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

摘要

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 boundarylayer solution to Navier-Stokes solutions with different Reynolds numbers. We show how Prandtl's solution develops a finite-time separation singularity. On the other hand, the Navier-Stokes solutions are characterized by the presence of two distinct types of viscousinviscid interactions that 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.