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On the nonlinear stability and the existence of selective decay states of 3D quasi-geostrophic potential vorticity equation

机译:基于3D拟地球滴势涡度方程的非线性稳定性与选择性衰减状态的存在

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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.
机译:在本文中,我们研究了大气和海洋的大规模运动的动态,通过具有恒定分层的3D准滴性潜在涡流(QGPV)方程来治理。 结果表明,对于kolmogorov强迫第一能量壳,存在一系列精确的解决方案,这些溶液是耗散的rossby波。 基于对迫使生长速率的假设来分析这些精确溶液的非线性稳定性。 在没有强迫的情况下,我们展示了3D QGPV方程的选择性衰变状态的存在。 选择性衰变状态是3D罗斯比波以恒定速度水平行驶。 所有这些结果都可以被认为是2D QGPV系统的扩展以及具有各向同性粘度的3D QGPV系统的情况。 最后,我们为模型提供了一种几何基础,作为非纤维纤维可逆 - 不可逆耦合的一般方程。

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