A similarity solution of a 3−dimensional boundary
layer is investigated. The outer flow is given by U =
(−xz, −yz, z2
), corresponding to an axisymmetric
poloidal circulation with constant potential vorticity.
This flow is an exact solution of the Navier–Stokes. A
wall is introduced at y = 0 along which a boundary
layer develops towards x = 0. We show that a
similarity reduction to a system of ODEs is possible.
Two distinct solutions are found, one of them through
numerical path-continuation, and their stability is
investigated. A second 3-D solution is also identified
for 2-D outer flow. The solutions are generalised for
outer flows scaling with different powers of z and
similar results are found. This behaviour is related to
the non-uniqueness of the Falkner-Skan flows in a 3-D
sense, with a transverse wall-jet.