Stokes drift

The flow associated with small amplitude non-breaking gravity waves on a perfect fluid in a wedge shaped domain is described by a second-order perturbation analysis. Retention of vertical accelerations to the leading order yields a (non-hydrostatic) model which is applicable to arbitrary slopes. A Wronskian W is written of the two fundamental solutions. It is shown that, for beaches of slope angle α=π/2M, M&z.ele;&z.openN;, RW is represented by a Taylor expansion in R, the distance from the fixed shoreline. An absolutely convergent integral expression is derived for the steady Eulerian velocity potential in a situation which is applicable to waves which are both standing and progressing in the far field. A derivation is used to compute induced steady bottom current, for a variety of slopes. The strength of this current is everywhere proportional to (1−Q 2 ), where Q is the reflection coefficient for the first-order wave motion. The computed current is found to have a reversal point typically at a few wavelengths from the shoreline. Following an application of the convolution theorem, an expression is derived which may be applied throughout the depth. This enables "stream function" contouring for the second-order Eulerian current from which an "updraught" is indicated above the reversal point. An expression for the Stokes drift is also derived, computed and mapped. It is found that "stream curves" for the resulting mass transport velocity are essentially horizontal except very close to the bed. Both Eulerian current and Stokes drift vanish identically in the case of perfect reflection. It is found, for gentle slopes, that values of W on the equilibrium surface Σ may be well approximated by kD 2 d/k∞, where Dd is the Airy theory shoaling coefficient and k and k∞ are the local and deep-water wave numbers respectively. This approximation permits the current to be expressed purely in terms of Airy theory parameters and is therefore computable without the need for computing first-order potential functions. Computations show excellent agreement with those obtained from the integral of the more exact theory. It is further established that the steady potential on Σ may be computed by a Cauchy principal value integral thus facilitating computation throughout the water column under the new approximation. A mapping of "equipotentials" is seen to be entirely consistent with the work under the more exact theory. WronskianWave numberShoaling coefficientSet-upSet-downMellin transformDigamma functionOverconvergence

Traditional atmosphere, ocean and wave models are run independently of each other. This means that the energy and momentum fluxes do not fully account for the impact of the oceanic wave field at the air-sea interface. In this study, the Stokes drift impact on mass and tracer advection, the Stokes-Coriolis forcing and, the sea-state-dependent momentum and energy fluxes are introduced into an ocean circulation model and tested for a domain covering the Baltic Sea and the North Sea. Sensitivity experiments are designed to investigate the influence on the simulation of storms and Baltic Sea upwelling. Inclusion of wave effects improves the model performance compared with the stand-alone circulation model in terms of sea level height, temperature and circulation. The direct sea-state-dependent momentum and turbulent kinetic energy fluxes prove to be of higher importance than the Stokes drift related effects investigated in this study (i.e., Stokes-Coriolis forcing and Stokes drift advection on tracers and on mass). The latter affects the mass and tracer advection but largely balances the influence of the Stokes-Coriolis forcing. The upwelling frequency changes by more than 10% along the Swedish coast when wave effects are included. In general, the strong (weak) upwelling probability is reduced (increased) when adding the wave effects. From the results, we

We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. We perform analytical calculations based on perturbation expansion which allows us to predict the dynamics of inertial particles in deep water regime. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift velocity. Moreover, we find that the vertical sedimentation velocity is also affected by a drift induced by waves. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that the vertical drift would also be observed in the (hypothetical) absence of the gravitational force. Kinematic numerical simulations are performed and the results are found to be in excellent agreement with the analytical predictions, even for values of parameters beyond the perturbative limit.

Results on the Mediterranean indicate a slight decrease of wind magnitude and an overall improvements in wave and wind statistics when comparing with altimeter and stations. Further coupling with Atmospheric local model, for example COSMO or WRF. Key issue is the physical parameterization of the sea surface.

