfer of laboratory data to field conditions requires a kind of theoretical model that describes how the initiation of disturbances occurs, which then lead to fragmentation events, what is the threshold for the fragmentation, what is the volume of liquid, which determines the size of spray droplets, that undergoes fragmentation, and how it depends on wind parameters, etc. The conclusions of the model can be first verified in the laboratory experiment and then applied to field conditions. In the present work, such a model is proposed. First of all, a linear theory of small-scale disturbances on the water surface under the action of a strong wind has been built, which makes it possible to describe their structure, dispersion properties and determine the threshold value of the dynamic airflow velocity at which such disturbances become growing. These disturbances comprise small-scale ripples concentrated within the thin surface layer and growing fast due to shear instability of the wind drift flow in the water. The peculiarity of the structure of these disturbances enables one to consider the nonlinear stage of their evolution within the Riemann simple wave equation modified to describe the increasing disturbances. The analytical solution of the obtained equation suggests the scaling of the volume of liquid undergoing the "bag-breakup" fragmentation, to estimate the scale of the formed droplets and the speed of their injection into the atmosphere. The scaling correctly describes the dependencies of these quantities on the wind friction velocity obtained in laboratory experiments. The obtained results are applied for the construction of the fetch-dependent spray generation function, which is applicable in the field. Within the Lagrangian stochastic model for the inertial droplets in the marine boundary layer, the momentum, heat, moisture, and enthalpy exchange coefficients are calculated. One should notice a substantial feedback effect on the atmosphere caused by the presence of spray in hurricane conditions.This work was supported by RFBR grant 19-05-00249 and RSF grant 19-17-00209.

Marine aerosol has a large impact on the earth system, including the physics and chemistry of the atmosphere over the oceans. It is a suspension in the air, consisting mainly of droplets injected from the ocean surface as a result of wave breaking in the coastal zone or during strong winds. A marine aerosol production model is an element of great importance in climate change and forecasting models.In this work, the calculation of the production of sea aerosol using the developed parameterization of the sea spray generation function is carried out taking into account the contribution of the «bags breakup» spume droplet generation mechanism. For example, the work [1] show the decisive contribution of this type of spray to the sea spray generation function. The calculation is carried out both on the basis of reanalysis data on the global distribution of wind speed (CFSv2 [2]) and wave parameters (WAVEWATCH III® Hindcast and Reanalysis Archives [3]), and on the basis of calculation data within the WRF atmospheric model and the WAVEWATCH III wave model. An assessment of the production of sea aerosol is carried out using the example of hurricane Irma. The wind data in the calculations in the WRF model is obtained using the Large Eddy Simulation (LES) technique of the planetary boundary layer (PBL) with the boundary conditions from the CFSv2 reanalysis. Wave parameters data is obtained from calculations within the WAVEWATCH III wave model. A comparison of the resulting sea spray generation function obtained using the WRF LES and WAVEWATCH III data and the distribution obtained using the reanalysis data is carried out. Conclusions are made about the advantages of using computational models of high spatial resolution.The work is supported by President Grant for young scientists MK-2489.2022.1.5.[1] Troitskaya, Y., Kandaurov, A., Ermakova, O., Kozlov, D., Sergeev, D., & Zilitinkevich, S. (2018). The “bag breakup” spume droplet generation mechanism at high winds. Part I: Spray generation function. Journal of physical oceanography, 48(9), 2167-2188.[2] Saha, S., et al. 2011, updated monthly. NCEP Climate Forecast System Version 2 (CFSv2) Selected Hourly Time-Series Products. Research Data Archive at the National Center for Atmospheric Research, Computational and Information Systems Laboratory. https://doi.org/10.5065/D6N877VB. Accessed 14 December 2021.[3] https://polar.ncep.noaa.gov/waves/hindcasts/

The work is concerned with the study of the breaking surface wave impact on the scattered radar signal in laboratory conditions using optical methods for analyzing the state of the water surface.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.At the beginning of the channel, a wavemaker was installed, operating in a pulsed mode and generating a train of three long waves every 15 seconds. In front of the area under study, an inclined plate was installed under the water, simulating shallow water and stimulating the breaking of waves in the zone of optical and radar measurements. In parallel, wind waves were generated. Due to the design features of the experimental setup, the distance from the beginning of the channel to the inclined plate in the case of optical measurements was 884 cm, and for radar measurements - 781 cm.Radar measurements were carried out using a Doppler scatterometer operating at a wavelength of 3.2 cm, with the ability to simultaneously receive two direct and two cross-polarizations (VV, HH, VH, HV). The dimensions of the observation window on the water surface varied depending on the selected incidence angles (30, 40, 50 degrees). Optical measurements were carried out independently of radar measurements using three cameras with a shooting frequency of 50 Hz. Using a specially developed algorithm based on threshold processing of the image brightness, the time dependences of the fraction of breakers on the area of the investigated water surface during the passage of a train of three waves were calculated. Due to the different configuration of the experiments, the data of radar and optical measurements are separated in time, their synchronization was performed using correlation analysis. Comparison of the data made it possible to find that, on cross-polarization, the received power monotonically increases with an increase in the fraction of breakers, while on direct polarization, the change in power remains within the values observed during collapses of wind waves. Further comparison of the values of the radar cross-section of the water surface and the relative area of the wave breaking will make it possible to determine the influence of the breaking on the formation of the scattered signal.This work was supported by the Russian Science Foundation (RSF) project No. 21-17-00214.

