Wall-bounded laminar sink flows

The laminar flow near an infinite plane wall perpendicular to a line sink of constant strength is investigated in the limit of large Reynolds numbers. Self-similarity requires that fluid is issuing from the boundary layer. The inviscid flow outside the boundary layer is governed by the Euler equations. A one-parametric set of solutions to the Euler equations with appropriate boundary conditions is given. Uniqueness of the inviscid flow solution is obtained from matching with the boundary layer expansion. The solution of the boundary-layer equations is given both in closed form and numerically. It is found that at the edge of the boundary layer the vorticity decays algebraically.