Editorial Type:
Article
Article Type:
Research Article

A Numerical Study of a Nonstationary Solution of the Hasselmann Equation

Igor V. Lavrenov State Research Center of the Russian Federation, Arctic and Antarctic Research Institute, St. Petersburg, Russia

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Print Publication:
01 Mar 2003
DOI:
https://doi.org/10.1175/1520-0485(2003)033<0499:ANSOAN>2.0.CO;2
Page(s):
499–511
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Abstract

The Hasselmann kinetic equation describing nonlinear spectrum evolution of gravity surface waves is investigated for their large periods of time. To solve the problem, the most optimal numerical algorithm of the nonlinear energy transfer computation is used. The nonlinear spectrum evolution is described by various features. The numerical results reveal some general details common for all cases of the spectrum evolution. There are two main domains in the spectrum: a sharply defined peak and a slowly decreasing high-frequency tail. Using the numerical results, an intermediate self-similar frequency spectrum asymptotic approximation is proposed. It is confirmed by field observations of swell spectrum propagating at large distances. This approximation describes the main features of the nonlinear spectrum evolution and provides a preservation of the total energy and wave action.

Corresponding author address: Igor V. Lavrenov, State Research Center of the Russian Federation, Arctic and Antarctic Research Institute, Bering 38, St. Petersburg 199397, Russia. Email: lavren@aari.nw.ru

Abstract

The Hasselmann kinetic equation describing nonlinear spectrum evolution of gravity surface waves is investigated for their large periods of time. To solve the problem, the most optimal numerical algorithm of the nonlinear energy transfer computation is used. The nonlinear spectrum evolution is described by various features. The numerical results reveal some general details common for all cases of the spectrum evolution. There are two main domains in the spectrum: a sharply defined peak and a slowly decreasing high-frequency tail. Using the numerical results, an intermediate self-similar frequency spectrum asymptotic approximation is proposed. It is confirmed by field observations of swell spectrum propagating at large distances. This approximation describes the main features of the nonlinear spectrum evolution and provides a preservation of the total energy and wave action.

Corresponding author address: Igor V. Lavrenov, State Research Center of the Russian Federation, Arctic and Antarctic Research Institute, Bering 38, St. Petersburg 199397, Russia. Email: lavren@aari.nw.ru

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