New numerical methods for calculating statistical equilibria of two-dimensional turbulent flows, strictly based on the Miller-Robert-Sommeria theory
New numerical methods for calculating statistical equilibria of two-dimensional turbulent flows, strictly based on the Miller-Robert-Sommeria theory
复制标题
严格基于 Miller-Robert-Sommeria 理论计算二维湍流统计平衡的新数值方法
DOI：
10.1088/1873-7005/ac9713
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发表时间：
2022
影响因子：
1.5
通讯作者：
Ishioka K
中科院分区：
文献类型：
--
作者：
Ryono K;Ishioka K
提出了新的数值方法的混合熵最大化问题的背景下，Miller-Robert-Sommeria（MRS）的统计力学理论的二维湍流，特别是在球面几何的情况下。其中两种方法是典型的问题，另一种是微典型的问题。该方法基于原始MRS理论，因此考虑到所有Casimir不变量。与以往研究中提出的方法相比，我们的新方法更容易检测多个统计平衡点，并寻找解与破缺带状对称。这些方法被应用到一个纬向对称的正压不稳定的初始涡度分布。得到两个统计平衡，其中一个具有带状波数为1的波状结构，另一个具有带状波数为2的波状结构。前者是混合熵的最大值点，而后者的波数2结构与涡度方程时间积分的终态结构几乎相同。新的方法允许有效的计算初始涡度分布的统计平衡组成的许多层次的涡度补丁，而不会丢失所有的保守量的信息。这意味着统计平衡可以从任意初始涡度分布中获得，这允许应用统计力学来解释地球物理流体中出现的各种各样的流动模式。
New numerical methods are proposed for the mixing entropy maximization problem in the context of Miller–Robert–Sommeria's (MRS) statistical mechanics theory of two-dimensional turbulence, particularly in the case of spherical geometry. Two of the methods are for the canonical problem; the other is for the microcanonical problem. The methods are based on the original MRS theory and thus take into account all Casimir invariants. Compared to the methods proposed in previous studies, our new methods make it easier to detect multiple statistical equilibria and to search for solutions with broken zonal symmetry. The methods are applied to a zonally symmetric initial vorticity distribution which is barotropically unstable. Two statistical equilibria are obtained, one of which has a wave-like structure with zonal wavenumber 1, and the other has a wave-like structure with zonal wavenumber 2. While the former is the maximum point of the mixing entropy, the wavenumber 2 structure of the latter is nearly the same as the structure that appears in the end state of the time integration of the vorticity equation. The new methods allow for efficient computation of statistical equilibria for initial vorticity distributions consisting of many levels of vorticity patches without losing information about all the conserved quantities. This means that the statistical equilibria can be obtained from an arbitrary initial vorticity distribution, which allows for the application of statistical mechanics to interpret a wide variety of flow patterns appearing in geophysical fluids.