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Structure and mechanism of oscillatory convection in a cube of fluid-saturated porous material heated from below

Published online by Cambridge University Press:  26 April 2006

Michael D. Graham  and
Paul H. Steen
Michael D. Graham
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
Paul H. Steen
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

The transition from steady to oscillatory three-dimensional convection in a cube of saturated porous material is calculated to occur at Rayleigh number R = 584 due to seven pairs of thermal blobs which circulate around the cube. This travelling wave instability is shown to be closely related, first as regards structural characteristics and then as regards mechanism of instability, to an analogous instability in two dimensions. The correspondence with the two-dimensional flow is established via a correspondence with a nonlinear base flow in a box of square planform of a different aspect ratio (l/√2) and ultimately derives from the symmetries of the base flow in the cube.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 591 - 609
Copyright
© 1991 Cambridge University Press

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