A stability analysis for interfacial waves using a Zakharov equation
A stability analysis for interfacial waves using a Zakharov equation
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使用 Zakharov 方程进行界面波稳定性分析
DOI：
10.1017/s0022112090000106
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发表时间：
1990
影响因子：
3.7
通讯作者：
A. Dixon
中科院分区：
文献类型：
--
作者：
A. Dixon
推导了波的弱相互作用振幅方程，用于描述具有刚性上下边界的不同密度流体界面上扰动的时间演化。该方程与水波的Zakharov方程类似，用于研究周期波的稳定性。我们发现，对于小的波陡，不稳定性是由于共振四重奏的扰动波数的数量级，或小于，主波。对于大的扰动波数和中等高的波陡，发现了第二种不稳定性。这仅限于Boussinesq参数很小的情况。结果表明，这是一种开尔文-亥姆霍兹不稳定性，是由波引起的流体速度在界面上的跳跃引起的。
An amplitude equation for weak interactions of waves is derived to describe the time evolution of disturbances on an interface between fluids of differing densities, with rigid upper and lower boundaries. This equation is analogous to the Zakharov equation for water waves and is used to investigate the stability of a periodic wave. It is found that, for small wave steepnesses, the instabilities are due to resonant quartets with perturbation wavenumbers of the order of, or less than, that of the main wave. A second instability is found for large perturbation wavenumbers and moderately high wave steepnesses. This is restricted to the case when the Boussinesq parameter is small. It is shown that this is a Kelvin–Helmholtz instability caused by a wave-induced jump in the fluid velocity across the interface.