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

(1)得到了准地转方程的一系列精确解，它对应于一个具有均匀背景涡度的均匀应变场中的一个具有常位涡度的椭球涡体。用Lame函数（宫崎）展开扰动来研究线性不稳定性. (2)得到了准地转方程的一系列精确解。其对应于恒定位涡的球形涡旋的倾斜体积。它围绕垂直轴稳定地旋转。角速度是纵横比的函数，并且不依赖于倾斜角。用勒让德函数展开扰动来研究线性不稳定性。一个长椭球体被证明是稳定的，如果它的倾角是小的，它的纵横比是不是大（接近1）。相反，即使扁球体的倾角非常小（几乎垂直），它也会因共振现象而不稳定（宫崎）。(3)通过考虑涡与涡之间的混沌相互作用和涡与涡的合并，建立了一个线涡耦合模型。基于该模型（宫崎）进行伪湍流模拟。(4)它表明，统计特性。例如涡流的数量和它们的间距。与直接数值模拟中获得的结果非常一致，这些数值模拟是使用频谱代码（2563）（HANAZAKI）在NEC-SX 4上进行的。

(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).