Asymptotic Theory of the Viscous Interaction Between a Vortex and a Plane

The problem of the viscous interaction between a flow induced by a vortex filament and an orthogonal rigid surface is solved for high Reynolds numbers using the method of matched asymptotic expansions. In view of the impossibility of matching the principal terms of the asymptotic expansions directly for the near-axial boundary layer and the main flow zone, the solution is obtained by introducing two intermediate zones. In this case a logarithmic singularity of the axial velocity arises inevitably on the vortex filament. In the near-axial and intermediate zones the solution is obtained numerically and analytically, respectively, while in the main zone the problem reduces to the problem of the flow induced by a line of weakly swirled vortex-sinks.