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Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution

Bichsel, Denis ; Wittwer, Peter

In: Journal of Statistical Physics, 2007, vol. 127, no. 1, p. 133-170

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    Title
    • Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution
    Author
    • Bichsel, Denis. Laboratoire de modélisation et simulation, HESSO, Ecole d'Ingénieurs de Genève, Switzerland
    • Wittwer, Peter. Département de Physique Théorique, Université de Genève, Genève, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Journal of Statistical Physics, 2007, vol. 127, no. 1, p. 133-170. Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:315298
    Summary
    We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical systems we analyze the vorticity equation for this problem and show that a symmetry-breaking term fits naturally into the downstream asymptotic expansion of a solution. Finally, in order to check that our asymptotic expressions can be completed to a symmetry-breaking solution of the Navier-Stokes equations we solve the problem numerically by using our asymptotic results to prescribe artificial boundary conditions for a sequence of truncated domains. The results of these numerical computations a clearly compatible with the existence of such a solution