We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an incompressible fluid (say, water). The flow is assumed to be unidirectional of finite depth and the water motion is supposed to be rotational. Our aim is to verify the Benjamin-Lighthill conjecture for flows whose total head (Bernoulli's constant) is close to the critical one; the latter is determined by the vorticity distribution so that no horizontal shear flows exist for smaller values of the total head. Originally, the conjecture was made about irrotational wave trains in order to describe them in terms of the parameters Q (rate of flow), R (total head/Bernoulli's constant) and S (flow force). Let r and s be dimensionless versions of R and S, respectively, for fixed Q, and let C be the region in the (r, s)-plane whose cusped boundary ∂C represents all possible uniform streams; moreover, the part of ∂C corresponding to supercritical streams is included into C, whereas the other part not. The Benjamin-Lighthill conjecture says that (a) each wave train is represented by a point of C and (b) every point of C corresponds to some wave train. In 2010-11, this form of the conjecture was proved by Kozlov and Kuznetsov for irrotational waves corresponding to nearcritical values of Bernoulli's constant. Here, we modify the Benjamin-Lighthill conjecture to adapt it for rotational waves on unidirectional flows. Let ω be a vorticity distribution, then the corresponding cusped region Cω (its boundary represents all possible horizontal shear flows) must be truncated by the line r = r0, where the constant r0 defined by ω is finite for some vorticity distributions. Under the assumptions that ω is Lipschitz continuous and the problem's parameter r attains nearcritical values, we prove the following extended version of the conjecture. Namely, along with the assertions (a) and (b) formulated above we show that the correspondence between wave trains and points in Cω is one-to-one. Our verification of the conjecture is based on the existence and uniqueness theorems for the problem with nearcritical values of r. These theorems also yield that there are two different parametrisations for each family of waves having their crests on a fixed vertical line.

The surface layer of the Southern Ocean is subject to the action of wind, waves and currents. We present solutions from a fine-resolution quasi-geostrophic model with surface friction, which is driven by a specified mean and fluctuating wind field, and predicts the surface current, and also the surface Stokes drift due to the wavefield. The resulting flow patterns control the dispersion of particles at the sea surface, and, using a proven Lagrangian algorithm, batches of particles of specified draught can be injected into the flow at various locations and tracked. The simulated patterns are compared with historical data on dispersion and with drift-card and satellite-drogue studies in the Southern Ocean, iceberg tracking and other studies to show the relative importance of dispersion by synoptic variability in the atmosphere and mesoscale eddies in the ocean.

This paper presents a model for the similarity structure of the velocity profiles in air and water in the wave boundary layer, which provides predictions in terms of two parameters, F and R, of all its important properties, including the Charnock parameter, the surface drift velocity and the condition for the cancellation of the surface Stokes velocity by the surface current. The parameter, F, arises from the fetch variability of the wave field, and the parameter, R, arises from the duration variability of the wave field. In the analysis two regimes emerge, namely the Ekman regime and the Hasselmann regime. In the Ekman regime, which occurs for R > ½ (1 + F), there is a net loss of energy from the wave field to the deep ocean, and in the Hasselmann regime which occurs for R < ½ (1 + F), there is a net gain of energy from the atmosphere to the wave field. The predictions are compared with observations from classical wave formulae, wind-wave studies, and also ROMS and SWAN modelling in the South Australian Basin. A general conclusion is that the condition, F = 1, which was used in the original inertial coupling model of Bye [1], is a good approximation for large scale theoretical ocean studies, and hence the wind-wave interaction is determined principally by R. Air-sea interaction; similarity air and water velocity profiles in the wave boundary layer; the Charnock parameter; the inertial coupling relation; classical wave prediction formulae; windwave campaign data; regional ocean modelling system and simulating waves nearshore modelling results; energy supply to the deep ocean by the wave spectrum

Stokes drift is a classical fluid effect in which travelling waves transfer momentum to tracers of the fluid, resulting in a non-zero drift velocity in the direction of the incoming wave. This effect is the driving mechanism allowing particles, i.e. impurities, to be transported by the flow; in a classical (viscous) fluid this happens usually due to the presence of viscous drag forces. Because of the eventual absence of viscosity in quantum fluids, impurities are driven by inertial effects and pressure gradients only. We present theoretical predictions of a Stokes drift analogous in quantum fluids for classical impurities obtained using multi-time analytical asymptotic expansions. We find that, at the leading order, the drift direction and amplitude depend on the initial impurity position with respect to the wave phase; at the second order, dominant after averaging over initial conditions, our theoretical model recovers the classical Stokes drift but with a coefficient that depends on the relative particle-fluid density ratio. Numerical simulations of a two-dimensional Gross-Piteaveskii equation coupled with a classical impurity corroborate our findings. Our predictions are experimentally testable, for instance, using fluids of light obtained in photorefractive crystals.

