Kats–Kontorovich anisotropic solution in simulations of ocean swell

Abstract

The physical setup of ocean swell is used as a testbed for the results of the weak turbulence theory. The numerical study with the novel Geogjaev-Zakharov approach highlights the importance of isotropic direct and inverse cascade solutions, along with the self-similarity concept of wave spectra, as developed by Vladimir Zakharov and his collaborators. The approximate anisotropic solution proposed by Kats and Kontorovich in 1970-ies is shown to fit wave spectra well at frequencies exceeding three times the spectral peak frequency. This solution can be interpreted as an attractor for a wide variety of initial distributions of a random wave field. In this context, it is a counterpart to the classic isotropic Kolmogorov-Zakharov solutions. The corresponding Kolmogorov constant of the wave momentum transfer is derived analytically. The study also discusses the implications of these results for sea wave modeling.