Longitudinal convection rolls in a rectangular channel heated from below

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The sidewall effect on Rayleigh-Bénard convection has been examined in a rectangular channel of infinite length having a cross section with a finite aspect ratio A (=width/height). Steady longitudinal rolls are obtained numerically. In a bifurcation diagram in which A is changed as a bifurcation parameter, the roll solution forms a single-valued branch when the Rayleigh number Ra exceeds but is still close to the critical value. When Ra is relatively higher, the solution branch has a folded structure, that is, it can be triple-valued. The secondary instability of the roll solution with respect to two-dimensional disturbances is investigated. The roll solutions with a certain symmetry are found to be linearly stable. Stable roll patterns are classified in the A-Ra plane. In a certain range of A and Ra, multiple roll patterns are simultaneously stable. The number of the stable patterns increases with Ra.

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