Two-dimensional stability analysis of finite-amplitude interfacial gravity waves in a two-layer fluid
Two-dimensional stability analysis of finite-amplitude interfacial gravity waves in a two-layer fluid
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两层流体中有限振幅界面重力波的二维稳定性分析
DOI：
10.1017/jfm.2022.145
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发表时间：
2022
影响因子：
3.7
通讯作者：
Choi, Wooyoung
中科院分区：
文献类型：
--
作者：
Murashige, Sunao;Choi, Wooyoung
我们探索有限振幅界面重力波的不稳定性的基本机制，通过一个二维线性稳定性分析的周期性和无旋平面运动的界面之间的两个无界的均匀流体的密度不同，在没有背景电流。流动域共形地映射到两个半平面上，其中时变界面总是映射到真实的轴上。这种非定常保角映射技术与适当的接口表示减少了线性稳定性问题的广义特征值问题，并允许我们准确地计算不稳定扰动的增长率叠加在稳定波的参数范围很广。数值结果表明，由定常波引起的切向速度跃变引起的波致Kelvin-Helmholtz（KH）不稳定性是主要的不稳定机制。任何主波数大于临界值的扰动都呈指数增长。这个临界波数取决于稳定的波陡和密度比，可以近似由当地KH稳定性分析，其中的波生电流的空间变化被忽略。然而，它示出的增长率需要被发现的数值与照顾和连续碰撞的特征值的结果在波诱导KH不稳定性。此外，本研究还将以往关于小振幅定常波的小波数不稳定性（如调制不稳定性）的结果推广到有限振幅波。
We explore basic mechanisms for the instability of finite-amplitude interfacial gravity waves through a two-dimensional linear stability analysis of the periodic and irrotational plane motion of the interface between two unbounded homogeneous fluids of different density in the absence of background currents. The flow domains are conformally mapped into two half-planes, where the time-varying interface is always mapped onto the real axis. This unsteady conformal mapping technique with a suitable representation of the interface reduces the linear stability problem to a generalized eigenvalue problem, and allows us to accurately compute the growth rates of unstable disturbances superimposed on steady waves for a wide range of parameters. Numerical results show that the wave-induced Kelvin–Helmholtz (KH) instability due to the tangential velocity jump across the interface produced by the steady waves is the major instability mechanism. Any disturbances whose dominant wavenumbers are greater than a critical value grow exponentially. This critical wavenumber that depends on the steady wave steepness and the density ratio can be approximated by a local KH stability analysis, where the spatial variation of the wave-induced currents is neglected. It is shown, however, that the growth rates need to be found numerically with care and the successive collisions of eigenvalues result in the wave-induced KH instability. In addition, the present study extends the previous results for the small-wavenumber instability, such as modulational instability, of relatively small-amplitude steady waves to finite-amplitude ones.
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影响因子：
3.7
作者：
D. Pullin;R. Grimshaw
通讯作者：
R. Grimshaw
使用 Zakharov 方程进行界面波稳定性分析
影响因子：
3.7
作者：
A. Dixon
通讯作者：
A. Dixon
界面波的非线性动力学
DOI：
10.1016/0167-2789(84)90515-3
发表时间：
1984
期刊：
Physica D: Nonlinear Phenomena
影响因子：
--
作者：
H. Yuen
通讯作者：
H. Yuen
有限振幅界面波的稳定性。
影响因子：
3.7
作者：
R. Grimshaw;D. Pullin
通讯作者：
D. Pullin
影响因子：
2.5
作者：
G. Baker;D. Meiron;S. Orszag
通讯作者：
S. Orszag