We examine the rotor–oscillator flow, a slow
viscous flow between long parallel plates
driven by the rotation of a slender cylinder (the rotor) and the
longitudinal oscillation
of one of the plates (the oscillator). For rotor locations of interest
to us,
this flow exhibits a hyperbolic mixing region, characterized by homoclinic
tangling associated
with a hyperbolic fixed point, and a degenerate mixing region, characterized
by
heteroclinic tangling associated with two degenerate fixed points on one
of the
boundary plates (normally the oscillator). These mixing regions are investigated
both
theoretically, by applying various dynamical tools to a mathematical
model of the flow,
and experimentally, by observing the advection of a passive tracer in a
specially
constructed apparatus. Although degenerate mixing regions have been largely
ignored
or undervalued in previous research on chaotic mixing, our results demonstrate
that
more mixing is associated with the degenerate mixing region than the hyperbolic
one
in many cases. We have also discovered a peculiar phenomenon, which we
call
Melnikov resonance, involving a rapid fluctuation in the
size of the hyperbolic mixing
region as the frequency of the oscillator is varied.