Results: Three shunts showed good mechanical durability over the 3 month period of testing and good stability of hydrodynamic performance over a 45 day period. The pressure-flow performance curves, operating, opening and closing pressures were stable. The shunt increases drainage rate when negative outlet pressure (siphoning) was applied. Hydrodynamic parameters fell within the limits specified by the manufacturer and changed according to the programmed performance levels. Hydrodynamic resistance was dependant on operating pressure changing from low values of 1.6 mmHg/(ml/min) on lowest level to 11 mm Hg/(ml/min) on highest performance level. External programming proved to be easy and reliable. Even very strong magnetic fields (3 Tesla) were not able to change the programming of the valve. However, distortion of MRI images was considerable. Conclusion: The Polaris Valve is a reliable, adjustable valve. Unlike other adjustable valves (except the Miethke ProGAV valve), the Polaris cannot be accidentally readjusted by an external magnetic field

The present paper reports on a study of the interaction of a current-free monochromatic surface wave field with a wave-free uniform current field in a three-dimensional flow frame. The wave and the current fields are not necessarily collinear with each other. The formulation of the wave-current field is done under the assumption of irrotational and inviscid flow. We have developed the three dimensional expressions describing the characteristics of the combined flow in terms of mass, momentum and energy transport conservation. These equations are found efficient to describe the sought-for combined wave-current field. The parameters describing the wave-current field after the interaction are the surface disturbance amplitude and length, mean water depth, mean current-like parameter and direction of the combined flow, which would be calculated from a set of equations that satisfy conservation of mean mass, momentum and energy flux and a dispersion relation on the free surface before and after the interaction. The results are shown in terms of relative changes in wave heights and lengths, current-like parameters and final directions obtained for the combined wave-current field with respect to currentfree wave and wave-free current pre-interaction parameters.

This paper shows that the method of uncertainty quantification via the introduction of Stratonovich cylindrical noise in the Hamiltonian formulation introduces stochastic Lie transport into the dynamics in the same form for both electromagnetic fields and fluid vorticity dynamics. Namely, the resulting stochastic partial differential equations (SPDE) retain their unperturbed form, except for an additional term representing induced Lie transport by a set of divergence-free vector fields associated with the spatial correlations of the cylindrical noise. The explanation lies in the method of construction of the Hamiltonian for the Stratonovich stochastic contribution to the motion in both cases, via pairing data correlation vector fields for cylindrical noise with the momentum map for the deterministic motion, which is responsible for the well-known analogy between hydrodynamics and electromagnetism. For the Maxwell and Born-Infeld theories of electromagnetism treated here, the momentu...

Rapidly melting sea ice processes during the summer tend to enlarge the open water in the Arctic region. The resulting larger potential fetch for surface waves can allow significant wave generation and development in the region. The sea ice plays an energy dissipation role for waves propagating into the ice-covered sea. A sphericalcoordinate surface wave model was established within the unstructured grid Finite-Volume Community Ocean Model (FVCOM) to examine the influence of ice-induced wave attenuation on waves propagating into the ice in the Arctic Ocean. Ice-induced wave attenuation parameterizations were implemented, with an effective methodology to reduce numerical dissipation during the energy advection in geographic space. Wave partition and source tracking methods were added to distinguish the windsea and swell, as well as to backtrack swell waves to their sources. The model-simulated significant wave heights and peak periods were compared with available buoy and Jason-2 satellite measurements. Results from a process-oriented model show that simulations of the surface waves in the Arctic region are improved when ice-induced attenuation is included in the model system. An empirical method is used to statistically estimate wave-induced ice breakage, based on the wave-induced internal ice strain, as waves penetrate into the ice zone. The simulation results support the 'ice retreat-wave growth' positive feedback mechanism.

