Barotropic instability of shear flows
Barotropic instability of shear flows
复制标题
剪切流的正压不稳定性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Hao Zhu
中科院分区：
文献类型：
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作者：
Zhiwu Lin;Jincheng Yang;Hao Zhu
我们考虑具有科里奥利效应的不可压缩流体的剪切流的正压不稳定性。对于一类剪切流，我们发展了一种新的方法来寻找尖锐的稳定性条件。我们详细地研究了具有正弦分布的流动，得到了整个参数空间内的尖锐稳定边界，修正了流体文献中的前人结果。我们的新结果被更精确的数值计算所证实。科里奥利力的加入使剪切流动的稳定性发生了根本性的变化。此外，我们还研究了切变流附近的动力学行为，包括非平凡行波解的分叉和线性无粘阻尼项。我们证明的第一个要素是对中性模式的仔细分类。第二种方法是将线性化的流体方程写成哈密顿形式，然后将不稳定指数理论用于一般的哈密顿偏微分方程组。最后利用Sturm-Liouville理论和超几何函数研究了奇异中立模和非共振中立模。
We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details and obtain the sharp stability boundary in the whole parameter space, which corrects previous results in the fluid literature. Our new results are confirmed by more accurate numerical computation. The addition of the Coriolis force is found to bring fundamental changes to the stability of shear flows. Moreover, we study dynamical behaviors near the shear flows, including the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping. The first ingredient of our proof is a careful classification of the neutral modes. The second one is to write the linearized fluid equation in a Hamiltonian form and then use an instability index theory for general Hamiltonian partial differential equations. The last one is to study the singular and nonresonant neutral modes using Sturm‐Liouville theory and hypergeometric functions.