Interactive boundary layer in a Hele Shaw cell

Abstract

AbstractThe steady laminar flow in a rectangular Hele Shaw cell is considered at high Reynolds number. The lower thin wall layer is perturbed by a small bump. Averaged equations obtained in averaging the Navier Stokes equations across the thin direction are used. This procedure allows to recover the nonlinear convective term in the equations. First a classical Boundary Layer theory is constructed, the weak coupling leads to a singularity. An Interacting Boundary Layer theory is then constructed in order to compute the strong coupling of the “Averaged ideal fluid” and the “Averaged boundary layer”. The “triple deck” counter part is presented as well. An asymptotic nonlinear approximation of the flow can be computed with short computation time. Positive comparisons of computation of the full Averaged Navier Stokes equation and Interacting Boundary Layer theory are shown. For instance, the boundary layer separation over a bump is obtained when either the bump height or the Reynolds number is increased.