| 講演要旨： |
Rotating Rayleigh-Benard convection encompasses the competition between rotation and thermal buoyancy in a paradigm problem that incorporates fundamental processes of great importance to atmospheric and oceanic circulations, as well as being of astrophysical importance. Idealizations in fluid dynamics have been, and continue to be, very useful in order to gain understanding of the dynamics of the physical system; rotating convection was first studied assuming periodicity in an infinite layer, and neglecting the centrifugal buoyancy. The inclusion of relistic bouncary conditions in the sidewall and also the inclusion of centrifugal buoyancy result in new and important effects.
Confined rotating convection introduces new phenomena which have no counter-part in unbounded rotating convection, such as the wall modes which result from the interaction between the Coriolis force and the cylinder sidewall, which in turn modifies the onset of bulk convection. We will present results showing the multiplicity of states and the onset of chaos in a cylinder of aspect ratio four.
The effect of centrifugal buoyancy is analyzed in a cylinder of aspect ratio one. The presence of centrifugal buoyancy changes the problem in a fundamental manner, driving a large scale circulation in which the cool denser fluid is centrifuged radially outward and the hot less dense fluid is centrifuged radially inward, and so there is no trivial conduction state. For small Froude numbers the transition to 3D flow happens around a Rayleigh number of 7,500. For Froude numbers larger than 3, the centrifugal buoyancy delays transition to Rayleigh 50,000. At intermediate Froude the transition to 3D flow happens via four different Hopf bifurcations, resulting in different coexisting branches of 3D solutions with complex interactions. The main conclusion is that centrifugal buoyancy changes quantitatively and qualitatively the flow dynamics.
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