Damping of inertial motions by parametric subharmonic instability in baroclinic currents
Damping of inertial motions by parametric subharmonic instability in baroclinic currents
复制标题
斜压电流中参数次谐波不稳定性对惯性运动的阻尼
DOI：
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发表时间：
2014
影响因子：
3.7
通讯作者：
John R. Taylor
中科院分区：
文献类型：
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作者：
L. Thomas;John R. Taylor
摘要本文描述了一种新的垂直剪切惯性运动的阻尼机制，它涉及一种惯性重力波，它以惯性频率的一半f$振荡，并以惯性剪切为代价增长。这种参数化的次谐波不稳定性形成于斜压地转流中，其中热风切变通过减少流体的位涡，允许频率小于f的惯性重力波。的稳定性分析和数值模拟研究的不稳定性标准，能量学，和有限振幅的不稳定行为。对于具有均匀切变和层结的气流，当地转流的Richardson数接近$Ri_{PSI}=4/3+\gamma \cos \phi $（$\gamma $为初始时刻惯性风切变和热成风切变的比值，$\phi $为初始时刻惯性风切变和热成风切变之间的夹角）时，参数亚谐不稳定发生。惯性切变进入不稳定性判据，因为它也可以修改位涡，从而修改惯性重力波的最小频率。当这个标准得到满足时，惯性重力波的频率为f/2，流动平行于等密度线，放大，通过剪切产生从惯性剪切中提取动能。数值模拟的解决方案与这些预测是一致的，另外还表明，有限振幅参数亚谐不稳定性既阻尼惯性剪切，本身是阻尼二次剪切不稳定性。通过这种方式，参数亚谐不稳定性打开了一条通向湍流的路径，惯性剪切中的动能被转移到小尺度并消散。
Abstract A new damping mechanism for vertically-sheared inertial motions is described involving an inertia–gravity wave that oscillates at half the inertial frequency, $f$ , and that grows at the expense of inertial shear. This parametric subharmonic instability forms in baroclinic, geostrophic currents where thermal wind shear, by reducing the potential vorticity of the fluid, allows inertia–gravity waves with frequencies less than $f$ . A stability analysis and numerical simulations are used to study the instability criterion, energetics, and finite-amplitude behaviour of the instability. For a flow with uniform shear and stratification, parametric subharmonic instability develops when the Richardson number of the geostrophic current nears $Ri_{PSI}=4/3+\gamma \cos \phi $ , where $\gamma $ is the ratio of the inertial to thermal wind shear magnitude and $\phi $ is the angle between the inertial and thermal wind shears at the initial time. Inertial shear enters the instability criterion because it can also modify the potential vorticity and hence the minimum frequency of inertia–gravity waves. When this criterion is met, inertia–gravity waves with a frequency $f/2$ and with flow parallel to isopycnals amplify, extracting kinetic energy from the inertial shear through shear production. The solutions of the numerical simulations are consistent with these predictions and additionally show that finite-amplitude parametric subharmonic instability both damps inertial shear and is itself damped by secondary shear instabilities. In this way, parametric subharmonic instability opens a pathway to turbulence where kinetic energy in inertial shear is transferred to small scales and dissipated.