Stability of non-Boussinesq convection via the complex Ginzburg-Landau model

Article

Suslov, Sergey A. and Paolucci, Samuel. 2004. "Stability of non-Boussinesq convection via the complex Ginzburg-Landau model." Fluid Dynamics Research. 35 (3), pp. 159-203. https://doi.org/10.1016/j.fluiddyn.2004.06.002
Article Title

Stability of non-Boussinesq convection via the complex Ginzburg-Landau model

ERA Journal ID3741
Article CategoryArticle
AuthorsSuslov, Sergey A. (Author) and Paolucci, Samuel (Author)
Journal TitleFluid Dynamics Research
Journal Citation35 (3), pp. 159-203
Number of Pages45
Year2004
Place of PublicationAmsterdam, Netherlands
ISSN0169-5983
1873-7005
Digital Object Identifier (DOI)https://doi.org/10.1016/j.fluiddyn.2004.06.002
Web Address (URL)http://www.sciencedirect.com/science/journal/01695983
Abstract

[Abstract]: A cubic complex Ginzburg-Landau model is derived for the flow of a general fluid near a bifurcation point.
Solutions are obtained for the natural convection flow of air in a differentially heated tall closed cavity under non-Boussinesq conditions.
The model is used to analyse various types of instabilities.
In particular, it is found that nonlinear fluid properties variations with temperature lead to a convective instability of the flow when the temperature difference becomes sufficiently large.
This is in contrast to classical results in the Boussinesq limit where the instability is found to be always absolute.
The results obtained using the model for an infinitely tall cavity are in excellent agreement with those of direct numerical simulations for a cavity of aspect ratio 40.

Keywordsnon-Boussinesq convection; weakly nonlinear stability theory; Ginzburg-Landau model
ANZSRC Field of Research 2020490399. Numerical and computational mathematics not elsewhere classified
490199. Applied mathematics not elsewhere classified
340799. Theoretical and computational chemistry not elsewhere classified
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsComputational Engineering and Science Research Centre
University of Notre Dame, United States
Permalink -

https://research.usq.edu.au/item/9x875/stability-of-non-boussinesq-convection-via-the-complex-ginzburg-landau-model

Log in to edit

Download files

Submitted Version
Suslov_Paolucci_AO.pdf
File access level: Anyone

  • 2174
    total views
  • 502
    total downloads
  • 1
    views this month
  • 1
    downloads this month

