Linear and nonlinear instabilities in rotating cylindrical Rayleigh-Bénard convection

Abstract

Linear and nonlinear convection in a rotating annular cylinder, under experimental boundary conditions, heated from below and rotating about a vertical axis are investigated. In addition to the usual physical parameters such as the Rayleigh and Taylor number, an important geometric parameter, the ratio of the inner to outer radius, enters into the problem. For intermediate ratios, linear stability analysis reveals that there exist two countertraveling convective waves which are nonlinearly significant: a retrograde wave located near the outer sidewall and a prograde wave adjacent to the inner sidewall. Several interesting phenomena of nonlinear convection are found: (i) tempospatially modulated countertraveling waves caused by an instability of the Eckhaus-Benjamin-Feir type, (ii) destructive countertraveling waves in which the existence or disappearance of the prograde wave is determined by its relative phase to the retrograde wave, and (iii) a saddle-node-type bifurcation in which the prograde wave takes an infinite amount of time to pass over the retrograde wave.