On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation
On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation
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DOI：
10.1002/mma.5962
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发表时间：
2019-11
影响因子：
2.9
通讯作者：
O. Esen;Daozhi Han;Taylan Şengül;Quan Wang
中科院分区：
文献类型：
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作者：
O. Esen;Daozhi Han;Taylan Şengül;Quan Wang
在本文中，我们研究了由恒定分层的 3D 准地转位涡 (QGPV) 方程控制的大气和海洋中大尺度运动的动力学。结果表明，对于第一个能量壳上的柯尔莫哥洛夫强迫，存在一系列耗散罗斯贝波的精确解。基于强迫增长率的假设，分析了这些精确解的非线性稳定性。在没有强迫的情况下，我们证明了 3D QGPV 方程存在选择性衰变态。选择性衰变态是以恒定速度水平传播的 3D Rossby 波。所有这些结果都可以看作是2D QGPV 系统和具有各向同性粘度的3D QGPV 系统情况下的扩展。最后，我们提出了该模型的几何基础，作为非平衡可逆-不可逆耦合的一般方程。
In this article, we study the dynamics of large‐scale motion in atmosphere and ocean governed by the 3D quasi‐geostrophic potential vorticity (QGPV) equation with a constant stratification. It is shown that for a Kolmogorov forcing on the first energy shell, there exist a family of exact solutions that are dissipative Rossby waves. The nonlinear stability of these exact solutions are analyzed based on the assumptions on the growth rate of the forcing. In the absence of forcing, we show the existence of selective decay states for the 3D QGPV equation. The selective decay states are the 3D Rossby waves traveling horizontally at a constant speed. All these results can be regarded as the expansion of that of the 2D QGPV system and in the case of 3D QGPV system with isotropic viscosity. Finally, we present a geometric foundation for the model as a general equation for nonequilibrium reversible‐irreversible coupling.