We compute the solutions of Prandtl’s and Navier-Stokes equations for the two dimensional flow induced by anarray of periodic rectilinear vortices interacting with a boundaryin the halfplane. This initial datum develops, in a finite time, aseparation singularity for Prandtl’s equation. We investigate thedifferent stages of unsteady separation in Navier-Stokes solutionsfor various Reynolds numbers. We show the presence of a large-scale interaction between viscous boundary layer and inviscidouter flow in all Re regimes, while the presence of a small-scaleinteraction is visible only for moderate-high Re numbers. Wealso investigate the asymptotic validity of boundary layer theoryin the limit of infinite Re numbers. The numerical solutions arecomputed using an efficient parallel spectral-finite differencesscheme for both Prandtl and Navier-Stokes, with a focusing ofthe grid points close to the boundary.
|Numero di pagine||9|
|Stato di pubblicazione||Published - 2007|