Within the framework of this study, the dynamics and thermodynamics of individual spherical droplets of various sizes injected into the air flow during their interaction with a marine atmospheric boundary layer were calculated within Lagrangian stochastic model (LSM). The fields of velocity, humidity, and temperature are presented as a superposition of the average component determined from the approximations of the Monin-Obukhov similarity theory and the fluctuation component. Turbulent fluctuations are calculated using a stochastic model based on the Langevin equation, containing the matrix of inverse relaxation times of turbulent fluctuations of the Lagrangian particles velocity. To define whether isotropic matrix or anisotropic one should be selected and also to determine the value of Kolmogorov constant the calculations within LSM were compared with the results of direct numerical simulation of the inertial particles in the atmospheric boundary layer above surface waves. It was shown that the isotropic diffusion matrix underestimates the turbulent diffusion of particles, so anisotropic one was selected.It was assumed that the injection of droplets into the air flow was carried out through two main mechanisms - fragmentation according to the "parachute" type (Troitskaya et al., Scientific Reports, 2017) and the rupture of floating bubbles. In the calculations, new modifications of the spray generation functions were used, taking into account the dependence of the number of generation events on the number of spray, obtained within the laboratory experiments done by the authors in their previous studies.The processes of heat-moisture exchange of droplets with a turbulent air flow, taking into account phase transitions, are described using the equations of droplet microphysics (Pruppatcher and Klett (1978)). Heat, moisture and momentum fluxes are calculated on the basis of averaging over the horizontal coordinate of the equations of thermoaerodynamics. These equations include volumetric sources of momentum, heat and moisture to take into account the effect of droplets on the temperature and humidity of atmospheric air, which are obtained by averaging the solution to the equations of microphysics of droplets. When calculating the profiles of average temperature and humidity, gradient hypotheses of closure with the coefficients of turbulent diffusion coefficients of heat and humidity were used.The work is supported by the Russian Science Foundation (RSF) project № 19-17-00209Troitskaya, Y., Kandaurov, A., Ermakova, O., Kozlov D., Sergeev D., Zilitinkevich S. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Sci Rep 7, 1614 (2017). https://doi.org/10.1038/s41598-017-01673-9. Prupatcher H.R., Klett J.D. Microphysics of Clouds and Precipitation. Dordrecht: D. Riedel. 1978, 714 p. https://doi.org/10.1007/978-94-009-9905-3.

The number of spume droplets increases rapidly with wind speed [1], [2], so that under hurricane conditions the spray-mediated heat and momentum fluxes can have a significant impact on the exchanging processes between the ocean and the atmosphere. The estimation of the additional enthalpy flux, as well as latent and sensible heat fluxes, is based on the solution of the microphysics equations for a single saline droplet, detailed in [3]. In theoretical studies [4]-[6] it was shown that the evolution of the radius and temperature of a droplet can be described accurate enough using the following formulas:T(t)=Twb+(Tw-Twb)e-t/τT,r(t)=req+(r0-req)e-t/τr,where Twb is the wet bulb temperature, req is the equilibrium radius, τT and τr is the e-folding time to reach that temperature Twb and radius req, T(0)=Tw is the temperature of the water, r(0)=r0 is the initial radius of the drop. However, the numerical solution of the microphysical equations of the droplet’s thermodynamics showed that for the characteristic conditions of a tropical cyclone at the initial stage evaporation occurs much more intensively than after reaching the wet bulb temperature, and the characteristic time of this change is the same as for a change in temperature. In the present study, we propose an updated parameterization of the evolution of the radius and temperature of a single saline droplet, which provides more accurate describing of the droplet’s thermodynamics. On its basis we obtained estimations of enthalpy, latent and sensible heat fluxes caused by droplets generated by bag break-up instability (the main source of spume droplets at extreme wind speeds [7]). [1] E. L. Andreas. A review of the sea spray generation function for the open ocean // Atmos. Interact. - 2002. - V. 1. - P. 1–46.[2] D. H. Richter and F. Veron. Ocean spray: An outsized influence on weather and climate // Phys. Today - 2016. - V. 69. - №11. - P. 34–39.[3] H. R. Pruppacher and J. D. Klett. Microphysics of clouds and precipitation, D. Reidel. Norwell: Mass., 2010.[4] E. L. Andreas. Time constants for the evolution of sea spray droplets // Tellus, Ser. B - 1990. - V. 42 B. - №5. - P. 481–497.[5] E. L. Andreas. Sea spray and the turbulent air-sea heat fluxes // J. Geophys. Res. - 1992. - V. 97. - №C7. - P. 11429–11441.[6] E. L. Andreas. Approximation formulas for the microphysical properties of saline droplets // Atmos. Res. - 2005. - V. 75. - №4. - P. 323–345.[7] Y. Troitskaya, A. Kandaurov, O. Ermakova, D. Kozlov, D. Sergeev, and S. Zilitinkevich. The “bag breakup” spume droplet generation mechanism at high winds. Part I: Spray generation function // J. Phys. Oceanogr. - 2018. - V. 48. - №9. - P. 2168–2188.

