ABSTRACT

Results of the direct numerical simulation of directional sea surface waves are discussed. We calculate statistical moments for the water displacement, which are determined by the free wave component and by bound harmonics directly from the simulated data using an appropriate spectral filtering. In the situation of a relatively narrow directional spread of intense waves the free wave kurtosis may possess the value comparable with the bound wave kurtosis, exhibiting abnormally extreme sea states. In such situations the evidence of emergence of coherent wave groups in the 3D fields is found in the Fourier domain, which results in a stronger smearing of the apparent dispersion relation. Soliton-type patterns may be revealed in the stochastic wave fields using the Windowed Inverse Scattering Transform; they exhibit specific statistical characteristics.

INTRODUCTION

The direct numerical simulation of primitive hydrodynamic equations is becoming now an available alternative to solving kinetic equations for wind waves in the Ocean. In contrast to the kinetic theory, the dynamic equations do not use the assumption of independent random wave phases and of a slow evolution, thus are capable of simulating rapidly developing processes. Hence the direct numerical simulation is a promising tool for exploring new problems, such as so-called rogue or freak waves, which suddenly appear on the sea surface with seemingly no precursors (Kharif et al., 2009).

A comparison of the simulations of irregular surface waves within the frameworks of the kinetic equations, the Zakharov dynamic spectral equations, and the Euler equations was carried out by Annenkov and Shrira (2018). All the models took into account up to four-wave nonlinear wave interactions. The comparison revealed a noticeable differences in the evolution of the fourth statistical moment of the surface displacement, kurtosis. This parameter determines the proportion between extreme and moderate surface displacements, and may be used to characterize the extremality of wave systems.

Zakharov's Hamiltonian formalism distinguishes resonant and non-resonant nonlinear wave interactions. Non-resonant modes (in other words, phase-locked or bound waves) do not participate in the evolution of "true" waves (normal modes, free waves). In the Zakharov theory, bound waves are calculated from the instantaneous values of the canonical variables. At the same time, the difference between free and bound waves is probably not always obvious, at least in situations of strongly nonlinear strongly modulated waves (Slunyaev, 2018); then important physical effects may occur, which are beyond the standard Zakharov equations.

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