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

Asymptotic expressions for the onset of convection in a horizontal flu id layer of finite extent heated from below and rotating about a verti cal 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 c lassical value for an infinitely extended layer. In particular, we fin d that R(c) grows in proportion to tau when the sidewall is insulating , where tau is the dimensionless rotation rate. When the sidewall is i nfinitely conducting, R(c) grows in proportion to tau4/3 as in the cas e of an infinitely extended layer but with a lower coefficient of prop ortionality. Numerical results obtained at finite values of tau show g ood agreement with the asymptotic formulae.