The interaction of small-scale turbulence with internal and surface waves is an urgent problem of hydrology and oceanology. In particular, this issue is especially important for the properties of the upper layer of the ocean and the inland waters.Small-scale processes that exist against the background of average profiles of various hydrophysical quantities (temperature, velocity, density, and large-scale currents caused, in particular, by wind forcing) are usually nonlinear and therefore effectively interact with each other. We consider some aspects of the interaction of internal waves and turbulence in the upper layer of the ocean and inland waters within the framework of the semi-empirical theory of turbulence in a stratified fluid. The model used in this study takes into account mutual transformation of the kinetic and potential energies of turbulent fluctuations [Ostrovsky&Troitskaya, 1987; Zilitinkevich et al., 2013]. The effects of amplification and maintenance of turbulence by low-frequency and high-frequency internal waves, quasi-stationary distributions of turbulent energy in the presence of a shear caused by a low-frequency internal wave are investigated; the role of the transformation of energies on the indicated processes is analyzed.A modification of the k-epsilon mixing scheme is also proposed, which removes the limitation on the existence of turbulence at large values of the gradient Richardson number. Within the framework of the modification, the parameterization of the Prandtl number is used, which makes it possible to take into account the influence of density stratification and velocity shear on mixing processes.A numerical study of the influence of vertical mixing schemes on the transfer processes of biochemical fields in an internal reservoir was also carried out. The modified scheme was implemented into a three-dimensional model of thermo-hydrodynamics and biochemistry of an inland water body [Gladskikh et al., 2021], and a series of numerical experiments was conducted.The work was supported by the RFBR (20-05-00776; 20-05-00322; 21-05-52005), and by Moscow Center of Fundamental and Applied Mathematics (agreement with the Ministry of Science and Higher Education 075-15-2019-1621).Ostrovsky LA, Troitskaya YuI (1987) A model of turbulent transfer and dynamics of turbulence in a stratified shear flow. Izv Akad Nauk SSSR, Fiz Atmos Okeana. 3:101–104.Zilitinkevich SS, Elperin T, Kleeorin N, Rogachevskii I, Esau I (2013) A hierarchy of Energyand Flux-Budget (EFB) turbulence closure models for stably-stratified geophysical flow. Boundary-Layer Meteorol. 146:341–373Gladskikh DS, Stepanenko VM, Mortikov EV (2021) The Effect of the Horizontal Dimensions of Inland Water Bodies on the Thickness of the Upper Mixed Layer. Water Resour 48:226–234

In the recent researches, the disagreement on the issue of the mechanisms of the polar low development is observed. Thus, in [1], on the basis of numerical experiments, the dominant role of baroclinic instability during the development of polar low at the initial stage of atmospheric vortex formation is noted, but then the polar low was maintained due to the sensible heat flux from the surface. At the same time, in [2], the dominant role of condensational heating was noted with a minor role of sensible and latent heat fluxes on the ocean surface. It was shown in [3] that sensible and latent heat fluxes between the ocean and the atmosphere play a decisive role both at the stage of baroclinic intensification of the polar low and at the stage of its maintenance; later experiments [4] showed that an increase in the ocean surface temperature leads to the emergence of more prolonged and long-lived polar lows. In this work, the simulations to elucidate the mechanisms of the development of polar low were carried out within the framework of the WRF atmosphere model. As a control experiment, an experiment with certain physical processes available in WRF was used. To assess the sensitivity of a polar low to convective processes in the model, calculations were carried out that were completely identical to the control experiment, but with the shutdown of certain physical processes. When the heat generated by condensation was turned off, the role of latent heat was studied. This was done by turning off the contribution of heat to the temperature profile in the module responsible for the microphysics of clouds. To assess the sensitivity to heat fluxes on the surface, a numerical experiment was carried out with such switching off. To reveal the role of the baroclinic growth as a mechanism for intensifying the atmospheric vortex, both heat fluxes on the surface and the release of latent heat during condensation were turned off. The role of energy fluxes on the ocean surface during the development of the polar low was demonstrated, which forms new directions for the study of this issue.This work was supported by a RSF grant № 21-77-00076.References Føre, I., Kristjánsson, J. E., Kolstad, E. W., Bracegirdle, T. J., Saetra, Ø. and Røsting, B. (2012), A ‘hurricane-like’ polar low fuelled by sensible heat flux: high-resolution numerical simulations. Q.J.R. Meteorol. Soc., 138: 1308–1324. doi:10.1002/qj.1876 Watanabe, S.I. and H. Niino, 2014: Genesis and Development Mechanisms of a Polar Mesocyclone over the Japan Sea. Mon. Wea. Rev., 142, 2248–2270, https://doi.org/10.1175/MWR-D-13-00226.1 Kolstad, E. W., T. J. Bracegirdle, and M. Zahn (2016), Re-examining the roles of surface heat flux and latent heat release in a “hurricane-like” polar low over the Barents Sea, J. Geophys. Res. Atmos., 121, 7853–7867, doi:10.1002/2015JD024633 Kolstad, E. W. and Bracegirdle, T. J. (2017), Sensitivity of an apparently hurricane-like polar low to sea-surface temperature. Q.J.R. Meteorol. Soc, 143: 966–973. doi:10.1002/qj.2980

This article describes the first step toward the development of the geophysical model function (GMF) for the retrieval of wind speed and wind stress in hurricanes, based on developing a relation between the cross-polarized satellite SAR data from Sentinel-1 and winds/stress observed from collocated NOAA GPS-dropsondes data. Field measurements and remote sensing data for tropical cyclones in the Atlantic Ocean were analyzed. Using the data measured by GPS-dropsondes, average wind velocity profiles were obtained, while the parameters of the wind boundary layer (drag coefficient and friction velocity) were restored from the “wake” part of the velocity profiles using the self-similarity property. The self-similarity of the velocity profile “defect” in the boundary layer, known from the fluid dynamics, was used to retrieve the parameters of the atmospheric boundary layer (the surface wind velocity, drag coefficient, and friction velocity) from the dropsonde wind velocity profiles in ten major hurricanes. Based on the processing of the measurements in the hurricanes Irma 2017/09/07 and Maria 2017/09/21 and 2017/09/23 at a time close to the time of acquisition of the Sentinel-1 images, the dependencies of the cross-polarized normalized radar cross section on the wind speed and wind friction velocity were obtained and used for constructing the GMFs.

