Because of the importance of oscillatory components in the oncoming
flow at certain oceanic topographic features, we investigate the oscillatory
flow
past a circular cylinder
in an homogeneous rotating fluid. When the oncoming flow is non-reversing,
and for
relatively low-frequency oscillations, the modifications to the equivalent
steady flow arise principally in the ‘quarter layer’ on the
surface of
the cylinder. An incipient-separation criterion is found
as a limitation on the magnitude of the Rossby number,
as in the steady-flow case. We present exact solutions for a number of
asymptotic
cases, at both large frequency and small nonlinearity. We also report numerical
solutions of the nonlinear quarter-layer equation for a range of parameters,
obtained
by a temporal integration. Near the rear stagnation
point of the cylinder, we find a
generalized velocity ‘plateau’ similar to that
of the steady-flow problem, in which all
harmonics of the free-stream oscillation may be present. Further, we determine
that,
for certain initial conditions, the boundary-layer flow develops a
finite-time singularity in the neighbourhood of the rear stagnation point.
Steady flow past a sphere in an aligned magnetic field at high Reynolds numbers
