Three-dimensional small-scale instabilities of plane internal gravity waves
Three-dimensional small-scale instabilities of plane internal gravity waves
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平面内重力波三维小尺度不稳定性
DOI：
10.1017/jfm.2018.921
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发表时间：
2019
影响因子：
3.7
通讯作者：
M. Mathur
中科院分区：
文献类型：
--
作者：
S. J. Ghaemsaidi;M. Mathur
用局部稳定性方法研究了三维、小尺度、小幅度扰动在平面重力内波上的演化。平面内波的特征是它的无量纲振幅$A$，以及群速度矢量与重力的夹角$\Unicode[stix]{x1D6F7}$。对于给定的$(A，\Unicode[STIX]{x1D6F7})$，在周期流体粒子轨迹上求解局部稳定性方程，以获得所有二维和三维扰动波矢的增长率。对于较小的$A$，局部稳定性方法恢复了以前二维参数亚谐不稳定(PSI)的结果，同时提供了对三维参数亚谐不稳定的新见解。高阶三元共振及其相关的偏差也在很小的$A$处被观测到。此外，对于较小的$A$，由参数共振引起的纯横向不稳定在$\Unicode[stix]{x1D6F7}$的选择值处发生。对于有限$A的横向扰动，存在非共振不稳定机制的可能性允许我们推导出一个启发式的、修正的引力不稳定性判据。然后，我们研究了小$A$到有限$A$内波不稳定性的扩展，其中我们恢复并建立了已有的小尺度、小幅度内波不稳定性的知识。基于主要失稳模式，确定了$(A，\Unicode[STIX]{x1D6F7})$平面的四个不同区域：二维PSI、三维倾斜、准二维剪切排列和三维横向。我们的研究表明，局域稳定性方法是一种物理上有洞察力和计算效率高的工具，对于基于其他理论方法的研究和各种情况下内波小尺度不稳定性的数值模拟具有潜在的广泛实用价值。
We study the evolution of three-dimensional (3-D), small-scale, small-amplitude perturbations on a plane internal gravity wave using the local stability approach. The plane internal wave is characterised by its non-dimensional amplitude, $A$ , and the angle the group velocity vector makes with gravity, $\unicode[STIX]{x1D6F7}$ . For a given $(A,\unicode[STIX]{x1D6F7})$ , the local stability equations are solved on the periodic fluid particle trajectories to obtain growth rates for all two-dimensional (2-D) and 3-D perturbation wave vectors. For small $A$ , the local stability approach recovers previous results of 2-D parametric subharmonic instability (PSI) while offering new insights into 3-D PSI. Higher-order triadic resonances, and associated deviations from them, are also observed at small $A$ . Moreover, for small $A$ , purely transverse instabilities resulting from parametric resonance are shown to occur at select values of $\unicode[STIX]{x1D6F7}$ . The possibility of a non-resonant instability mechanism for transverse perturbations at finite $A$ allows us to derive a heuristic, modified gravitational instability criterion. We then study the extension of small $A$ to finite $A$ internal wave instabilities, where we recover and build upon existing knowledge of small-scale, small-amplitude internal wave instabilities. Four distinct regions of the $(A,\unicode[STIX]{x1D6F7})$ -plane based on the dominant instability modes are identified: 2-D PSI, 3-D oblique, quasi-2-D shear-aligned, and 3-D transverse. Our study demonstrates the local stability approach as a physically insightful and computationally efficient tool, with potentially broad utility for studies that are based on other theoretical approaches and numerical simulations of small-scale instabilities of internal waves in various settings.