Hamiltonian moment reduction for describing vortices in shear
Hamiltonian moment reduction for describing vortices in shear
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用于描述剪切涡流的哈密顿矩减少
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
G. Flierl
中科院分区：
文献类型：
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作者：
S. Meacham;P. Morrison;G. Flierl
本文讨论了一种近似二维和准等转的三维流体流动的一般方法。该方法以理想流体的非正则哈密顿结构为基础，采用涡度的特殊泛函作为动力变量。它允许从描述涡旋动力学的偏微分方程中提取精确或近似的有限自由度哈密顿系统。我们给出了选择函数作为涡度空间矩的例子。该方法给出了称为卡西米尔不变量的运动常数，并基于李代数理论为简化有限系统的全局相空间结构提供了一种分类方案。以木田涡旋为例说明了该方法的应用。木田，J.物理学。Soc。[Jpn. 50, 3517(1981)]和嵌入在背景流中的均匀涡度椭球的准地转演化问题。
This paper discusses a general method for approximating two-dimensional and quasigeostrophic three-dimensional fluid flows that are dominated by coherent lumps of vorticity. The method is based upon the noncanonical Hamiltonian structure of the ideal fluid and uses special functionals of the vorticity as dynamical variables. It permits the extraction of exact or approximate finite degree-of-freedom Hamiltonian systems from the partial differential equations that describe vortex dynamics. We give examples in which the functionals are chosen to be spatial moments of the vorticity. The method gives rise to constants of motion known as Casimir invariants and provides a classification scheme for the global phase space structure of the reduced finite systems, based upon Lie algebra theory. The method is illustrated by application to the Kida vortex [S. Kida, J. Phys. Soc. Jpn. 50, 3517 (1981)] and to the problem of the quasigeostrophic evolution of an ellipsoid of uniform vorticity, embedded in a background flo...