Available potential vorticity and wave-averaged quasi-geostrophic flow
Available potential vorticity and wave-averaged quasi-geostrophic flow
复制标题
可用位涡和波平均准地转流
DOI：
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发表时间：
2015
影响因子：
3.7
通讯作者：
W. Young
中科院分区：
文献类型：
--
作者：
G. Wagner;W. Young
本文导出了一个描述重力惯性内波场中强层结、快速旋转准地转（QG）流演化的波平均位涡方程。推导依赖于欧拉Boussinesq方程的多时间尺度渐进展开。我们的结果证实并扩展了Bühler & McIntyre（J. Fluid Mech.，第354卷，1998年，第354页。609-646）到浮力频率为$N（z）$的非均匀层结，因此不需要波浪和平衡流之间的空间尺度分离。我们对非均匀背景位涡的兴趣促使我们引入了一个新的量：“可用位涡”（APV）。与Ertel位涡一样，APV在流体粒子上是完全守恒的。但与Ertel位涡不同的是，线性内波在欧拉APV场中没有特征，标准QG位涡是低Rossby数下APV的简单截断。APV的定义精确地消除了与非均匀背景状态的平流相关的Ertel位涡信号，从而隔离了可用于平衡流演化的Ertel位涡部分。内波对QG流的影响简明地表示为对物质守恒的QG位涡的波平均贡献。我们应用该理论计算波诱导QG流垂直传播的波包和模式一波场，都在垂直有界域。
We derive a wave-averaged potential vorticity equation describing the evolution of strongly stratified, rapidly rotating quasi-geostrophic (QG) flow in a field of inertia-gravity internal waves. The derivation relies on a multiple-time-scale asymptotic expansion of the Eulerian Boussinesq equations. Our result confirms and extends the theory of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998, pp. 609–646) to non-uniform stratification with buoyancy frequency $N(z)$ and therefore non-uniform background potential vorticity $f_{0}N^{2}(z)$ , and does not require spatial-scale separation between waves and balanced flow. Our interest in non-uniform background potential vorticity motivates the introduction of a new quantity: ‘available potential vorticity’ (APV). Like Ertel potential vorticity, APV is exactly conserved on fluid particles. But unlike Ertel potential vorticity, linear internal waves have no signature in the Eulerian APV field, and the standard QG potential vorticity is a simple truncation of APV for low Rossby number. The definition of APV exactly eliminates the Ertel potential vorticity signal associated with advection of a non-uniform background state, thereby isolating the part of Ertel potential vorticity available for balanced-flow evolution. The effect of internal waves on QG flow is expressed concisely in a wave-averaged contribution to the materially conserved QG potential vorticity. We apply the theory by computing the wave-induced QG flow for a vertically propagating wave packet and a mode-one wave field, both in vertically bounded domains.
影响因子：
3.7
作者：
Jin-Han Xie;J. Vanneste
通讯作者：
Jin-Han Xie;J. Vanneste