Resonance patterns in spatially forced Rayleigh–Bénard convection

Abstract

Abstract We report on the influence of a quasi-one-dimensional periodic forcing on the pattern selection process in Rayleigh–Bénard 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 ( $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ra}$ ) and the dimensionless forcing wavenumber ( $q_f$ ). For small $\mathit{Ra}$ , convection takes the form of straight parallel rolls that are locked to the underlying forcing pattern. With increasing $\mathit{Ra}$ , 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.