Suslov, S. A. (2008) Twoequation model of mean flow resonances in subcritical flow systems. Discrete and Continuous Dynamical Systems Series S, Selected Topics, 1 (1). pp. 165176. ISSN 19371632

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Abstract
[Abstract]: Amplitude equations of Landau type, which describe the dynamics ofthe most amplified periodic disturbance waves in slightly supercritical flow systems, have been known to form reliable and sufficiently accurate lowdimensional models capable of predicting the asymptotic magnitude of saturated perturbations. However the derivation of similar models for estimating the threshold disturbance amplitude in subcritical systems faces multiple resonances which lead to the singularity of model coefficients. The observed resonances are traced back to the interaction between the mean flow distortion induced by the decaying fundamental disturbance harmonic and other decaying disturbance modes. Here we suggest a methodology of deriving a twoequation dynamical system of coupled cubic amplitude equations with nonsingular coefficients which resolve the resonances and are capable of predicting the threshold amplitude for weakly nonlinear subcritical regimes. The suggested reduction procedure is based on the consistent use of an appropriate orthogonality condition which is different from a conventional solvability condition. As an example, a developed procedure is applied to a system of NavierStokes equations describing a subcritical plane Poiseuille flow. Predictions of the sodeveloped model are found to be in reasonable agreement with experimentally detected threshold amplitudes reported in literature.
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Item Type:  Article (Commonwealth Reporting Category C) 

Refereed:  Yes 
Item Status:  Live Archive 
Additional Information:  Invited paper for the Inaugural issue of DCDSS. 
Depositing User:  Dr Sergey Suslov 
Faculty / Department / School:  Historic  Faculty of Sciences  Department of Maths and Computing 
Date Deposited:  04 Feb 2008 02:02 
Last Modified:  05 Sep 2014 04:16 
Uncontrolled Keywords:  amplitude expansion, resonances, subcritical instability 
Fields of Research (FOR2008):  02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics 01 Mathematical Sciences > 0199 Other Mathematical Sciences > 019999 Mathematical Sciences not elsewhere classified 01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems 
SocioEconomic Objective (SEO2008):  E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences 
URI:  http://eprints.usq.edu.au/id/eprint/3824 
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