Undulating rolls and their instabilities in a Rayleigh-Bénard layer

It has recently become apparent that undulating rolls and modulated undulating rolls represent physically realizable steady solutions of Rayleigh-Bénard convection in the neighborhood of the critical value of the Rayleigh number in addition to the solution of two-dimensional rolls. The relative regions of stability of these three types of convection are studied through analytical as well as through numerical methods. Symmetric stress-free as well as no-slip boundary conditions are considered; in the former case the analysis is restricted to moderate and high values of the Prandtl number.