Instability mechanisms of a two-dimensional progressive internal gravity wave
Instability mechanisms of a two-dimensional progressive internal gravity wave
复制标题
二维渐进内重力波的不稳定机制
DOI：
10.1017/s0022112005007524
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发表时间：
2006
影响因子：
3.7
通讯作者：
C. Staquet
中科院分区：
文献类型：
--
作者：
C. Koudella;C. Staquet
我们提出了一个详细的调查的参数亚谐共振机制，导致平面，单色，小振幅的内部重力波，也被称为主波，不稳定。共振波相互作用理论是用来推导出一个简单的运动学模型的参数强迫扰动，并直接数值模拟的Boussinesq方程在一个垂直的平面允许内部重力波场的非线性模拟。最终驱动波场打破的过程也得到了解决。我们表明，参数不稳定性可以被看作是一个优化的方案，从主波，也就是说，从一个周期性的流动与振荡剪切和密度梯度的能量。最佳的能量交换最大化扰动增长实现时，扰动有一个明确的时空结构：它的能量是锁相与初级波的涡度。这种组织允许扰动能量在局部主波切变为负时的动能形式和当主波切变为正时的势能形式之间交替，当局部主波切变为负时，然后最大化从主波提取的动能，然后最小化向该波的反向传递。扰动势能通过主波密度梯度增加，无论后者是正的，即当介质具有降低的静态稳定性时，还是负的（增加的静态稳定性）。当主波振幅较小时，运动学模型能很好地预测所有能量传递项。一个重要的结果是，从主波到扰动的势能转移率总是大于动能转移率，无论主波是什么。随着扰动的放大，翻转的等密度线首先出现在静态稳定性降低的区域，这意味着通过浮力引起的（或瑞利-泰勒）不稳定性，总场应该变得不稳定。因此，二维模型不再适用于研究随后的流动发展。
We present a detailed investigation of the parametric subharmonic resonance mechanism that leads a plane, monochromatic, small-amplitude internal gravity wave, also referred to as the primary wave, to instability. Resonant wave interaction theory is used to derive a simple kinematic model for the parametrically forced perturbation, and direct numerical simulations of the Boussinesq equations in a vertical plane permit the nonlinear simulation of the internal gravity wave field. The processes that eventually drive the wave field to breaking are also addressed. We show that parametric instability may be viewed as an optimized scenario for drawing energy from the primary wave, that is, from a periodic flow with both oscillating shear and density gradient. Optimal energy exchange maximizing perturbation growth is realized when the perturbation has a definite spatio-temporal structure: its energy is phase-locked with the vorticity of the primary wave. This organization allows the perturbation energy to alternate between kinetic form when locally the primary wave shear is negative, then maximizing kinetic energy extraction from the primary wave, and potential form when the primary wave shear is positive, then minimizing the reverse transfer to that wave. The perturbation potential energy increases through the primary wave density gradient whether the latter is positive, that is when the medium is of reduced static stability, or negative (increased static stability). When the primary wave amplitude is small, all energy transfer terms are predicted well by the kinematic model. One important result is that the rate of potential energy transfer from the primary wave to the perturbation is always larger than the rate of kinetic energy transfer, whatever the primary wave. As the perturbation amplifies, overturned isopycnals first appear in reduced static stability regions, implying that the total field should become unstable through a buoyancy induced (or Rayleigh–Taylor) instability. Hence, a two-dimensional model is no longer valid for studying the subsequent flow development.