The ratio of the periods of oceanic surface waves (wind waves and swells) and the inertial period is about 10, and the earth&#39;s rotation does not greatly affect the orbital motion of fluid particles. Waves, however, do modify mean flow under the influence of Coriolis force. This is because the slight tilt of the orbital plane of fluid particle generates Reynolds stress. Hasselmann (1970) and Huang (1979) demonstrated that this Reynolds stress induced by waves can be expressed as the Coriolis force acting on the Stokes drift. The latter expression is called Coriolis-Stokes forcing. In ocean surface layer studies, Coriolis-Stokes forcing has been used as a standard formulation to incorporate the wave-stress effect. However, Coriolis-Stokes forcing is derived under several assumptions, and there has been no research that directly examined the appropriateness of the forcing. Here we investigated the Coriolis-Stokes forcing, by performing direct numerical simulations of deep-water wav...

The present study performs a wave-resolving simulation of wind-driven currents under monochromatic surface gravity waves using the latest nonhydrostatic free-surface numerical model. Here, phase speed of the waves is set much greater than the current speed. Roll structures very similar to observed Langmuir circulations (LCs) appear in the simulation only when both waves and down-wave surface currents are present, demonstrating that the rolls are driven by the wave–current interaction. A vorticity analysis of simulated mean flow reveals that the rolls are driven by the torque associated with wave motion, which arises from a correlation between wave-induced vorticity fluctuation and the wave motion itself. Furthermore, it is confirmed that the wave-induced torque is very well represented by the curl of the vortex force (VF), that is, the vector product of mean vorticity and Stokes drift velocity. Therefore, it is concluded that the simulated rolls are LCs and that the wave effects are...

Abstract: With morphodynamic-numerical models the development of estuarine systems can be simulated for a period of several years. In areas exposed to high waves the effects from waves on the sediment dynamics can not be neglected. Especially if there are also currents acting on the sediments. In order to simulate these effects the hydrodynamic-morphodynamic-numerical-model TIMOR3 (TidalMorphodynamics) was coupled to the spectral wave model WWM (WindWaveModel). This coupling procedure enables ...

Wind-wave interaction in the Western Mediterranean Sea is analyzed using 16 years of model data. The mass transport and energy distribution due to wind and waves are integrated through the Ekman-Stokes layer and then spatially and seasonally analyzed. The Stokes drift is estimated from an empirical parameterization accounting for local surface wind and the significant wave height. The impact of the Stokes drift depends on wind variability at the ocean surface and also on the geographical configuration of the basin. The Western Mediterranean Sea has on average a wind energy input two times higher in winter than in summer, and the Stokes-Ekman mass transport interaction term contributes approximately 10% to 15% of the total wind induced transport, but at some locations the contribution is as much as 40% or more.

Classical Stokes' drift is the small time-averaged drift velocity of suspended nondiffusing particles in a fluid due to the presence of a wave. We consider the effect of adding diffusion to the motion of the particles, and show in particular that a nonzero time-averaged drift velocity exists in general even when the classical Stokes' drift is zero. Our results are obtained from a general procedure for calculating ensembleaveraged Lagrangian mean velocities for motion that is close to Brownian, and are verified by numerical simulations in the case of sinusoidal forcing.

The effect of ocean waves on near-surface currents is a topic about which interest has recently revived, as a result of various factors including the prediction of the drift of oil spills from marine accidents. In order to evaluate properly the effect of waves, it is necessary to employ a ...

A new method to determine near-surface vertical current shear from noncoherent marine Xband radar (MR) data is introduced. A three-dimensional fast Fourier transform is employed to obtain the wave number-frequency spectrum of a MR image sequence. Near-surface currents are estimated from the Doppler-shifted surface gravity wave signal within the spectrum. They represent a weighted mean of the upper ocean flow. The longer the ocean waves on which the current estimates are based, the greater their effective depth. The novelty lies in the wave number-dependent retrieval method, yielding $100 independent current estimates at effective depths from $2 to 8 m per $12 min measurement period. First, MR nearsurface vertical current shear measurements are presented using data collected from R/V Roger Revelle during the 2010 Impact of Typhoons on the Ocean in the Pacific experiment in the Philippine Sea. Shipboard acoustic Doppler current profiler (ADCP) and anemometer measurements as well as WAVEWATCH III (WW3) model results are used to demonstrate that results are in accord with physical expectations. The wind and wave-driven Ekman flow is obtained by subtracting ADCP-based background currents from the radar measurements. At $2 m, it is on average $1.6% of the wind speed and $38.98 to the right of the wind. With increasing effective depth, the speed factor decreases and the deflection angle increases. Based on WW3 results, the MR-sensed Stokes drift speed

