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Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

Straughan, Brian

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection Thumbnail


Authors

Brian Straughan



Abstract

We investigate the effects of anisotropic permeability and changing boundary conditions upon the onset of penetrative convection in a porous medium of Darcy type and of Brinkman type. Attention is focussed on the critical eigenfunctions which show how many convection cells will be found in the porous layer. The number of cells is shown to depend critically upon the ratio of vertical to horizontal permeability, upon the Brinkman coefficient, and upon the upper boundary condition for the velocity which may be of Dirichlet type or constant pressure. The critical Rayleigh numbers and wave numbers are determined, and it is shown how an unconditional threshold for nonlinear stability may be derived.

Citation

Straughan, B. (2022). Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection. Environmental Fluid Mechanics, 22, 1233–1252. https://doi.org/10.1007/s10652-022-09888-9

Journal Article Type Article
Acceptance Date Jul 5, 2022
Online Publication Date Aug 17, 2022
Publication Date 2022-12
Deposit Date Sep 13, 2022
Publicly Available Date Sep 13, 2022
Journal Environmental Fluid Mechanics
Print ISSN 1567-7419
Electronic ISSN 1573-1510
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 22
Pages 1233–1252
DOI https://doi.org/10.1007/s10652-022-09888-9
Public URL https://durham-repository.worktribe.com/output/1191588

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http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.






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