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