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Resonance patterns in spatially forced Rayleigh–Bénard convection

Published online by Cambridge University Press:  01 September 2014

S. Weiss ,
G. Seiden  and
E. Bodenschatz
S. Weiss*
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, D-37073 Göttingen, Germany
G. Seiden
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, D-37073 Göttingen, Germany
E. Bodenschatz
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, D-37073 Göttingen, Germany Department of Physics, Cornell University, Ithaca, NY 14853-2501, USA
*
†Present address: Department of Physics, University of California, Santa Barbara, CA 93106, USA. Email address for correspondence: stwe@umich.edu
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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.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 293 - 308
Copyright
© 2014 Cambridge University Press 

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Footnotes

‡

Present address: Department of Earth and Planetary Sciences, Faculty of Chemistry, Weizemann Institute of Science, Rehovot, Israel.

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