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Evolution of a narrow-band spectrum of random surface gravity waves

Published online by Cambridge University Press:  17 March 2003

KRISTIAN B. DYSTHE ,
KARSTEN TRULSEN ,
HARALD E. KROGSTAD  and
HERVÉ SOCQUET-JUGLARD
KRISTIAN B. DYSTHE
Affiliation:
Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
KARSTEN TRULSEN
Affiliation:
SINTEF Applied Mathematics, P.O. Box 124 Blindern, N-0314 Oslo, Norway
HARALD E. KROGSTAD
Affiliation:
Department of Mathematical Sciences, NTNU, N-7491 Trondheim, Norway
HERVÉ SOCQUET-JUGLARD
Affiliation:
Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway Current address: Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway
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Abstract

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 478 , 10 March 2003 , pp. 1 - 10
Copyright
© 2003 Cambridge University Press

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