Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves
Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves
复制标题
有限振幅界面波的稳定性。
DOI：
10.1017/s0022112085003494
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发表时间：
1985
影响因子：
3.7
通讯作者：
D. Pullin
中科院分区：
文献类型：
--
作者：
R. Grimshaw;D. Pullin
在之前的两篇论文（Pullin & Grimshaw 1983a，b）中，我们研究了两层流体中有限振幅界面行进波的波廓线和其他特性。在本文和下一篇论文（Pullin & Grimshaw 1985）中，我们讨论了这些波对小扰动的稳定性。在本文中，我们获得了小振幅波的长波长调制不稳定性的分析结果。使用多尺度展开，我们获得了与波诱导平均流方程耦合的非线性薛定谔方程来描述缓慢调制的波。从这些耦合方程我们可以确定平面行波的稳定性。我们的结果通过确定 (p, q) 平面中的不稳定带来表示，其中 (p, q) 是调制波数，并且是针对基本密度比和未扰动层深度的一系列值获得的。
In two previous papers (Pullin & Grimshaw 1983a, b) we studied the wave profile and other properties of finite-amplitude interfacial progressive waves in a two-layer fluid. In this and the following paper (Pullin & Grimshaw 1985) we discuss the stability of these waves to small perturbations. In this paper we obtain anatytical results for the long-wavelength modulational instability of small-amplitude waves. Using a multiscale expansion, we obtain a nonlinear Schrödinger equation coupled to a wave-induced mean-flow equation to describe slowly modulated waves. From these coupled equations we determine the stability of a plane progressive wave. Our results are expressed by determining the instability bands in the (p, q)-plane, where (p, q) is the modulation wavenumber, and are obtained for a range of values of basic density ratio and undisturbed layer depths.