Stability of finite-amplitude interfacial waves. Part 3. The effect of basic current shear for one-dimensional instabilities
Stability of finite-amplitude interfacial waves. Part 3. The effect of basic current shear for one-dimensional instabilities
复制标题
有限振幅界面波的稳定性。
DOI：
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发表时间：
1986
影响因子：
3.7
通讯作者：
R. Grimshaw
中科院分区：
文献类型：
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作者：
D. Pullin;R. Grimshaw
我们考虑了两层无粘流体中界面行波的线性化稳定性，当两种流体中的一种或两种都有基本的电流切变时。对于这种构型，Pullin和Grimshaw（1983 b）计算了基波。这里我们的结果主要限于二维空间不稳定性（即一维的传播空间），并获得解析和数值。分析结果是针对小振幅波的长波长调制不稳定性。数值结果仅限于下层流体无限深的情况，并采用Boussinesq近似。它们是通过求解截断傅立叶级数的线性化稳定性问题，并求解由此产生的增长率特征值问题而得到的。对于小值的基本电流剪切，并为小或中等的基本波振幅，不稳定性是由一组低阶共振;对于较大的基本波振幅，这些主要是由一个本地波引起的开尔文-亥姆霍兹不稳定性的发病。对于较大的基本电流剪切值，由于出现了许多新效应，这种解释被修改。
We consider the linearized stability of interfacial progressive waves in a two-layer inviscid fluid, for the case when there is a basic current shear in either, or both, of the fluids. For this configuration the basic wave has been calculated by Pullin & Grimshaw (1983b). Our results here are mainly restricted to two-space-dimensional instabilities (i.e. one-dimensional in the propagation space), and are obtained both analytically and numerically. The analytical results are for the long-wavelength modulational instability of small-amplitude waves. The numerical results are restricted to the case when the lower fluid is infinitely deep, and for the Boussinesq approximation. They are obtained by solving the linearized stability problem with truncated Fourier series, and solving the resulting eigenvalue problem for the growth rate. For small values of the basic current shear, and for small or moderate basic wave amplitude, the instabilities are determined by a set of low-order resonances; for larger basic wave amplitude, these are dominated by the onset of a local wave-induced Kelvin–Helmholtz instability. For larger values of the basic current shear, this interpretation is modified owing to the appearance of a number of new effects.