Rotating Convection in a Finite Cylinder

Abstract

This paper is devoted to analyzing numerically experimental observations of azimuthally travelling waves that appear in rotating convection in a circular container at intermediate Prandtl numbers. The instability is a Hopf bifurcation that gives rise to a pattern precessing generally counter to the rotation direction. Two types of modes can be differentiated, the fast modes with relatively high precession velocity whose amplitude peaks near the sidewall, and the slow modes whose amplitude peaks near the center. Results are presented for Prandtl number 6.8 and aspect ratio Γ ≡ d/h equal to 2.5 as a function of the rotation rate. For rigid insulating sidewalls, and rigid thermally conducting top and bottom lids, the results agree well with those mesured experimentally.