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Crossed Rolls at Onset of Convection in a Rigid Box

Document Type

Article

Journal/Book Title/Conference

Journal of Fluid Mechanics

Volume

191

Publisher

Cambridge University Press

Publication Date

1988

First Page

583

Last Page

597

Abstract

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.

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http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=394447

Published by Cambridge University Press in "Journal of Fluid Mechanics." Publisher PDF is available through the link above. Publisher requires a subscription to access the article.

https://doi.org/10.1017/S0022112088001727

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