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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)得到了准地转方程的一系列精确解，对应于在具有均匀背景涡量的均匀应变场中嵌入一定体积的等位涡量椭球体涡。用Lame函数（MIYAZAKI）展开扰动研究了线性不稳定性。(2)得到了拟等转方程的一系列精确解。这相当于一个倾斜体积的等位涡球体。它沿垂直轴稳定地旋转。角速度是纵横比的函数，与倾角无关。用勒让德函数展开扰动研究了线性不稳定性。长形球体在倾角较小且长径比不大（接近于一）的情况下是稳定的。相比之下，一个扁圆球体即使其倾角很小（接近垂直）也会被共振现象破坏（MIYAZAKI）。(3)将涡旋之间的混沌相互作用及其合并考虑在内，建立了线涡湍流模型。基于该模型进行了伪湍流模拟（MIYAZAKI）。(4)结果表明：比如漩涡的数量和它们的间距。与利用谱码（2563）（HANAZAKI）在NEC-SX4上进行的直接数值模拟结果吻合较好。