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

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Abstract

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.

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Authors and Affiliations

  1. Laboratoire de modélisation et simulation, HESSO, Ecole d’Ingénieurs de Genève, Switzerland

    Denis Bichsel

  2. Département de Physique Théorique, Université de Genève, Genève, Switzerland

    Peter Wittwer

Authors
  1. Denis Bichsel
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  2. Peter Wittwer
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Correspondence to Peter Wittwer.

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Mathematics Subject Classification (2000). 76D05, 76D25, 76M10, 41A60, 35Q35

Supported in part by the Fonds National Suisse.

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Bichsel, D., Wittwer, P. Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution. J Stat Phys 127, 133–170 (2007). https://doi.org/10.1007/s10955-006-9248-y

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  • DOI: https://doi.org/10.1007/s10955-006-9248-y

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