The preliminary attempts to develop of the geophysical model function (GMF) for the retrieval of wind speed and wind stress in hurricanes, based on a dependency between the cross-polarized satellite SAR data from Sentinel-1 and wind speed or turbulent stress obtained from collocated NOAA GPS-dropsondes data array. Field measurements in the Atlantic Ocean during hurricane season in the period 2001-2018 were analyzed. Using the data measured by GPSdropsondes, due to the ensemble averaging, mean wind velocity profiles were obtained, and the atmospheric boundary layer parameters drag coefficient and turbulent stress (or friction velocity) were retrieved from the “wake” part of the velocity profiles taking into account a self-similarity property of the velocity profile “defect”. The parameters were retrieved for 25 major hurricanes of categories 4 and 5. The collocation of Sentinel-1 images and GPS-dropsonde data was made for the hurricanes Irma 2017/09/07, Maria 2017/09/21 and 2017/09/23, taking into account the assumption that turbulent boundary layer parameters in the hurricanes remain quasistationary. The dependencies of the cross-polarized normalized radar cross-section (NRCS) on the wind speed and wind friction velocity were obtained, the results were compared to the data for small and moderate winds, represented in [1], a good agreement is demonstrated. In the region of high wind speeds the relation between NRCS and the wind friction velocity becomes ambiguous, it may be explained by the dependency on the hurricane sector.

On the base of laboratory experiments on co- and cross-polarized microwave signal scattering on a wavy water surface, the dependences of NRCS on wind speed and friction velocity at high wind speeds were obtained. It is shown that the cross-polarized NRCS demonstrates sensitivity to the wind speed when its value is more than 20 m/s, in contrast to the co-polarized NRCS. Based on the analysis of the Doppler spectra, it was suggested that the backscattered signal is formed mainly on wave breakers. This assumption was verified by analyzing the dependence of the scattered signal power at both polarizations on the area of the white-cap coverage, which revealed their direct dependence. Based on the phenomenological approach used in statistical physics, a parametrization of the dependence of the white-cap coverage fraction on the wind friction velocity was proposed. This parametrization was based on the use of the universal Gibbs method, the central concept of which is a canonical ensemble or an ensemble of a thermodynamic system states which are in a weak thermal contact with a "thermostat". In this case, the atmospheric boundary layer acts as a thermostat, and the entire ensemble of states of the sea surface, including breakers, is the canonical ensemble. Based on this parametrization, the GMF was proposed to retrieve the wind speed and wind friction velocity for wind speeds above 40 m/s, which also considering the angular dependence of the NRCS.

OT 081 is a luminous blazar well known for its variability in many energy bands. The very-high-energy (VHE; E >100 GeV) gamma-ray emission from the source was discovered by MAGIC and H.E.S.S. during flaring activity in July 2016, after a trigger from the Large Area Telescope (LAT) onboard the Fermi satellite. By analysing the multiwavelength light curves andthe broadband spectral energy distribution (SED), we study the activity of the source and investigate four individual states of activity in the window from MJD 57575 to 57602. The intrinsic gamma-ray spectrum can be described by a power law with spectral indices of 3.27 ± 0.44(MAGIC)and 3.39 ± 0.58(H.E.S.S.) over energy ranges 60–300 GeV and 120–500 GeV, respectively. The combined contemporaneous high-energy (HE;E >100 MeV) through VHE SED shows curvatureand can be described by a log-parabola shape. A simple one-zone synchrotron self-Compton (SSC)model is not sufficient to describe the broadband SED. The presence of broad emission lines in the optical spectrum of the source challenges the categorisation of OT 081 as a BL Lac and, together with the emission scenarios tested, points to the possibility that the source is transitional in nature between a BL Lac and a flat-spectrum radio quasar.

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.

The ice cover decrease in the Arctic in the past decade has led to polar hurricanes (polar lows) occurring along the entire Northern Sea Route. Wind speeds of these hurricanes reach 35-40 m / s. Over the past 20 years, significant progress in predicting storm trajectories has been achieved, while the quality of forecasting their intensity is still poor. This is due to the fact that the intensity (maximum wind speed and minimum pressure) is determined by the interaction of the atmosphere and the ocean, and at high wind speeds it has significant uncertainty, especially for the smallest-scale processes: splashes, wave collapses and foam bubbles [1].Numerical modeling of the polar low development was carried out within the framework of the WRF model [2] in order to develop methods for modeling such extreme events. The water area of the Barents Sea was considered, where a large number of polar hurricanes were observed. Among the identified polar hurricanes [3], a hurricane that took place on 02/05/2009 and was observed at coordinates 69º N, 40º E was chosen. Several approaches were considered to simulate the weather conditions in the studied area of the Barents Sea in the presence of a polar hurricane. The WRF model simulation with the CFSR reanalysis was carried out. The configuration of the model consisted in using, first, the well-proven technique of Large Eddy Simulation (LES) modeling of the planetary boundary layer (PBL). Secondly, the simulation was performed using the WRF add-in for the polar region, Polar WRF [4]. The comparison of the approaches is made. The mechanism of intensification of the atmospheric vortex is considered whether it is baroclinic shear, heat fluxes on the surface or outcome of latent heat during condensation.This work was supported by a RFBR grant № 18-05-60299.References1. Troitskaya, Yu, et al. "Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds." Scientific reports7.1 (2017): 1-4.2. A Description of the Advanced Research WRF Version 3 / W. C. Skamarock, J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, M. G. Duda, X.-Y. Huang, W. Wang, J. G. Powers // NCAR TECHNICAL NOTE. - 2008. - №NCAR/TN–475+STR. - С. 113 pp.3. Noer, G., & Lien, T. (2010). Dates and Positions of Polar lows over the Nordic Seas between 2000 and 2010. Norwegian Meteorological Institute Rep.4. Hines, Keith M., et al. "Development and testing of Polar WRF. Part III: Arctic land." Journal of Climate24.1 (2011): 26-48.

