The theory of weak turbulence developed for wind-driven waves in theoretical works and recent extensive numerical studies concludes that non-dimensional features self-similar wave growth (i.e. energy characteristic frequency) have to be scaled by internal wave-field properties (fluxes energy, momentum or action) rather than external attributes (e.g. wind speed) which been widely adopted since the 1960s. Based on hypothesis dominant nonlinear transfer, an asymptotic weakly turbulent relation...

Abstract. The results of theoretical and numerical study the Hasselmann kinetic equation for deep water waves in presence wind input dissipation are presented. guideline study: nonlinear transfer is dominating mechanism wind-wave evolution. In other words, most important features wind-driven sea could be understood a framework conservative while forcing determine parameters solution equation. has rich family self-similar solutions duration-limited fetch-limited growth. These closely related...

Extensive numerical simulations of fetch-limited growth wind-driven waves are analysed within two approaches: a ‘traditional’ wind-speed scaling first proposed by Kitaigorodskii ( Bull. Acad. Sci. USSR, Geophys. Ser., Engl. Transl. , vol. N1, 1962, p. 105) in the early 1960s and an alternative weakly turbulent developed recently Badulin et al . J. Fluid Mech. 591 2007, 339–378). The latter one uses spectral fluxes wave energy, momentum action as physical scales problem allows for advanced...

We present a self‐consistent analytic theory of the wind‐driven sea—the weak‐turbulent theory. The base statement is that four‐wave resonant interactions play leading role in energy balance sea. study exact solution stationary wave kinetic equation and self‐similar solutions both fetch‐ duration‐limited cases. makes possible to explain nature universal power‐like spectra as well dependence total peak frequency from fetch duration.

Abstract A physical model for sea wave period from altimeter data is presented. Physical roots of the are in recent advances theory weak turbulence wind‐driven waves that predicts link instant energy to flux to/from waves. The operates with height and its spatial derivative does not refer normalized radar cross‐section σ 0 measured by altimeter. Thus, resulting formula contain any empirical parameters require features particular satellite or calibration specific region measurements. single...

Modern day studies of wind-driven sea waves are usually focused on wind forcing rather than the effect resonant nonlinear wave interactions. The authors assume that these effects dominating and propose a simple relationship between instant steepness time or fetch development expressed in periods lengths. This law does not contain speed explicitly relies upon this asymptotic theory. validity is illustrated by results numerical simulations, situ measurements growing seas tank experiments....

The work suggests a simple qualitative model of the wind wave 'horse-shoe' patterns often seen on sea surface. is aimed at explaining persistent character and their specific asymmetric shape. It based idea that dominant physical processes are quintet resonant interactions, input due to dissipation, which balance each other. These described lowest order in nonlinearity. consideration confined most essential modes: central (basic) harmonic two symmetric oblique satellites, rapidly growing ones...

We study wave patterns of gravity–capillary waves from moving localized sources within the classic setup problem ship wakes. The focus is on co-existence two systems with opposite signatures group velocity relative to source. It leads choice signs for phase functions gravity (“slow”) and capillary (“fast”) branches dispersion relation: question generally ignored when constructing solutions. detail characteristic angles wake patterns: (i) angle demarcation waves—“the Mach” cone, (ii) minimal...

The work is concerned with the problem of linear instability symmetric short-crested water waves, simplest three-dimensional wave pattern. Two complementary basic approaches were used. first, previously developed by Ioualalen & Kharif (1993, 1994), based on application Galerkin method to set Euler equations linearized around essentially nonlinear states calculated using Stokes-like series for waves great precision. An alternative analytical approach starts so-called Zakharov equation,...

The propagation of guided internal waves on non-uniform large-scale flows arbitrary geometry is studied within the framework linear inviscid theory in WKB-approximation. Our study based a set Hamiltonian ray equations, with being determined from Taylor-Goldstein boundary-value problem for stratified shear flow. Attention focused fundamental fact that generic smooth non-uniformities flow result specific singularities Hamiltonian. Interpreting wave packets as particles momenta equal to their...

The global visual wave observations are reanalyzed within the theoretical concept of self‐similar wind‐driven seas. core analysis is one‐parametric dependencies height on period. Theoretically, seas governed by power‐like laws with exponents close to Toba's one 3/2 while corresponding swell exponent (−1/2) has an opposite signature. This simple criterion was used and appeared be adequate problem waves discrimination. theoretically based discrimination does not follow exactly Voluntary...

This paper studies the propagation of a wave packet in regions where central frequency ω is close to local maximum effective Väisälä N f ( z ) = )/[1 − k · U )/ω], wavevector and mean current with vertical velocity shear. The approaches layer m asymptotically, i.e. trapping takes place. guided internal waves investigated within framework linearized equations motion an incompressible stratified fluid WKB approximation, viscosity, spectral bandwidth packet, shear non-stationarity environment...

Wave steepness is presented as an extension and a valuable add-on to the conventional set of sea state parameters retrieved from satellite altimetry data.Following physical model based on recent advances weak turbulence theory wave estimated directly measured spatial gradient height.In this way method works with trajectories rather than point-wise data.Moreover, in contrast widely used parametric models approach provides us instantaneous values period.Relevance single-track estimates...

Abstract. Results of extensive simulations swell evolution within the duration-limited setup for kinetic Hasselmann equation long durations up to 2 × 106 s are presented. Basic solutions theory weak turbulence, so-called Kolmogorov–Zakharov solutions, shown be relevant results simulations. Features self-similarity wave spectra detailed and their impact on methods ocean monitoring is discussed. Essential drop in energy (wave height) due wave–wave interactions found at initial stages (on order...

A generalization of the kinetic equation is proposed for explaining observed shapes wind wave spectra. The approach allows to fix a critical uncertainty in modeling spectra using condition equilibrium nonlinear transfer and dissipation due breaking. We demonstrate transition from Kolmogorov-Zakharov spectrum $E(ω)\sim ω^{-4}$ Phillips ω^{-4}$. This routinely field experiments. first results generalized simulations are presented.

Abstract The article presents a joint analysis of wind and wave characteristics derived from Voluntary Observing Ship (VOS) data measurements the innovative Ku‐band radar SWIM (Surface Waves Investigation Monitoring) carried by Chinese‐French Ocean SATellite (CFOSAT). Global distributions significant height speed in both sets demonstrate good qualitative quantitative agreement, especially regions with high spatio‐temporal density visual observations. A particular focus is made on...