Index 3. Shearless turbulence mixings by means of the angular momentum large eddy model 1. Overview 2. Initial conditions 3. Mixing without gradient of integral scale 4. Mixing with opposite gradients of integral scale and energy 5. Mixing with concurrent gradients of integral scale and energy 6. Accuracy estimates 7. Discussion Conclusions Bibliography

This numerical work aims to better understand the behavior of extreme Adriatic Sea wave storms under projected climate change. In this spirit, 36 characteristic events-22 bora and 14 sirocco storms occurring between 1979 and 2019, were selected and ran in evaluation mode in order to estimate the skill of the kilometer-scale Adriatic Sea and Coast (AdriSC) modelling suite used in this study and to provide baseline conditions for the climate change impact. The pseudo-global warming (PGW) methodology-which imposes an additional climatological change to the forcing used in the evaluation simulations, was implemented, for the very first time, for a coupled ocean-wave-atmosphere model and used to assess the behavior of the selected storms under Representative Concentration Pathway (RCP) 4.5 and RCP 8.5 greenhouse gas projections. The findings of this experiment are that, on the one hand, the AdriSC model is found capable of reproducing both the Adriatic waves associated with the 36 storms and the northern Adriatic surges occurring during the sirocco events and, on the other hand, the significant wave heights and peak periods are likely to decrease during all future extreme events but most particularly during bora storms. The northern Adriatic storm surges are in consequence also likely to decrease during sirocco events. As it was previously demonstrated that the Adriatic extreme wind-wave events are likely to be less intense in a future warmer climate, this study also proved the validity of applying the PGW methodology to coupled ocean-wave-atmosphere models at the coastal and nearshore scales.

In this paper, we consider the Cauchy problem for the fractional Camassa-Holm equation which models the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. Using Kato's semigroup approach for quasilinear evolution equations, we prove that the Cauchy problem is locally well-posed for data in H s (R), s > 5 2 .

An intense cold air outbreak affected the northern Adriatic Sea during winter 2012, determining an exceptional persistence of northeasterly Bora wind over the basin, which lasted for about 3 weeks. The cold air coming from the Balkans produced icing in the Venice lagoon and very intense snowfall in the Apennines Mountains and even near the coasts. In order to understand the importance and role of air-sea interactions for the evolution of the atmospheric fields, simulations with the Weather Research and Forecasting (WRF) model encompassing the whole period have been performed using sea surface temperature (SST) fields with an increasing level of complexity. Starting from a large-scale static sea temperature, the SST in the initial and boundary conditions has been progressively made more realistic. First, a more refined field, retrieved from a satellite radiometer was used; then, the same field was updated every 6 h. Next, the effect of including a simplified 1D ocean model reproducing the Oceanic Mixed Layer (OML) evolution has been tested. Finally, the potential improvements coming from a coupled description of atmosphere-ocean and atmosphere-ocean-waves interactions have been explored within the Coupled Ocean-Atmosphere-Wave Sediment Transport (COAWST) modeling system. Results highlight that the energy exchange between air and sea does not significantly impact the atmospheric fields, in particular 10 m wind and 2 m temperature, also because of the geography of the basin and the predominance of synoptic-scale flow in intense events of Bora, in the northern Adriatic. However, when sensible and latent heat fluxes, which are dependent on atmospheric and oceanic variables, are analyzed, the more realistic representation of SST drastically improves the model performances.

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.

