We consider a toy model with the Prandtl mixing lenght as eddy viscosity, that vanishes at the boundary, and a Navier like friction law as boundary condition. We address the paradox of the degeneracy of the boundary condition, which we 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 blow up cases and convergence cases for well-prepared data
Singular boundary condition for a degenerated turbulent toy model
Luigi C. Berselli;Roger Lewandowski
2023-01-01
Abstract
We consider a toy model with the Prandtl mixing lenght as eddy viscosity, that vanishes at the boundary, and a Navier like friction law as boundary condition. We address the paradox of the degeneracy of the boundary condition, which we 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 blow up cases and convergence cases for well-prepared dataFile in questo prodotto:
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