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）获得了一系列的准真诚方程的精确溶液，该溶液对应于嵌入具有均匀背景涡流的均匀应变场中的恒定电势涡度的椭圆形涡流。通过在la脚功能（Miyazaki）方面扩大干扰来研究线性不稳定性。（2）获得了一系列准真实性方程的精确解。对应于恒定电势涡度的倾斜体积的球体涡流。它在垂直轴上稳步旋转。角速度是纵横比的函数，不取决于倾斜角。线性不稳定性通过扩大legendre函数方面的干扰来研究。如果其倾斜角度很小，并且其长宽比不大（接近统一），则显示出一个pr酸的球体是稳定的。相比之下，即使其倾斜度很小（几乎垂直）（Miyazaki）（3）涡轮涡流涡轮模型是通过不形成涡流之间的混乱相互作用而开发的。伪扰动模拟是根据该模型（Miyazaki）进行的。（4）显示统计特性。例如涡流的数量及其间距。与在直接数值模拟中获得的那些相符，该模拟是使用光谱代码（2563）（Hanazaki）在NEC-SX4上进行的。