Journal of Fluid Mechanics



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


KRISTIAN B. DYSTHE a1, KARSTEN TRULSEN a2, HARALD E. KROGSTAD a3 and HERVÉ SOCQUET-JUGLARD a1p1
a1 Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
a2 SINTEF Applied Mathematics, P.O. Box 124 Blindern, N-0314 Oslo, Norway
a3 Department of Mathematical Sciences, NTNU, N-7491 Trondheim, Norway

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.

(Received April 10 2002)
(Revised August 27 2002)


Correspondence:
p1 Current address: Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway


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