Fundamental contribution to the formation of sea spray under strong winds is provided by the bag-breakup phenomenon - rupture of film in the form of parachute [1]. Breaking of water film into droplets is caused, among other factors, by processes occurring on the free edge of the film moving under action of surface tension forces. The study of these processes will help to understand how characteristics of the film and the drops appearing after its rupture are related.Using the Basilisk software package with Volume of Fluid advection scheme for interfacial flows, numerical simulation of three-dimensional water film placed in domain filled with air was carried out. The water film was placed into domain filled with air. One of the edges of the film is free, and the second is fixed on the left boundary of the domain; along the third coordinate, the boundary conditions are periodic. At the initial moment of time, the film is defined by a sheet with variable thickness - the upper boundary has the form of a cosine. The change in the shape of the film over time was recorded. It is revealed that the inhomogeneity of the film thickness leads to the appearance of a significant curvature of the edge of the film as it moves under the action of surface tension forces.This work was supported by the RFBR grants (20-05-00322, 21-55-50005, 21-55-52005) and RSF grant 19-17-00209.[1] Troitskaya, Y. et al. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Sci. Rep. 7, 1614 (2017).

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).

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

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).

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.

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

The "bag breakup" fragmentation is the dominant mechanism for generating spray in hurricane winds, which parameters substantially affect the exchange processes between the ocean and the atmosphere and, thereby, the dynamics of the development of sea storms. This fast process can only be studied in lab using sophisticated experimental techniques based on high-speed video filming. In such circumstances, the transfer of laboratory data to field conditions requires a kind of theoretical model that describes how the initiation of disturbances occurs, which then lead to fragmentation events, what is the threshold for fragmentation, what is the volume of liquid, which determines the size of spray droplets, that undergoes fragmentation, and how it depends on wind parameters, etc. The conclusions of the model can be first verified in the laboratory experiment and then applied to field conditions.In the present work, such a model is proposed. First of all, a linear theory of small-scale disturbances on the water surface under the action of a strong wind has been built, which makes it possible to describe their structure, dispersion properties and determine the threshold value of the dynamic air flow velocity at which such disturbances become growing. These disturbances comprise small-scale ripples concentrated within the thin surface layer and growing fast due to shear instability of the wind drift flow in the water. The peculiarity of the structure of these disturbances enables one to consider the nonlinear stage of their evolution within the Riemann simple wave equation modified to describe the increasing disturbances. The analytical solution of the obtained equation suggests the scaling of the volume of liquid undergoing the "bag-breakup" fragmentation, to estimate the scale of the formed droplets and the speed of their injection into the atmosphere. The scaling correctly describes the dependencies of these quantities on the wind friction velocity obtained in laboratory experiments.The obtained results are applied for the construction of the fetch-dependent spray generation function, which is applicable in the field. Within the Lagrangian stochastic model for the inertial droplets in the marine boundary layer, the momentum, heat, moisture and enthalpy exchange coefficients are calculated. One should notice substantial feedback effect on the atmosphere caused by the presence of spray in hurricane conditions.This work was supported by RFBR grant 19-05-00249 and RSF grant 19-17-00209.

Using the Basilisk software package, direct numerical simulation of the process of deformation of a liquid drop in a gas stream was carried out. The calculations were carried out for Reynolds numbers Re = 50–3000, Weber numbers We = 2–30. Two main modes of drop deformation were observed: bowl-shaped and dome-shaped, there is a transitional deformation mode between them. A map of deformation modes is constructed for comparison with the experimental data available in the literature. It was found that the dependence of the Weber number, corresponding to the transition from one deformation mode to another, on the Reynolds number is well described by the power law proposed in the literature.

This paper describes laboratory experiments (using a high-speed wind-wave flume) of the effects of water waves on heat and momentum exchange in the near-water atmospheric boundary layer at high win...

It is important to investigate the effects of current on wind waves, called the Doppler shift, at both normal and extremely high wind speeds. Three different types of wind-wave tanks along with a fan and pump are used to demonstrate wind waves and currents in laboratories at Kyoto University, Japan, Kindai University, Japan, and the Institute of Applied Physics, Russian Academy of Sciences, Russia. Profiles of the wind and current velocities and the water-level fluctuation are measured. The wave frequency, wavelength, and phase velocity of the significant waves are calculated, and the water velocities at the water surface and in the bulk of the water are also estimated by the current distribution. The study investigated 27 cases with measurements of winds, waves, and currents at wind speeds ranging from 7 to 67 m s−1. At normal wind speeds under 30 m s−1, wave frequency, wavelength, and phase velocity depend on wind speed and fetch. The effect of the Doppler shift is confirmed at normal wind speeds; i.e., the significant waves are accelerated by the surface current. The phase velocity can be represented as the sum of the surface current and artificial phase velocity, which is estimated by the dispersion relation of the deepwater waves. At extremely high wind speeds over 30 m s−1, a similar Doppler shift is observed as under the conditions of normal wind speeds. This suggests that the Doppler shift is an adequate model for representing the acceleration of wind waves by current, not only for wind waves at normal wind speeds but also for those with intensive breaking at extremely high wind speeds. A weakly nonlinear model of surface waves at a shear flow is developed. It is shown that it describes dispersion properties well not only for small-amplitude waves but also strongly nonlinear and even breaking waves, which are typical for extreme wind conditions (over 30 m s−1).

In the framework of the modernized RANS model of turbulent closure [1], the evolution in the pycnocline and shear flow in the upper mixed layer of the ocean is studied. For this purpose, one of the variants of the model situation is considered, which consists in studying the mutual transformation of the buoyancy frequency, shear flow, as well as the kinetic and potential turbulence energies determined at the initial time at different depths. It is shown that the kinetic energy of turbulence increases with time, and its maximum shifts to the maximum of the the horizontal shear flow. However, unlike the standard gradient scheme, in the beginning there is a mutual transformation of the kinetic and potential turbulence energies, after which they quickly reach a stationary equilibrium level (at large values of the Richardson numbers). A significant change in stratification, initially having a maximum at a certain depth, was also found in the process of establishing a stationary turbulence regime.The work was financially supported by the Russian Foundation for Basic Research (projects № 18-05-00292, 18-35-00602).References:1. Ostrovsky, L.A., Troitskaya, Yu.I., The model of turbulent transport and the dynamics of turbulence in a stratified shear flow/ Izvestiya, Atmospheric and Oceanic Physics., 1987. v.3. pp. 1031–1040

