Resonance patterns in spatially forced Rayleigh-Bénard convection

We report on the influence of a quasi-one-dimensional periodic forcing on the pattern selection process in Rayleigh-Benard convection (RBC). The forcing was introduced by a lithographically fabricated periodic texture on the bottom plate. We study the convection patterns as a function of the Rayleigh number (Ra) and the dimensionless forcing wavenumber (q(f)). For small Ra, convection takes the form of straight parallel rolls that are locked to the underlying forcing pattern. With increasing Ra, these rolls give way to more complex patterns, due to a secondary instability. The forcing wavenumber q(f) was varied in the experiment over the range of 0.6q(c) < q(f) < 1.4q(c), with q(c) being the critical wavenumber of the unforced system. We investigate the stability of straight rolls as a function of q(f) and report patterns that arise due to a secondary instability