Linear growth rates for the Rayleigh-Bénard instability in cylindrical geometry

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Abstract
We report theoretical growth rates for the Rayleigh–Bénard instability when the fluid layer is contained by non-slip walls in a cylindrical geometry with diameter D and height L. Our results are for the growth rates of the first two axisymmetric modes as functions of the Prandtl number P and the aspect ratio γ≡D/2L. We have considered the two extreme cases of ideally insulating and ideally conducting side walls, and found that the growth rate is relatively insensitive to the choice of the thermal boundary conditions on the side walls. Our results are useful in understanding recent experimental measurements of the convective time-scale.

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