Undulating rolls and domain instability

Abstract

The problem of the existence and of the stability of steady undulating rolls evolving from the zigzag instability of convection rolls in a Rayleigh-B\'enard layer are considered. Finite amplitude solutions are given and the onset of a new type of instability leading to a long wavelength domain type pattern is described. Domains of straight rolls with a larger than average wave number and undulating rolls alternate in this pattern. The structure appears to be stable and should be realizable in laboratory experiments.