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The nonlinear interactions of convection modes in a box of a saturated porous medium

Citation

Florio, BJ and Bassom, AP and Fowkes, N and Judd, K and Stemler, T, The nonlinear interactions of convection modes in a box of a saturated porous medium, Physica D: Nonlinear Phenomena, 301-302 pp. 48-58. ISSN 0167-2789 (2015) [Refereed Article]

DOI: doi:10.1016/j.physd.2015.03.010

Abstract

A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.

Item Details

Item Type:Refereed Article
Keywords:dynamical systems, fluid dynamics, porous medium, Horton-Rogers-Lapwood problem
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:105673
Year Published:2015
Web of Science® Times Cited:1
Deposited By:Mathematics and Physics
Deposited On:2016-01-12
Last Modified:2016-07-06
Downloads:0

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