Stability of bichromatic gravity waves on deep water

被引：12
|
作者：
Leblanc, Stephane [1 ]
机构：
[1] Univ Toulon & Var, CNRS, LSEET, F-83957 La Garde, France
来源：
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS | 2009年 / 28卷 / 05期
关键词：
Gravity waves; Modulational instability; Nonlinear interactions; LINEAR ENERGY TRANSFER; RESONANT INTERACTIONS; FINITE-AMPLITUDE; INSTABILITIES; SPECTRUM; TRAINS; EVOLUTION; DYNAMICS;
D O I：
10.1016/j.euromechflu.2009.05.001
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The stability of bichromatic gravity waves with small but finite amplitudes propagating in two directions on deep water is considered. Starting from the Zakharov equation, elementary quartet interactions are isolated and stability criteria are formulated. Results are illustrated for various combinations of bichromatic wave trains, from long-crested to standing waves. Two generic mechanisms operate: the first one is a modulational instability of one of the two components of the bichromatic wave train; the second mechanism is a modulation which couples both components of the wave train. However a third mechanism eventually comes into play: the resonant interaction of Phillips and Longuet-Higgins which leads initially to the linear growth of a third wave. When this latter is active, in particular for wave trains with wave vectors close together, it is shown by numerical integration that the long-time recurrence is destroyed. (C) 2009 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：605 / 612
页数：8
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