Numerical Validation of Quasigeostrophic Ellipsoidal Vortex Model
Numerical Validation of Quasigeostrophic Ellipsoidal Vortex Model
复制标题
准地转椭球涡模型的数值验证
DOI：
10.1143/jpsj.71.2687
复制
发表时间：
2002
影响因子：
1.7
通讯作者：
Shinsuke Fujishima
中科院分区：
文献类型：
--
作者：
T. Miyazaki;Akinori Asai;Masahiro Yamamoto;Shinsuke Fujishima
在地球物理流动中，相干涡旋结构持续时间较长，它们的相互作用主导着地球物理湍流的动力学。Meacham等人。得到了均匀三维剪切场中嵌入均匀椭球涡团的准地转方程的一系列精确非定常解。宫崎骏等人。推导了一个描述N个椭球涡间相互作用的哈密顿动力学系统，其中每个相干涡用一个均匀位涡的椭球来描述。本文基于等高线平流半拉格朗日算法(CASL)进行了直接数值模拟，以评估哈密顿模式的有效性。首先，研究了倾斜椭球的不稳定性。当长宽比小于0.44，倾角大于0.48时，长椭球对勒让德第三模不稳定。弱不稳定的扁平椭球旋涡从顶部和底部发出细丝，而应力涡流则从顶部和底部射出细丝。
In geophysical flows, coherent vortex structures persist for long time and their interactions dominate the dynamics of geophysical turbulence. Meacham et al. obtained a series of exact unsteady solution of the quasigeostrophic equation, which represents a uniform ellipsoidal vortex patch embedded in a uniform 3D shear field. Miyazaki et al. derived a Hamiltonian dynamical system describing the interactions of N ellipsoidal vortices, where each coherent vortex was modeled by an ellipsoid of uniform potential vorticity. In this paper, direct numerical simulations based on a Contour Advective Semi-Lagrangian algorithm (CASL) are performed in order to assess the validity of the Hamiltonian model. First, the instability of a tilted spheroid is investigated. A prolate spheroid becomes unstable against the third Legendre mode when the aspect ratio is less than 0.44 and the inclination angle is larger than 0.48. Weakly unstable flatter spheroidal vortices emit thin filaments from their top and bottom, whereas str...