Analysis of instability patterns in non-Boussinesq mixed convection using a direct numerical evaluation of disturbance integrals

Suslov, Sergey A. (2009) Analysis of instability patterns in non-Boussinesq mixed convection using a direct numerical evaluation of disturbance integrals. Computers and Fluids, 38 (3). pp. 590-601. ISSN 0045-7930

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The Fourier integrals representing linearised disturbances arising from an initially localised source are evaluated numerically for natural and mixed convection flows between two differentially heated plates. The corresponding spatio-temporal instability patterns are obtained for strongly non-Boussinesq high-temperature convection of air and are contrasted to their Boussinesq counterparts. A drastic change in disturbance evolution scenarios is found when a large cross-channel temperature gradient leads to an essentially nonlinear variation of the fluid's transport properties and density. In particular, it is shown that non-Boussinesq natural convection flows are convectively unstable while forced convection flows can be absolutely unstable. These scenarios are opposite to the ones detected
in classical Boussinesq convection. It is found that the
competition between two physically distinct instability mechanisms which are due to the action of the shear and the buoyancy are responsible for such a drastic change in spatio-temporal characteristics of instabilities. The obtained numerical results confirm and complement semi-analytical conclusions of Suslov 2007 on the absolute/convective instability transition in non-Boussinesq mixed convection. Generic features of the chosen numerical approach are discussed and its advantages and shortcomings are reported.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 13 Jul 2009 12:20
Last Modified: 02 Jul 2013 23:05
Uncontrolled Keywords: non-Boussinesq convection; spatio-temporal instability
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.compfluid.2008.06.002

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