Threedimensional vortices and their instability in a geophysical flowA quasigeostrophic vortexturbulence model
Project/Area Number  09640522 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Meteorology/Physical oceanography/Hydrology

Research Institution  The University of ElectroCommunications 
Principal Investigator 
MIYAZAKI Takeshi Univ.ElectroCommunications, Dept.Mechanical & Control Engn.Prof., 電気通信学研究科, 教授 (50142097)

CoInvestigator(Kenkyūbuntansha) 
HANAZAKI Hideshi Tohoku Univ., Institute of Fluid Science Associated Prof., 流体科学研究所, 助教授 (60189579)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,200,000 (Direct Cost : ¥3,200,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥2,700,000 (Direct Cost : ¥2,700,000)

Keywords  Geophysical fluid dynamics / Threedimensional vortices / Ellipsoidal vortices / Instability / Vortexturbulence model / Potential vorticity / Eigenvalue problem / Numerical simulations / 地球流体力学 / 3次元渦構造 / 楕円体渦領域 / 不安定性 / 乱流渦モデル / ポテンシャル渦度 / 固有値問題 / 数値シミュレーション / 渦合体・一本化 / 傾斜回転楕円体渦 / 乱流統計データ / 一般化固有値問題 / Lame関数 
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 wirevortex turbulnece model is developed by incoorprating chaotic interactions between vortices and their merger. Pseudoturbulence 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 NECSX4 using the spectral code (2563) (HANAZAKI).

Report
(4results)
Research Output
(18results)