Journal of Fluid Mechanics

Crossed rolls at onset of convection in a rigid box

Boyd F.  Edwards a1
a1 Department of Physics, West Virginia University, Morgantown, WV 26506, USA

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Critical Rayleigh numbers, roll configurations, and growth-rate derivative are calculated at onset of convection for a rigid box with conducting upper and lower plates and insulating sidewalls. When the sidewalls form a square or a near square, the linearized Oberbeck–Boussinesq equations favour crossed rolls, a superposition of three-dimensional rolls in the x- and y-directions, over unidirectional rolls. These crossed rolls preserve the four-fold rotation symmetry about the vertical axis of a square box only when the aspect ratio (ratio of width to depth of the box) demands an even number of rolls in each direction. The analysis explains patterns observed by Stork & Müller.

(Published Online April 21 2006)
(Received October 4 1985)
(Revised September 4 1987)