The occurrence of parametric instabilities in finite-amplitude internal gravity waves
The occurrence of parametric instabilities in finite-amplitude internal gravity waves
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有限振幅内重力波中参数不稳定性的发生
DOI：
10.1017/s0022112076002735
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发表时间：
1976
影响因子：
3.7
通讯作者：
R. Mied
中科院分区：
文献类型：
--
作者：
R. Mied
考虑平面内部重力波的参数不稳定性。当涡度和质量守恒的二维方程在扰动量中线性化时，就会产生具有周期系数的偏微分方程。将 Floquet 理论规定的形式的扰动代入这些方程中产生相容性条件，当进行数值评估时，给出中性稳定性和恒定扰动增长率的曲线。这些结果表明，对于即使是无限小的振幅的内波，扰动波的振幅也会开始增加。此外，这些参数不稳定性被证明可以在基态振幅极小的极限下简化为非线性共振相互作用的经典情况。任何振幅的内波都可能存在这些不稳定扰动，这一事实表明，这种现象可能是从内部重力波中提取能量的重要机制。
The parametric instability of a plane internal gravity wave is considered. When the two-dimensional equations of vorticity and mass conservation are linearized in the disturbance quantities, partial differential equations with periodic coefficients result. Substitution of a perturbation of the form dictated by Floquet theory into these equations yields compatibility conditions which, when evaluated numerically, give the curves of neutral stability and constant disturbance growth rate. These results reveal that, for an internal wave of even infinitesimal amplitude, disturbance waves can begin to grow in amplitude. Moreover, these parametric instabilities are shown to reduce to the classical case of the nonlinear resonant interaction in the limit of vanishingly small basic-state amplitude. The fact that these unstable disturbances can exist for an internal wave of any amplitude suggests that this phenomenon may be an important mechanism for extracting energy from an internal gravity wave.