A Procedure to Find a Discrete Counterpart of a Quasi-Invariant for Two-Dimensional Beta-Plane Turbulence
A Procedure to Find a Discrete Counterpart of a Quasi-Invariant for Two-Dimensional Beta-Plane Turbulence
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寻找二维 Beta 平面湍流准不变量的离散对应部分的过程
DOI：
10.11345/nctam.62.13
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Izumi Saito and Keiichi Ishioka
中科院分区：
文献类型：
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作者：
松原立真;小嶋美紀子;田原美智留;Syed Bilal Ahmad Andrabi;福士路花;川原史也;山野安規徳;榊原均;永宗喜三郎;松原立真;Izumi Saito and Keiichi Ishioka
分带性是β平面上二维准地转方程的准不变量，由Balk于1991年发现。分带性有助于解释有利于分带拉长结构的各向异性能量级联，即莱茵效应。在目前的研究中，我们提出了一种一般的方法来数值计算对应于有限物理域的离散波数系统的拟不变量，并推导出了分带性的离散对应物，我们称之为第三类拟不变量。我们还进行了数值实验来比较第三类准不变量和分带不变量的守恒性质。此外，我们证明了第三个准不变量与Lee和Smith在2007年引入的近共振三联相互作用的概念密切相关。
Zonostrophy, which was discovered by Balk in 1991, is a quasi-invariant for the two-dimensional quasi-geostrophic equation on a beta-plane. Zonostrophy is useful for explaining the anisotropic energy cascade that favors zonally elongated structures, that is, the Rhines effect. In the present study, we propose a general procedure to numerically obtain a quasi-invariant for discrete wavenumber systems, which correspond to finite physical domains, and derive a discrete counterpart of zonostrophy, which we refer to as the third quasi-invariant. We also conduct numerical experiments to compare the conservation properties of the third quasi-invariant and the zonostrophy. In addition, we show that the third quasi-invariant is closely related to the concept of near-resonant triad interactions, which was introduced by Lee and Smith in 2007.