The axisymmetric boundary-layer separation of an incompressible
impulsively started
flow in a wavy-walled tube is analysed at moderate to high values of the
Reynolds
number. The investigation is carried out by numerical integration of either
the
Navier–Stokes equations or Prandtl's asymptotic formulation
of the boundary-layer
problem. The presence of an adverse pressure gradient induces reverse flow
at the tube
wall independently of the Reynolds number; its occurrence can be predicted
by a
timescale analysis. Following that, the viscous calculations show different
dynamics
depending on the Reynolds number. As the Reynolds number increases, the
boundary
layer has in a well-defined internal structure where longitudinal lengthscales
become
comparable with the viscous one. Thus the boundary-layer scaling fails
locally, with a
minimum of pressure inside the boundary layer itself. The formation of
the primary
recirculation is well captured by the asymptotic model which, however,
is not able to
describe the roll-up of the vortex structure inside the recirculating region.
This
inadequacy appears well before the flow evolves to the characteristic terminal
singularity usually assumed as foreshadowing the vortex shedding phenomenon.
The
outcomes are compared with the existing results of analogous problems giving
an
overall agreement but improving, in some cases, the physical picture.