E-221 準地衡風多重回転楕円体渦の不安定性

概要

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A family of exact solutions of the quasigeostrophic equation (in uniformly stratified fluid on f-plane) is presented. They are the generalizations of the Meacham-Miyazaki spheroidal vortex to N-confocal tilted prolate spheroids. They rotate steadily in an otherwise quiescent fluid of infinite extent. The angular velocity of rigid rotation is independent of the inclination angle of the axis of symmetry from the vertical axis. The linear instability of double spheroids is investigated by expanding the disturbances in terms of the associated Legendre functions. Three types of instabilities are found. The first instability seems to be linked with the instability of a highly tilted single slender spheroidal vortex. The second instability, which is observed even for vertically standing spheroids, is caused by resonance between two vortex waves traveling along the inner and outer spheroids. The third instability is the Rayleigh-type instability that occurs for concentric vortex patches with non-monotonic radial vorticity distribution.
日本流体力学会の論文
2003-07-28