1998 Fiscal Year Final Research Report Summary
Three-dimensional vortices and their instability in a geophysical flow-A quasigeostrophic vortex-turbulence model-
| Project/Area Number |
09640522
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Meteorology/Physical oceanography/Hydrology
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
MIYAZAKI Takeshi Univ.Electro-Communications, Dept.Mechanical & Control Engn.Prof., 電気通信学研究科, 教授 (50142097)
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| Co-Investigator(Kenkyū-buntansha) |
HANAZAKI Hideshi Tohoku Univ., Institute of Fluid Science Associated Prof., 流体科学研究所, 助教授 (60189579)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Geophysical fluid dynamics / Three-dimensional vortices / Ellipsoidal vortices / Instability / Vortex-turbulence model / Potential vorticity / Eigenvalue problem / Numerical simulations |
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| Research Abstract |
(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).
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