Dynamics of Travelling Waves in Finite Containers

A multiscale expansion is used to show that distant sidewalls can cause a travelling wave to reverse periodically its direction of propagation. These reversing states are two-frequency waves and appear via a secondary Hopf bifurcation from a pattern of counterpropagating waves. With increasing Rayleigh number the reversal period diverges and the reversals may become chaotic, before a hysteretic transition to nonreversing waves takes place. The predictions are in qualitative agreement with existing experiments.