The current investigation is concerned with the study of the dependence of the scattered cross-polarized microwave signal from the Sentinel-1 satellite on the parameters of the marine atmospheric boundary layer based on data obtained from falling NOAA GPS-sondes under tropical cyclone conditions.Field measurements and remote sensing data for hurricanes in the Atlantic and Pacific oceans were analyzed for the period 2016 - 2018. Based on the analysis of data measured by GPS-sondes, averaged wind speed profiles were obtained, while the parameters of the atmospheric boundary layer (drag coefficient and wind friction velocity) were retrieved using the self-similarity property of velocity profiles from measurements in the “wake” part.Sentinel-1 SAR images were used as remote sensing data. Images with cross polarization have a high level of thermal noise (NESZ), which leads to errors when retrieving the NRCS. In this regard, preliminary image processing was performed in the SNAP application.Using the obtained parameters of the atmospheric boundary layer, the data of GRS-sonde measurements and Sentinel-1 SAR images on cross polarization were collocated and the dependences of the NRCS on the parameters of the atmospheric boundary layer were obtained.This work was supported by the RFBR projects No. 19-05-00249, 19-05-00366, 18-35-20068 (remote sensing data analysis) and RSF No. 19-17-00209 (GPS-sondes data assimilation and processing).

Arctic storms pose a great danger to developing commercial and passenger shipping, coastal infrastructure, and also for oil production from offshore platforms. This is primarily due to high waves and extreme winds. Such episodes of adverse weather conditions due to their rapid development are poorly predicted by modern models. For this purpose, the representation of the event of polar law is studied in the wave model WAVEWATCH III.Wind waves were simulated under conditions of polar depression on ice-free water. To simulate wind waves under conditions of polar depression, the Barents Sea was selected, where, according to the data of [1, 2], a large number of polar hurricanes are observed. Among the identified polar hurricanes, for example, in [3], a hurricane that took place on 05.02.2009, observed at coordinates 69 N 40 E is chosen. The preliminary results in the wave model are obtained without the ice influence consideration. The developed model was configured using the CFSR wind reanalysis data. The resulting distribution of significant wave heights is obtained. Then, to consider the attenuation by sea ice, the reanalysis data of the Arctic System Reanalysis Version 2 (ASRv2), which is based on Polar WRF with a resolution of 15 km for the Arctic region, is used. Modeling the destruction of ice by waves during an intense arctic storm will be implemented using WW3 models with an IS2 module.The work is supported by RFBR grant 18-05-60299.Smirnova, J. E., Golubkin, P. A., Bobylev, L. P., Zabolotskikh, E. V., & Chapron, B. (2015). Polar low climatology over the Nordic and Barents seas based on satellite passive microwave data. Geophysical Research Letters, 42(13), 5603-5609. Smirnova, J., & Golubkin, P. (2017). Comparing polar lows in atmospheric reanalyses: Arctic System Reanalysis versus ERA-Interim. Monthly Weather Review, 145(6), 2375-2383. Noer, G., & Lien, T. (2010). Dates and Positions of Polar lows over the Nordic Seas between 2000 and 2010. Norwegian Meteorological Institute Rep.

Wind-wave interaction at extreme wind speed is of special interest now in connection with the problem of explanation of the sea surface drag saturation at the wind speed exceeding 30 m/s. Now it is established that at hurricane wind speed the sea surface drag coefficient is significantly reduced in comparison with the parameterization obtained at moderate to strong wind conditions.The subject of this work is investigation of aerodynamic resistance of the waved water surface under severe wind conditions (up to U10 ≈ 50 m/s). Laboratory experiments were carried out at the new high-speed wind-wave flume in the Large Thermally Stratified Tank (at the Institute of Applied Physics, Russia) built in 2019. The main difference between the new wind-wave flume and the old one is the absence of a pressure gradient along the main axis of the new flume. Aerodynamic resistance of the water surface was measured by the profile method with Pitot tube. A method for data processing taking into account the self-similarity of the air flow velocity profile in the aerodynamic tube was applied for retrieving wind friction velocity and surface drag coefficients. Simultaneously with the airflow velocity measurements, the wind-wave field parameters in the flume were investigated by system of wire gauges.Analysis of the wind velocity profiles and wind-wave spectra showed tendency to decrease for surface drag coefficient for wind speed exceeding 25 m/s simultaneously with the mean square slope and significant wave height.Acknowledgments This work was carried out with the financial support of the RFBR according to the research project 18-55-50005, 20-05-00322, 18-35-20068, 18-05-00265. Data processing was carried out with the financial support of Russian Science Foundation grant 19-17-00209.

A lot of experimental works is devoted to studying behaviour of a droplet in the flow of the external medium. It is shown in [1] that mode of the deformation of droplet in the stationary flow is affected by the Weber number and the Reynolds number. The authors distinguish two types of the droplet deformation in the external flow: the dome-shaped deformation and the bowl-shaped one.Using the Basilisk software package, direct numerical simulation of the process of deformation of liquid drop in the gas stream was carried out. We examined the problem of the following geometry: a drop of liquid with diameter of 5 mm was placed in the gas stream at the speed of 30 m/s. The density of liquid and gas correspond to the density of water and air, the viscosity of liquid is equal to the viscosity of water. The viscosity of gas and the surface tension at the interface between liquid and gas are determined by the set values of the Reynolds (50 - 3000) and the Weber (2 - 30) numbers. Two main modes of the drop deformation were observed: the dome-shaped deformation and the bowl-shaped one, there is a transitional deformation mode between them. The map of deformation modes is constructed for comparison with the experimental data available in the literature. It was found that the dependence of the Weber number corresponding to the transition from one deformation mode to another on the Reynolds number is well described by the power law proposed in the literature. This work was supported by the RFBR projects 19-05-00249, 18-35-20068, 18-55-50005, 18-05-60299, 20-05-00322 (familiarization with the Basilisk software package) and the Grant of the President No. MK-3184.2019.5, work on comparison with experimental data was supported by the RSF project No. 18-77-00074, carrying out numerical experiment was supported by the RSF project No. 19-17-00209, A.N. Zotova is additionally supported by the Ministry of Education and Science of the Russian Federation (Government Task No. 0030-2019-0020). The authors are grateful to the FCEIA employee: UNR - CONICET (Rosario, Rep. Argentina) Dr. Ing. César Pairetti.[1] Hsiang, L.-P., Faeth, G. M., Int. J. Multiphase Flow 21(4), 545-560 (1995).