A modification of the classical Ekman model of oceanic wind-driven currents including the Stokes drift and stratification effects is discussed. The modification is formulated as an application of turbulence mechanics accounting for the curvature effect of velocity fluctuation streamlines. It is shown that similar to the Stokes drift effect, the presence of a density jump layer (pycnocline) decreases the veering of the flow velocity vector at the surface from the direction of the wind stress. It is shown also that in the pycnocline the decrease of the norm of the velocity vector as well as its rotation with depth is smaller than in the regions adjacent to the pycnocline. If the Stokes drift and stratification effects are neglected, the model reduces to the classical Ekman solution with the coefficient of the turbulent shear viscosity replaced by an effective viscosity coefficient. The vertical distributions of velocity predicted by the modified model are compared with the velocity data measured in the Drake Passage and within the Long-Term Upper Ocean Study (LOTUS) in the North Atlantic.

A deep-water approximation of the Stokes drift velocity profile is explored as an alternative to the monochromatic profile. The alternative profile investigated relies on the same two quantities required for the monochromatic profile, namely, the Stokes transport and the surface Stokes drift velocity. Comparisons with parametric spectra and profiles under wave spectra from the Interim ECMWF Re-Analysis (ERA-Interim) and buoy observations reveal much better agreement than the monochromatic profile even for complex sea states. That the profile gives a closer match and a more correct shear has implications for ocean circulation models since the Coriolis-Stokes force depends on the magnitude and direction of the Stokes drift profile, and Langmuir turbulence parameterizations depend sensitively on the shear of the profile. The alternative profile comes at no added numerical cost compared to the monochromatic profile.

In the current review, the most pessimistic events of the globe in history are addressed when we present severe impacts caused by storm surges. During previous decades, great progresses in storm surge modeling have been made. As a result, people have developed a number of numerical software such as SPLASH, SLOSH etc. and implemented routine operational forecast by virtue of powerful supercomputers with the help of meteorological satellites and sensors as verification tools. However, storm surge as a killer from the sea is still threatening human being and exerting enormous impacts on human society due to economic growth, population increase and fast urbanization. To mitigate the effects of storm surge hazards, integrated research on disaster risk (IRDR) as an ICSU program is put on agenda. The most challenging issues concerned such as abrupt variation in TC's track and intensity, comprehensive study on the consequences of storm surge and the effects of climate change on risk estimation are emphasized. In addition, it is of paramount importance for coastal developing countries to set up forecast and warning system and reduce vulnerability of affected areas.

A new approximation to the Stokes drift velocity profile based on the exact solution for the Phillips spectrum is explored. The profile is compared with the monochromatic profile and the recently proposed exponential integral profile. ERA-Interim spectra and spectra from a wave buoy in the central North Sea are used to investigate the behaviour of the profile. It is found that the new profile has a much stronger gradient near the surface and lower normalized deviation from the profile computed from the spectra. Based on estimates from two open-ocean locations, an average value has been estimated for a key parameter of the profile. Given this parameter, the profile can be computed from the same two parameters as the monochromatic profile, namely the transport and the surface Stokes drift velocity.

The effect of mean mass transport on the surface of the sea due to wave movement and known as "Stokes Drift" plays an important role in forecasting the movement of floating pollutants and is also of paramount importance when evaluating the boundary conditions for the computation of coastal circulation; this paper presents an attempt to supplement the usual approach based on monochromatic waves or standard spectral simulations with an analysis of measured time series of waves. Wave heights and periods are computed from records of water height data obtained with a Datawell wave gauge located in the Bay of Naples in different sea states through the usual zeroupcrossing procedure, and wave parameters are estimated; once such parameters are known and a wave theory is assumed the computation of the drift velocity is quite straightforward. These computations yield a mean drift velocity for all available sea records, which include both calm and very rough sea conditions; correlations are found to relate drift to the sea state.

In this paper we present mean velocity distributions measured in several different wave flumes. The flows shown involve different types of mechanical wavemakers, channels of differing sizes, and two different end conditions. In all cases, when surface waves, nominally deep-water Stokes waves, are generated, counterflowing Eulerian flows appear that act to cancel locally, i.e. not in an integral sense, the mass transport associated with the Stokes drift. No existing theory of wave-current interactions explains this behaviour, although it is symptomatic of Gerstner waves, rotational waves that are exact solutions to the Euler equations. In shallow water (kH ≈ 1), this cancellation of the Stokes drift does not hold, suggesting that interactions between wave motions and the bottom boundary layer may also come into play.

