Convective and absolute instabilities in non-Boussinesq mixed convection Authors Sergey A. Suslov Department of Mathematics and Computing and Computational Engineering and Science Research Centre University of Southern Queensland Original Article

First Online: 04 May 2007 Received: 12 September 2006 Accepted: 20 March 2007 DOI :
10.1007/s00162-007-0049-y

Cite this article as: Suslov, S.A. Theor. Comput. Fluid Dyn. (2007) 21: 271. doi:10.1007/s00162-007-0049-y
Abstract
The problem of non-Boussinesq mixed convection in a vertical channel formed by two differentially heated infinite plates is investigated and the complete convective/absolute instability boundary is computed for a wide range of physical parameters. A physical insight into the mechanisms causing instabilities is given. In particular, it is shown that the appearance of absolute instability is always dictated by a flow reversal within a channel; however, existence of the flow reversal does not exclude the possibility of convective instability. It is also shown that fluid’s non-linear transport property variations have a dramatic effect on the structure and complexity of spatio-temporal instabilities of the co-existing buoyancy and shear modes as the temperature difference across the channel increases. The validity of the stability results obtained using the procedure described in Suslov (J Comp Phys 212, 188–217, 2006) is assessed using the method of steepest descent.

Keywords
Spatio-temporal instability
Non-Boussinesq convection
Mixed convection
Communicated by R. Grimshaw.

This work was partially supported by a computing grant from the Australian Partnership for Advanced Computing, 2000–2003.

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