Hopf Bifurcation with Broken Reflection Symmetry in Rotating Rayleigh-Bénard Convection

Abstract

Experimental observations of azimuthally traveling waves in rotating Rayleigh-Bénard convection in a circular container are presented and described in terms of the theory of bifurcation with symmetry. The amplitude of the convective states varies as √ε and the traveling-wave frequency depends linearly on ε with a finite value at onset. Here ε = R/R_c - 1, where R_c is the critical Rayleigh number. The onset value of the frequency decreases to zero as the dimensionless rotation rate Ω decreases to zero. These experimental observations are consistent with the presence of a Hopf bifurcation from the conduction state expected to arise when rotation breaks the reflection symmetry in vertical planes of the nonrotating apparatus.