Singular boundary condition for a degenerated turbulent toy model
Résumé
We consider a turbulent toy model with the Prandtl mixing length, that vanishes at the boundary, as eddy viscosity and a Navier-like friction law as boundary condition. We address the paradox of the degeneracy of the boundary condition, by means of an approach by a problem of singular perturbations. We show a convergence theorem for well-prepared source terms, and we illustrate our analysis with a series of analytical examples, showing both blow-up cases for ill-prepared data and convergence cases for well-prepared data.
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