Flow patterns near codimension-2 bifurcation in non-Boussinesq mixed convection

Suslov, Sergey A. (2002) Flow patterns near codimension-2 bifurcation in non-Boussinesq mixed convection. In: Progress in Nonlinear Science, International Conference dedicated to the 100th Anniversary of A.A. Andronov, 2-6 Jul 2001, Nizhniy Novgorod, Russia.

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Abstract

Realistic nonlinear (non-Boussinesq) fluid property variations with temperature (expressed, for example, by the Sutherland formulae for viscosity and thermal conductivity and by the ideal gas equation of state for the density) are shown to lead to a rich variety of flow instability phenomena in the classical problem of mixed convection in a differentially heated vertical channel. The instabilities are caused by competing buoyancy and shear effects. One of the most complicated and interesting flow regimes arises when two instability modes bifurcate simultaneously at the so-called codimension-2 point. It is shown that such a situation can be modelled successfully by coupled cubic complex Landau-type equations derived using a weakly nonlinear stability theory. In this paper the unfoldings of one of the double Hopf bifurcations detected in non-Boussinesq mixed convection are investigated. The complete set of resulting flow patterns is studied as functions of governing physical parameters. This paper complements a general classification of unfoldings of codimension-2 bifurcations and interprets the results obtained for the model dynamical system from the physical point of view.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Depositing User: Dr Sergey Suslov
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:52
Last Modified: 02 Jul 2013 22:40
Uncontrolled Keywords: bifurcation; non-Boussinesq convection; codimension-2 point; weakly non-linear stability
Fields of Research (FOR2008): 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
01 Mathematical Sciences > 0105 Mathematical Physics > 010599 Mathematical Physics not elsewhere classified
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/1816

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