Hopf bifurcation in a broken-parity pattern

Abstract

In this paper we report both experimental and theoretical results on a Rayleigh-B\'enard convection experiment with a static spatially periodic forcing. For reduced Rayleigh number of order 100, the system undergoes a secondary Hopf bifurcation involving novel and surprising spatially inhomogeneous temporally periodic states. We give a description of these various inhomogeneous states, and develop a simple phenomenological model based on symmetry considerations which seems to capture all the essential qualitative features.