Many features of nonlinear water wave dynamics can be explained within the assumption that the motion of fluid is strictly potential. At the same time, numerically solving exact equations of motion for a three-dimensional potential flow with a free surface (by means of, for example, boundary integral method) is still often considered too computationally expensive, and further simplifications are made, usually implying limitations on wave steepness. A quasi-three-dimensional model, put forward by V. P. Ruban [1], represents another approach at reducing computational cost. It is, in its essence, a two-dimensional model, formulated using conformal mapping of the flow domain, augmented by three-dimensional corrections. The model assumes narrow directional distribution of the wave field and is exact for two-dimensional waves. It was successfully applied by its author to study a nonlinear stage of of Benjamin-Feir instability and rogue waves formation.The main aim of the present work is to explore the behaviour of the quasi-three-dimensional model outside the formal limits of its applicability. From the practical point of view, it is important that the model operates robustly even in the presence of waves propagating at large angles to the main direction (although we do not attempt to accurately describe their dynamics). We investigate linear stability of Stokes waves to three-dimensional perturbations and suggest a modification to the original model to eliminate a spurious zone of instability in the vicinity of the perpendicular direction on the perturbation wavenumber plane. We show that the quasi-three-dimensional model yields a qualitatively correct description of the instability zone generated by resonant 5-wave interactions. The values of the increment are reasonably close to those obtained from the exact equations of motion [2], despite the fact that the corresponding modes of instability consist of harmonics that are relatively far from the main direction. Resonant 5-wave interactions are known to manifest themselves in the formation of the so-called “horse-shoe” or “crescent-shaped” wave patterns, and the quasi-three-dimensional model exhibits a plausible dynamics leading to formation of crescent-shaped waves.This research was supported by RFBR (grant No. 20-05-00322).[1] Ruban, V. P. (2010). Conformal variables in the numerical simulations of long-crested rogue waves. The European Physical Journal Special Topics, 185(1), 17-33.[2] McLean, J. W. (1982). Instabilities of finite-amplitude water waves. Journal of Fluid Mechanics, 114, 315-330.

Recently, much attention has been paid to the study and numerical simulation of wind waves in the Arctic regions of the oceans. Their distinctive feature is the presence of ice cover of various types, which can significantly affect the processes of wind wave interaction, including momentum exchange. A detailed study of such processes under natural conditions is very difficult, especially for the forming ice (including pancake ice), therefore, laboratory simulation is preferable. Previously studies of the influence of floating ice on the evolution of waves that were generated by wavemakers were carried out only. In this paper we present preliminary results of studies performed on the AELOTRON circular wind wave flume of the University of Heidelberg, where the interaction of air flow with a water surface was simulated for the first time in the presence of forming ice of the pancake type. Synchronous measurements of wave characteristics were carried out using a laser wavegauge, as well as airflow velocity fields were measured with PIV-methods. Shims made of rubber with a diameter of 7 cm and a thickness of 1 cm with a density of about 0.8 kg /m3 were used as elements of artificial ice. The measurements were carried out in clean water and at three concentrations of artificial ice: maximum, 2/3 of the maximum, 1/3 of the maximum. Ice covered about half the surface at maximum concentration. The measurements were carried out in the range of equivalent wind speeds U10 from 7 to 16 m/s. The threshold character of excitation of long waves was obtained (the length is much greater than the average distance between the elements of ice). The higher the density, the higher the threshold for wind speed. According to the results of processing the velocity fields, the dependence of the aerodynamic drag coefficient on the equivalent wind speed was constructed. It is shown that the presence of ice weakly affects the momentum exchange for all concentrations and over the entire wind speed range.Investigation was supported by Russian Found Basic Research project # 18-05-60299 Arctic.

Active microwave sensing using satellite instruments has great advantages, since in this range the absorption by clouds and atmospheric gases is noticeably reduced, it allows for round-the-clock and all-weather monitoring of the ocean. One of the main problems is concerned with obtaining the dependency between the RCS of radar signal scattered by the wavy water surface and the parameters of the atmospheric boundary layer in hurricane conditions. To obtain this dependence, we used field measurements of wind speed in a hurricane from falling NOAA GPS-sondes and SAR images from the Sentinel-1 satellite. However, there is the problem of correct collocation of remote sensing data with field measurements of the atmospheric boundary layer parameters, since they are separated in time and space. In this regard, the amount of data suitable for analysis is very limited, which forces us to look for new data sources for processing. A six-channel SFMR radiometer is also installed on board of NOAA research aircraft that measures the emissivity of the ocean surface beneath the aircraft. Thus, it becomes possible to relate the radiometric measurements of SFMR with the parameters of the atmospheric boundary layer in a tropical cyclone obtained from wind velocity profiles, since they are carried out as close as possible in time and space. Using this relation, the SFMR data and the hurricane radar images were analyzed together and an alternative method was found for constructing the dependence of the RCS on the parameters of the boundary layer.This work was supported by the RFBR projects No. 19-05-00249, 19-05-00366, 18-35-20068 (remote sensing data analysis) and RSF No. 19-17-00209 (GPS-sondes data assimilation and processing).

