The unsteady interaction between a vortex and a wall-bounded vorticity
layer is
studied as a model for transport and mixing between rotational and irrotational
flows.
The problem is formulated in terms of contour integrals and a kinematic
condition
along the interface which demarcates the vortical and potential regions.
Asymptotic
solutions are derived for linear, weakly nonlinear and nonlinear long-wave
approximations.
The solutions show that the initial process of ejection of vorticity into
the irrotational
flow occurs at a stationary point along the interface. A nonlinear model
is derived and
shows that such a stationary point is more likely to exist when the circulation
of the vortex is counter to the vorticity in the layer. A Lagrangian numerical
method
based on contour dynamics is then developed for the general nonlinear problem.
Two
sets of results are presented where for every initial height of the vortex
its magnitude
and sign are varied. In both sets, it is observed that when the magnitude
of the vortex
is held constant a much stronger interaction occurs when the sign of the
vortex circulation
is opposite to that of the vorticity in the layer. Moreover, when the horizontal
velocity of the vortex is close to the velocity of the interfacial waves
a strong nonlinear
interaction between the vortex and the layer ensues and results in the
ejection of thin
filaments of vorticity into the irrotational flow. In order to study the
dynamical consequences
of strong unsteady interaction, the wall pressure distribution is computed.
The
results indicate that a significant rise in the magnitude of the wall pressure
is associated
with ejection of vorticity from the wall. The present analysis confirms
that coherent
vortical structures in the outer layer of a turbulent boundary layer can
cause ejection
of concentrated wall-layer vorticity and explains how and when this process
occurs.
Influence of contact interface morphology on the nonlinear interaction between a longitudinal wave and a contact interface with friction : A numerical study
