ASYMPTOTIC THEORY OF WALL-ATTACHED CONVECTION IN A ROTATING FLUID LAYER

Asymptotic expressions for the onset of convection in a horizontal fluid layer of finite extent heated from below and rotating about a vertical axis are derived in the limit of large rotation rates in the case of stress-free upper and lower boundaries. In the presence of vertical sidewalls, the critical Rayleigh number R(c) is much lower than the classical value for an infinitely extended layer. In particular, we find that R(c) grows in proportion to tau when the sidewall is insulating, where tau is the dimensionless rotation rate. When the sidewall is infinitely conducting, R(c) grows in proportion to tau4/3 as in the case of an infinitely extended layer but with a lower coefficient of proportionality. Numerical results obtained at finite values of tau show good agreement with the asymptotic formulae.