Stability of finite-amplitude interfacial waves. Part 2. Numerical results
Stability of finite-amplitude interfacial waves. Part 2. Numerical results
复制标题
有限振幅界面波的稳定性。
DOI：
10.1017/s0022112085003500
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发表时间：
1985
影响因子：
3.7
通讯作者：
R. Grimshaw
中科院分区：
文献类型：
--
作者：
D. Pullin;R. Grimshaw
在前一篇论文（Grimshaw & Pullin 1985）中，我们讨论了两层流体中界面前进波的长波调制不稳定性。在本文中，我们补充我们的分析结果的数值结果的线性化稳定性的有限振幅波。我们限制注意的情况下，下层是无限深，并使用Boussinesq近似。在这种情况下，Pullin和Grimshaw（1983 a，B）计算了基本的波浪剖面。线性化的稳定性问题的扰动的基本波的数值求解通过寻求解决方案的截断傅立叶级数的形式，并解决由此产生的本征值问题的增长率作为扰动波数的函数。对于较小或中等的基本波振幅，我们表明不稳定性是由一组低阶共振决定的。最低的共振，其中包含调制不稳定性，被认为是占主导地位的所有情况下考虑。对于更高的波幅，共振不稳定性淹没了当地波诱导的开尔文-亥姆霍兹不稳定性。
In the preceding paper (Grimshaw & Pullin 1985) we discussed the long-wavelength modulational instability of interfacial progressive waves in a two-layer fluid. In this paper we complement our analytical results by numerical results for the linearized stability of finite-amplitude waves. We restrict attention to the case when the lower layer is infinitely deep, and use the Boussinesq approximation. For this case the basic wave profile has been calculated by Pullin & Grimshaw (1983a, b). The linearized stability problem for perturbations to the basic wave is solved numerically by seeking solutions in the form of truncated Fourier series, and solving the resulting eigenvalue problem for the growth rate as a function of the perturbation wavenumber. For small or moderate basic wave amplitudes we show that the instabilities are determined by a set of low-order resonances. The lowest resonance, which contains the modulational instability, is found to be dominant for all cases considered. For higher wave amplitudes, the resonance instabilities are swamped by a local wave-induced Kelvin–Helmholtz instability.