To improve sea surface wind speed in coastal regions, we used nadir satellite altimeter measurements in the Persian Gulf and Arabian Sea. With combining normalized radar cross section for two bands of satellite altimeter measurements and significant wave height suggested the method to obtain "true" sea surface wind speed. In the coastal regions, we used a dimensionless significant wave height to gain empirical dependency to fetch-limited wind wave development. In this research, normalized radar cross section is simulated by using inverse wave age and fetch laws. As established this method helps to refine altimeter measurements of sea surface wind in the coastal regions.

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It has been proposed that Langmuir circulations arise as an inshbility of the equations describing the Eulerian-mean flow in bodies of water supporting surface waves and subject to an applied wind stress. I n infinitely deep density-stratified water, the solution of an appropriate initial-value problem is a unidirectional, time-dependent current. The stability of this current to two-dimensional (roll) disturbances is investigated by an energy analysis and by linear theory. It is found that the energy stability estimates and linear stability limits are very close, showing that subcritical instability, if it occurs, is limited to a very narrow region in parameter space. According to the present results, conditions typically occurring in the ocean are highly unstable to the Langmuir circulation instability.

Air bubble penetration depths are investigated with a bottom‐mounted echosounder at a seabed observatory in northern Norway. We compare a 1‐year time series of observed bubble depth against modeled and estimated turbulent kinetic energy flux from breaking waves as well as wind speed and sea state. We find that the hourly mean and maximum bubble depths are highly variable, reaching 18 and 38 m, respectively, and strongly correlated with wind and sea state. The bubble depth is shallowest during summer following the seasonal variations in wind speed and wave height. Summertime shallowing of the mixed layer depth is not limiting the penetration depth. A strong relationship between bubble depth and modeled turbulent kinetic energy flux from breaking waves is found, similar in strength to the relationship between bubble depth and wind speed. The wind sea is more strongly correlated with bubble depth than the total significant wave height, and the swell is only weakly correlated, suggestin...

We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin–Lighthill conjecture for flows with values of Bernoulli’s constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.

Recent developments in the physical parameterizations available in spectral wave models have already been validated, but there is little information on their relative performance especially with focus on the higher order spectral moments and wave partitions. This study concentrates on documenting their strengths and limitations using satellite measurements, buoy spectra, and a comparison between the different models. It is confirmed that all models perform well in terms of significant wave heights; however higher-order moments have larger errors. The partition wave quantities perform well in terms of direction and frequency but the magnitude and directional spread typically have larger discrepancies. The high-frequency tail is examined through the mean square slope using satellites and buoys. From this analysis it is clear that some models behave better than the others, suggesting their parameterizations match the physical processes reasonably well. However none of the models are entirely satisfactory, pointing to poorly constrained parameterizations or missing physical processes. The major space-time differences between the models are related to the swell field stressing the importance of describing its evolution. An example swell field confirms the wave heights can be notably different between model configurations while the directional distributions remain similar. It is clear that all models have difficulty in describing the directional spread. Therefore, knowledge of the source term directional distributions is paramount in improving the wave model physics in the future. Highlights ► The best 4 spectral wave parameterizations have been compared to satellites and buoys. ► Higher order spectral moments and wave partitions are rigorously validated. ► All models describe the loworder wave moments; some perform better for higher ones. ► The models are sensitive to the far-field swell and have similar spatial distribution. ► The directional spread within the wave spectra performs poorly and needs improvement. Please note that this is an author-produced PDF of an article accepted for publication following peer review. The definitive publisher-authenticated version is available on the publisher Web site.

The sea states numerical modeling has been developed for years, it used for very varied fields such as the sizing of coastal work, the safety of navigation, the study of the stability of the beaches or the water leisure.  The spectral third-generation ocean wind-wave model WAVEWATCH III (WW3) software was adopted and developed for simulating wave propagation in the Mediterranean basin.  In this study, a more detailed study was carried out on the port of Algiers. Two different atmospheric models have been used to get the wind forcing: ALADIN (Area Limited Dynamic Adaptation Inter National Development) with an 8 km resolution. And AROME (Application to Operational Research at Meso-scale) with a 3 km resolution. The results obtained using both of the atmospheric models have been compared and analyzed.