Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

Abstract

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.