Three-dimensional vortices and their instability in a geophysical flow-A quasigeostrophic vortex-turbulence model-

地球物理流中的三维涡旋及其不稳定性-准地转涡旋-湍流模型-

基本信息

批准号：
09640522
负责人：
MIYAZAKI Takeshi
金额：
$ 2.05万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

(1) A series of exact solution of the quasigeostrophic equation is obtained, which corresponds to a volume of ellipsoidal vortex of constant potential vorticity embedded in a uniform strain field with a uniform background vorticity. The linear instability is investigated by expanding disturbances in terms of Lame functions (MIYAZAKI).(2) A series of exact solution of the quasigeostrophic equation is obtained. which corresponds to a tilted volume of spheroidal vortex of constant potential vorticity. It rotates steadily about the vertical axis. The angular velocity is a function of the aspect ratio and does not depend on the inclination angle. The linear instability is investigated by expanding disturbances in terms of Legendre functions. A prolate spheroid is shown to be stable if its inclination angle is small and its aspect ratio is not large (close to unity). In contrast, an oblate spheroid is destabilized by resonance phenomena even if its inclination is very small (nearly vertical) (MIYAZAKI).(3) A wire-vortex turbulnece model is developed by incoorprating chaotic interactions between vortices and their merger. Pseudo-turbulence simulations are performed based on this model (MIYAZAKI).(4) It is shown that the statistical properties. such as the number of vortices and their spacing. are in good accordance with those obtained in the direct numerical simulations, which were performed on NEC-SX4 using the spectral code (2563) (HANAZAKI).

(1) 得到准地转方程的一系列精确解，其对应于嵌入背景涡度均匀的均匀应变场中的恒定位涡的椭球涡体积。通过用拉梅函数(MIYAZAKI)扩展扰动来研究线性不稳定性。(2)获得了准地转方程的一系列精确解。它对应于恒定位涡的球状涡旋的倾斜体积。它绕垂直轴稳定旋转。角速度是纵横比的函数，与倾斜角无关。通过根据勒让德函数扩展扰动来研究线性不稳定性。如果长椭球体的倾角较小且纵横比不大（接近于 1），则表明长椭球体是稳定的。相反，即使扁球体的倾角非常小（接近垂直），也会因共振现象而不稳定（MIYAZAKI）。（3）通过合并涡流及其合并之间的混沌相互作用开发了线涡流湍流模型。基于该模型(MIYAZAKI)进行了伪湍流模拟。(4)表明了其统计特性。例如漩涡的数量及其间距。与使用光谱代码 (2563) (HANAZAKI) 在 NEC-SX4 上执行的直接数值模拟中获得的结果非常一致。