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

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(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).