Poincaré oscillations and geostrophic adjustment in a rotating paraboloid
Free liquid oscillations (Poincaré oscillations) in a rotating paraboloid are investigated theoretically and experimentally. Within the framework of shallow-water theory, with account for the centrifugal force, expressions for the free oscillation frequencies are obtained and corrections to the freq...
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| Veröffentlicht in: | Fluid dynamics 2009-10, Vol.44 (5), p.759-770 |
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| container_title | Fluid dynamics |
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| creator | Kalashnik, M. V. Kakhiani, V. O. Patarashvili, K. I. Tsakadze, S. J. |
| description | Free liquid oscillations (Poincaré oscillations) in a rotating paraboloid are investigated theoretically and experimentally. Within the framework of shallow-water theory, with account for the centrifugal force, expressions for the free oscillation frequencies are obtained and corrections to the frequencies related with the finiteness of the liquid depth are found. It is shown that in the rotating liquid, apart from the wave modes of free oscillations, a stationary vortex mode is also generated, that is, a process of geostrophic adjustment takes place. Solutions of the shallow-water equations which describe the wave dynamics of the adjustment process are presented. In the experiments performed the wave and vortex modes were excited by removing a previously immersed hemisphere from the central part of the paraboloid. Good agreement between theory and experiment was obtained. |
| doi_str_mv | 10.1134/S0015462809050159 |
| format | Article |
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V. ; Kakhiani, V. O. ; Patarashvili, K. I. ; Tsakadze, S. J.</creator><creatorcontrib>Kalashnik, M. V. ; Kakhiani, V. O. ; Patarashvili, K. I. ; Tsakadze, S. J.</creatorcontrib><description>Free liquid oscillations (Poincaré oscillations) in a rotating paraboloid are investigated theoretically and experimentally. Within the framework of shallow-water theory, with account for the centrifugal force, expressions for the free oscillation frequencies are obtained and corrections to the frequencies related with the finiteness of the liquid depth are found. It is shown that in the rotating liquid, apart from the wave modes of free oscillations, a stationary vortex mode is also generated, that is, a process of geostrophic adjustment takes place. Solutions of the shallow-water equations which describe the wave dynamics of the adjustment process are presented. In the experiments performed the wave and vortex modes were excited by removing a previously immersed hemisphere from the central part of the paraboloid. 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In the experiments performed the wave and vortex modes were excited by removing a previously immersed hemisphere from the central part of the paraboloid. 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| subjects | Classical and Continuum Physics Classical Mechanics Engineering Fluid Dynamics Fluid dynamics Fluid flow Fluid- and Aerodynamics Hemispheres Liquids Mathematical analysis Oscillations Physics Physics and Astronomy Rotating Vortices |
| title | Poincaré oscillations and geostrophic adjustment in a rotating paraboloid |
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