Export as

Related outputs

Magnetic flux density distribution in axial flux machine cores
Hewitt, Andrew, Ahfock, Tony L. and Suslov, Sergey A.. 2005. "Magnetic flux density distribution in axial flux machine cores." IET Electric Power Applications. 152 (2), pp. 192-196. https://doi.org/10.1049/ip-epa:20055039
Searching convective/absolute instability boundary for flows with fully numerical dispersion relation
Suslov, Sergey A.. 2001. "Searching convective/absolute instability boundary for flows with fully numerical dispersion relation." Computer Physics Communications. 142 (1-3), pp. 322-325. https://doi.org/10.1016/S0010-4655(01)00360-5
Multi-mode spatio-temporal instability in non-Boussinesq convection
Suslov, Sergey A.. 2004. "Multi-mode spatio-temporal instability in non-Boussinesq convection." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal.
Convective and absolute instabilities in non-Boussinesq mixed convection
Suslov, Sergey A.. 2007. "Convective and absolute instabilities in non-Boussinesq mixed convection ." Theoretical and Computational Fluid Dynamics. 21 (4), pp. 271-290. https://doi.org/10.107/s00162-007-0049-y
A Petrov-Galerkin method for flows in cavities: enclosure of aspect ratio 8
Suslov, Sergey A. and Paolucci, Samuel. 2002. "A Petrov-Galerkin method for flows in cavities: enclosure of aspect ratio 8." International Journal for Numerical Methods in Fluids. 40 (8), pp. 999-1007. https://doi.org/10.1002/fld.386
Numerical aspects of searching convective/absolute instability transition
Suslov, Sergey A.. 2005. "Numerical aspects of searching convective/absolute instability transition." Journal of Computational Physics. 212 (1), pp. 188-217. https://doi.org/10.1016/j.jcp.2005.06.017
Analysis of coupling between hydrodynamic and thermal instabilities in non-Boussinesq convection
Suslov, Sergey A.. 2005. "Analysis of coupling between hydrodynamic and thermal instabilities in non-Boussinesq convection." Nonlinear Analysis Theory Methods and Applications. 63 (5-7), pp. e1435-e1443. https://doi.org/10.1016/j.na.2005.01.057
Magneto-hydrodynamic interaction in a vertical slot filled with ferrofluid
Bozhko, Alexandra A., Suslov, Sergey A. and Putin, Gennady F.. 2008. "Magneto-hydrodynamic interaction in a vertical slot filled with ferrofluid." Alemany, A., Chopart, Jean-Paul and Freibergs, J. (ed.) 7th PAMIR International Conference on Fundamental and Applied MHD. Giens Peninsula, France 08 - 12 Sep 2008 Grenoble, France.
Stability of plane Poiseuille flow of a fluid with pressure-dependent viscosity
Tran, Thien Duc and Suslov, Sergey A.. 2008. "Stability of plane Poiseuille flow of a fluid with pressure-dependent viscosity ." Denier, J., Finn, M. D. and Mattner, T. (ed.) 22nd International Congress of Theoretical and Applied Mechanics ICTAM 2008. Adelaide, Australia 24 - 29 Aug 2008 Adelaide, Australia.
Thermo-magneto-convective instabilities in a vertical layer of ferro-magnetic fluid
Suslov, Sergey A., Bozhko, Alexandra A. and Putin, Gennady F.. 2008. "Thermo-magneto-convective instabilities in a vertical layer of ferro-magnetic fluid." Indeitsev, Dmitry A. (ed.) 36th International Conference Advanced Problems in Mechanics. Repino, Russia 06 - 10 Jul 2008 St Petersburg, Russia.
Stability of plane Poiseuille-Couette flows of a piezo-viscous fluid
Tran, Thien Duc and Suslov, Sergey A.. 2009. "Stability of plane Poiseuille-Couette flows of a piezo-viscous fluid." Journal of Non-Newtonian Fluid Mechanics. 156 (3), pp. 139-149. https://doi.org/10.1016/j.jnnfm.2008.07.009
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. https://doi.org/10.1016/j.compfluid.2008.06.002
Advection-dispersion in symmetric field-flow fractionation channels
Suslov, Sergey A. and Roberts, A. J.. 1998. Advection-dispersion in symmetric field-flow fractionation channels. Toowoomba, Australia. University of Southern Queensland.
Bifurcations in convection of incompressible fluid in a rotated square cylinder
Sharifulin, Albert and Suslov, Sergey A.. 2008. "Bifurcations in convection of incompressible fluid in a rotated square cylinder." Denier, J., Finn, M. D. and Mattner, T. (ed.) 22nd International Congress of Theoretical and Applied Mechanics ICTAM 2008. Adelaide, Australia 24 - 29 Aug 2008 Adelaide, Australia.
Revisiting plane Couette-Poiseuille flows of a piezo-viscous fluid
Suslov, Sergey A. and Tran, Thien Duc. 2008. "Revisiting plane Couette-Poiseuille flows of a piezo-viscous fluid." Journal of Non-Newtonian Fluid Mechanics. 154 (2-3), pp. 170-178. https://doi.org/10.1016/j.jnnfm.2008.04.010.
Thermo-magnetic convection in a vertical layer of ferromagnetic fluid
Suslov, Sergey A.. 2008. "Thermo-magnetic convection in a vertical layer of ferromagnetic fluid." Physics of Fluids. 20 (8), pp. 084101-084118. https://doi.org/10.1063/1.2952596
Phenomenological approach to 3D spinning combustion waves: numerical experiments with a rectangular rod
Strunin, Dmitry V. and Suslov, Sergey A.. 2005. "Phenomenological approach to 3D spinning combustion waves: numerical experiments with a rectangular rod." International Journal of Self Propagating High Temperature Synthesis. 14 (1), pp. 33-39.
New spatio-temporal instability scenarios in non-Boussinesq mixed convection
Suslov, Sergey A.. 2007. "New spatio-temporal instability scenarios in non-Boussinesq mixed convection." Sathyasheelappa, Vinaya K. (ed.) 60th Annual Meeting of the Divison of Fluid Dynamics, American Physical Society. Salt Lake City, United States 18 - 20 Nov 2007 College Park, MD.
Two-equation model of mean flow resonances in subcritical flow systems
Suslov, S. A.. 2008. "Two-equation model of mean flow resonances in subcritical flow systems." Discrete and Continuous Dynamical Systems Series S, Selected Topics. 1 (1), pp. 165-176.
Spatio-temporal instabilities in mixed convection of air subject to large temperature gradient
Suslov, Sergey A.. 2004. "Spatio-temporal instabilities in mixed convection of air subject to large temperature gradient ." Lyubimov, Dmitry V. (ed.) International Conference: Advanced Problems in Thermal Convection (2004). Perm, Russia 24 - 27 Nov 2003 Perm, Russia.
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 ." Shalfeev, V. D. (ed.) Progress in Nonlinear Science, International Conference dedicated to the 100th Anniversary of A.A. Andronov. Nizhniy Novgorod, Russia 02 - 06 Jul 2001 Nizniy Novgorod, Russia.
Effect of fluid properties variations on spatio-temporal instability of convection
Suslov, Sergey A.. 2002. "Effect of fluid properties variations on spatio-temporal instability of convection." Indeitsev, Dmitry A. (ed.) APM 2001: 29th Summer School on 'Advanced Problems in Mechanics. Repino, Russia 21 - 30 Jun 2001 St. Petersburg, Russia.