Anisotropy of ocean surface wave turbulence

TL;DR

This paper investigates the anisotropy in ocean surface wave turbulence by deriving a quasi 1-D approximation of Hasselmann's kinetic equation and comparing theoretical spectra with observed P-M and JONSWAP spectra.

Contribution

It introduces a new derivation of the quasi 1-D Hasselmann equation and compares resulting spectra with experimental data, highlighting features of JONSWAP spectra.

Findings

Simple solutions align with P-M spectrum

Self-similar solutions exhibit features of JONSWAP spectra

Theoretical spectra match experimental observations

Abstract

The paper continues to study the long-standing problem of quasi 1-D (one dimensional) spectrum of sea surface wave turbulence. The study is based on Hasselmann's kinetic equation, which significantly simplifies for the quasi 1-D turbulence. The goal of the paper is to compare the theoretical predictions with experimental observations. The paper starts with new derivation of the quasi 1-D approximation of Hasselmann's equation. The present work does not support the imposition of boundary conditions. Instead, the family of theoretical spectra is compared with P-M (Pierson-Moskowitz) and JONSWAP (Joint North Sea Wave Project) spectra. First, a simple solution (first approximation) of the quasi 1-D equation is obtained and compared with the P-M spectrum. Then self-similar solutions are considered; they are shown to satisfy the second order ordinary differential equation. The solutions of this equation have many features of the JONSWAP spectra.