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 ( ) and the dimensionless forcing wavenumber ( ). For small , convection takes the form of straight parallel rolls that are locked to the underlying forcing pattern. With increasing , these rolls give way to more complex patterns, due to a secondary instability. The forcing wavenumber was varied in the experiment over the range of , with being the critical wavenumber of the unforced system. We investigate the stability of straight rolls as a function of and report patterns that arise due to a secondary instability.