Stability analysis of deep-water waves on a linear shear current using unsteady conformal mapping
Stability analysis of deep-water waves on a linear shear current using unsteady conformal mapping
复制标题
使用非定常共形映射对线性剪切流深水波进行稳定性分析
DOI：
10.1017/jfm.2019.1021
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发表时间：
2020
影响因子：
3.7
通讯作者：
W. Choi
中科院分区：
文献类型：
--
作者：
S. Murashige;W. Choi
本文描述了具有对称非悬垂剖面的周期性深水波在线性剪切流（即具有恒定涡度的垂直剪切流）上传播的二维定常运动的线性稳定性分析。为了高精度地数值研究大振幅波浪的稳定性，我们采用了保角映射的方法，将时变水面映射到复平面的真实的轴上。这种提法使我们能够应用数值方法开发的大振幅无旋波没有剪切流直接到目前的问题，并减少了线性稳定性问题的广义特征值问题。数值解描述了超和次谐波不稳定性的周期波的波振幅范围很广，并澄清了主导特征值的行为如何改变与剪切流的强度。特别是，它示出，即使在线性剪切流的存在下，稳定的周期波失去稳定性，由于超谐波扰动在波的振幅，波能量达到极值，类似于无旋波的情况下，没有剪切流。研究还发现，随着波幅的增加，弱剪切流的亚谐不稳定性表现为再稳定，而强剪切流的再稳定性消失。
This paper describes linear stability analysis of the two-dimensional steady motion of periodic deep-water waves with symmetric non-overhanging profiles propagating on a linear shear current, namely a vertically sheared current with constant vorticity. In order to investigate numerically with high accuracy the stability of large-amplitude waves, we adopt a formulation using conformal mapping, in which the time-varying water surface is always mapped onto the real axis of a complex plane. This formulation allows us to apply numerical methods developed for large-amplitude irrotational waves without a shear current directly to the present problem, and reduces the linear stability problem to a generalized eigenvalue problem. Numerical solutions describe both super- and sub-harmonic instabilities of the periodic waves for a wide range of wave amplitudes and clarify how the behaviours of dominant eigenvalues change with the strength of the shear current. In particular, it is shown that, even in the presence of a linear shear current, the steady periodic waves lose stability due to superharmonic disturbances at the wave amplitude where the wave energy attains an extremum, similarly to the case of irrotational waves without a shear current. It is also found that re-stabilization with an increase in wave amplitude characterizes subharmonic instability for weak shear currents, but the re-stabilization disappears for strong shear currents.
具有恒定涡度的斯托克斯波：一、数值计算
影响因子：
2.7
作者：
Dyachenko, Sergey A.;Hur, Vera Mikyoung
通讯作者：
Hur, Vera Mikyoung