Boundary layer induced by a conical vortex

Abstract

The structure of the boundary layer induced by a family of inviscid vortices with conical symmetry over a solid plane is analyzed. Though the equations governing the problem over an infinite plane may be written in a self-similar form, they have no self-similar solutions connecting the no-slip boundary condition at the plane with the inviscid external vortex. Numerical computations on a finite circular disk of radius R suggest new variables in terms of which the solution tends to an asymptote as the axis is approached. Further, a similarity solution for the finite disk problem is given. This solution provides a relatively simple `initial' velocity profile to consistently model the effusing core structure in actual vortices of interest.