arXiv subjects

V. E. Zakharov

Publications and source records attributed to V. E. Zakharov.

31 records · Page 2Linked to original sources

arXiv2012

On the applicability of the Hasselmann kinetic equation to the Phillips spectrum

We investigate applicability of the Hasselmann kinetic equation to the spectrum of surface gravity waves at different levels of nonlinearity in the system, which is measured as average steepness. It is shown that even in the case of relatively high average steepness, when Phillips spectrum is present in the system, the spectral lines are still very narrow, at least in the region of direct cascade spectrum. It allows us to state that even in the case of Phillips spectrum the kinetic equation can be applied to the description of the ensembles of ocean waves.

physics.ao-ph↗

arXiv2012

New wind input term consistent with experimental, theoretical and numerical considerations

We offer a new method for determining the wind source term for energy and momentum fluxes transfer from the atmosphere to the wind-driven sea. This new source-term formulation is based on extensive analysis of experimental data collected at different sites around the world. It is shown that this new wind source term to be consistent both with numerical solution of exact equation for resonant four-wave interactions and available experimental data.

physics.ao-ph↗

arXiv2012

Quasibreathers in MMT model

We report numerical detection of new type of localized structures in the frame of Majda-McLaughlin-Tabak (MMT) model adjusted for description of essentially nonlinear gravity waves on the surface of ideal deep water. These structures -- quasibreathers, or oscillating quasisolitons -- can be treated as groups of freak waves closely resembling experimentally observed "Three Sisters" wave packs on the ocean surface. The MMT model has quasisolitonic solutions. Unlike NLSE solitons, MMT quasisolitons are permanently backward radiating energy, but nevertheless do exist during thousands of carrier wave periods. Quasisolitons of small amplitude are regular and stable, but large-amplitude ones demonstrate oscillations of amplitude and spectral shape. This effect can be explained by periodic formation of weak collapses, carrying out negligibly small amount of energy. We call oscillating quasisolitons "quasibreathers".

nlin.PS↗

arXiv2012

Free-Surface Hydrodynamics in the conformal variables

The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the equations helped to discover new integrals of motion. These integrals are connected with the analytical properties of conformal mapping and complex velocity. Simple form of the equations also makes the numerical simulations of the free surface evolution very straightforward. In the limit of almost flat surface the equations can be reduced to the Hopf equation.

physics.flu-dyn↗

arXiv2012

Collision of two breathers at surface of deep water

We applied canonical transformation to water wave equation not only to remove cubic nonlinear terms but to simplify drastically fourth order terms in Hamiltonian. This transformation explicitly uses the fact of vanishing exact four waves interaction for water gravity waves for 2D potential fluid. After the transformation well-known but cumbersome Zakharov equation is drastically simplified and can be written in X-space in compact way. This new equation is very suitable as for analytic study as for numerical simulation. Localized in space breather-type solution was found. Numerical simulation of collision of two such breathers strongly supports hypothesis of integrability of 2-D free surface hydrodynamics.

physics.flu-dyn↗

arXiv2010

Communication through plasma sheaths

We wish to transmit messages to and from a hypersonic vehicle around which a plasma sheath has formed. For long distance transmission, the signal carrying these messages must be necessarily low frequency, typically 2 GHz, to which the plasma sheath is opaque. The idea is to use the plasma properties to make the plasma sheath appear transparent.

physics.plasm-ph↗

arXiv2007

Numerical Verification of the Weak Turbulent Model for Swell Evolution

The purpose of this article is numerical verification of the theory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. In both cases we observed effects predicted by this theory: frequency downshift, angular spreading and formation of Zakharov-Filonenko spectrum $I_ω \sim ω^{-4}$. To achieve quantitative coincidence of the results obtained by different methods, one has to supply the Hasselmann kinetic equation by an empirical dissipation term $S_{diss}$ modeling the coherent effects of white-capping. Using of the standard dissipation terms from operational wave predicting model ({\it WAM}) leads to significant improvement on short times, but not resolve the discrepancy completely, leaving the question about optimal choice of $S_{diss}$ open. In a long run {\it WAM} dissipative terms overestimate dissipation essentially.

physics.flu-dyn↗

arXiv2007

Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modelling the strongly nonlinear process of white-capping. Fitting the two experiments, we determined the dissipation function due to wave breaking and found that it depends very sharply on the parameter of nonlinearity (the surface steepness). The onset of white-capping can be compared to a second-order phase transition. This result corroborates with experimental observations by Banner, Babanin, Young.

physics.ao-ph↗

arXiv2007

Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions

Several theories for weakly damped free-surface flows have been formulated. In this paper we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schrödinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.

physics.ao-ph↗

arXiv2005

Mesoscopic wave turbulence

We report results of sumulation of wave turbulence. Both inverse and direct cascades are observed. The definition of "mesoscopic turbulence" is given. This is a regime when the number of modes in a system involved in turbulence is high enough to qualitatively simulate most of the processes but significantly smaller then the threshold which gives us quantitative agreement with the statistical description, such as kinetic equation. Such a regime takes place in numerical simulation, in essentially finite systems, etc.

physics.flu-dyn↗

arXiv2004

Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves

We study the long-time evolution of gravity waves on deep water exited by the stochastic external force concentrated in moderately small wave numbers. We numerically implement the primitive Euler equations for the potential flow of an ideal fluid with free surface written in canonical variables, using expansion of the Hamiltonian in powers of nonlinearity of up to fourth order terms. We show that due to nonlinear interaction processes a stationary energy spectrum close to $|k| \sim k^{-7/2}$ is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.

physics.flu-dyn↗

arXiv2003

Decay of the monochromatic capillary wave

It was demonstrated by direct numerical simulation that, in the case of weakly nonlinear capillary waves, one can get resonant waves interaction on the discrete grid when resonant conditions are never fulfilled exactly. The waves's decay pattern was obtained. The influence of the mismatch of resonant condition was studied as well.

physics.flu-dyn↗

arXiv2003

Weak turbulence of gravity waves

For the first time weak turbulent theory was demonstrated for the surface gravity waves. Direct numerical simulation of the dynamical equations shows Kolmogorov turbulent spectra as predicted by analytical analysis from kinetic equation.

physics.flu-dyn↗