It is important to measure the momentum flux across the air–water interface in the droplet- and bubble-laden turbulent flow at extremely high-wind speeds. Generally, the momentum flux is measured by a profile method, eddy correlation method, or momentum budget (balance) method at normal wind speeds. We assessed the usage of three measurement method at extremely high wind speeds in three wind-wave tanks, Kyoto, Kindai, and Kyushu Universities, JAPAN. Here, the Kyoto tank is 15 m long, 0.8 m wide, 0.8 m high and the maximum wind speed is 68 m/s. The Kyushu tank is 64 m long and the max. speed is 40 m/s. Moreover, we will show the preliminary results for the effects of the fetch on the momentum flux.

Showing the record strengths and growth-rates, a number of recent hurricanes have highlighted needs for improving forecasts of tropical cyclone intensities most sensitive to models of the air-sea coupling. Especially challenging is the nature and effect of the very small-scale phenomena, the sea-spray and foam, supposed to strongly affecting the momentum- and heat- air-sea fluxes at strong winds. This talk will focus on our progress in understanding and describing these "micro-scale" processes, their physical properties, the spray and foam mediated air-sea fluxes and the impact on the development of marine storms.The starting points for this study were two laboratory experiments. The first one was designed for investigation of the spray generation mechanisms at high winds. We found out 3 dominant spray generating mechanisms: stretching liquid ligaments, bursting bubbles, splashing of the falling droplets and "bag-breakup". We investigated the efficiency spray-production mechanisms and developed the empirical statistics of the numbers of the spray generating events of each type. Basing on the "white-cap method" we found out the dependence of the spray-generating events on the wind fetch. The main attention was paid to the "bag-breakup" mechanism. Here we studied in detail the statistics of spray produced from one "bag-breakup" event. Basing on these developments, we estimated heat and momentum fluxes from the spray-generating events of different types and found out the dominant role of the "bag-breakup" mechanism.To estimate the direct heat and momentum fluxes from the ocean surface to the atmosphere, we studied in the special experiment the foam impact on the short-wave part of the surface waves and the heat momentum exchange in the atmospheric boundary layer at high winds. Based on these results, we suggest a simple model for the aerodynamic and temperature roughness and the eddy viscosity in the turbulent boundary layer over a fractionally foam-covered water surface.The synergetic effect of foam at the water surface and spray in the marine atmospheric boundary layer on ocean surface resistance at high winds is estimated so as to be able to explain the observed peculiarities of the air-sea fluxes at stormy conditions. Calculations within the nonhydrostatic axisymmetric model show, that the "microphysics" of the air-sea coupling significantly accelerate development of the ocean storm.This work was supported by RFBR grant 19-05-00249 and RSF grant 19-17-00209.

Insufficient knowledge of the atmosphere layer momentum, heat and moisture transfer between the wavy water surface and marine atmospheric boundary layer under hurricane conditions lead to the uncertainties while using weather forecasting models and models of climate. In particular, there is a significant lack of data for heat and moisture exchange coefficients. In this regard, it is necessary to analyze and process the vertical profiles of wind speed and thermodynamic quantities. The present study is concerned with the analysis and processing of measurements from the NOAA falling GPS-sondes for hurricanes of categories 4 and 5 of 2003-2017, which represent an array of data on wind speed, temperature, altitude, coordinates, etc.The proposed approach for describing a turbulent boundary layer formed in hurricane conditions is based on the use of the self-similarity properties of the velocity and enthalpy profiles in the atmospheric boundary layer, which includes a layer of constant flows, transferring into its “wake” part with height. Based on the proposed approach, the aerodynamic drag coefficients Cd and the enthalpy exchange coefficient Ck for a selected group of hurricanes were restored. As the value of Ck/Cd represents a determining factor in the formation of a hurricane, the dependence of this ratio on the wind speed was constructed.This work was supported by the RFBR projects No 19-05-00249, 19-05-00366, 18-35-20068 (remote sensing data analysis) and RSF No 19-17-00209 (GPS-sonde data assimilation and processing).

Whitecap coverage were retrieved from high-speed video recordings of the water surface obtained on the unique laboratory faculty Heidelberg Small-Scale Air-Sea Interaction Facility, the Aeolotron (annular wind-wave facility, 60 cm width, 2.4 m height, circumference of 27.3 m at the inner wall; water depth during experiments 1.0 m, water volume 18.0 m³, air space volume 24 m³; wind was generated by two axial fans mounted into the ceiling).Records were made in the vertical direction (from top to bottom) in a shadowgraph configuration with backlight located under the channel. On the annular channel, regimes with an abrupt start of wind under an unperturbed surface condition were implemented, including the case of butanol presence in water simulating salinity. At the same time, the wave parameters varying depending on the time elapsed after the wind was turned on, made it possible to study the characteristics of the generation of spray at various effective fetches.As a result of semi-automatic processing of image sequences using specially developed software that allows marking the moment and position of the bag-breakup formation on the videos, the dependences of the frequency of occurrence of these phenomena per unit surface area versus time after turning on the wind were obtained. From the same images, using the developed software for automatic detection of areas of wave breaking, the values of the whitecap coverage area were obtained. In this case, 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 (water characteristics and wind speed), 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. Since the same high-speed surface images were used to study the statistics of occurrence of events leading to the spray generation and the dependences of the whitecap coverage on time after turning on the wind for each regime were obtained, we were able to estimate the average number of fragmentation events per unit area of the collapse area.The work was supported by the RFBR grant 18-35-20068 (conducting an experiment), President grant for young scientists MK-3184.2019.5 (software development) and the RSF grant No. 18-77-00074 (data processing).