Thermal cellular convection in rotating rectangular boxes

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Abstract
The thermal cellular convection in rotating rectangular boxes has been investigated both theoretically and experimentally. In the theoretical analysis, a linear stability theory is used to calculate the stability behaviour and the configuration of the three-dimensional convection flow. The numerical results show that the rolls change their orientation for a Taylor number greater than a critical value. In the experimental investigation, the flow patterns were visualized by a special differential interferometer. The experimental results are presented in stability diagrams and interferogram series which demonstrate the influence of rotation as well as initial and boundary conditions on the convective flow. We found that the effects of the Coriolis force and those of centrifugal forces could be studied separately by the choice of different test fluids, e.g. nitrogen is good for the Coriolis-force effect while silicone oil is good for the centrifugal-force effect.When compared with experimental results, our theoretical model is shown to be good for fluids of small Prandtl number such as nitrogen gas. We also compare our results with the well-known asymptotic behaviour of the critical Rayleigh number and wavenumber.