Slow oscillatory Stokes flow

Two transient problems in slow viscous flow are considered where the corresponding steady-state behaviour leads to the paradoxical results of Stokes and Jeffery. First, the oscillatory flow past a circular cylinder is investigated when the frequency $\lambda$ tends to zero, where an outer domain of size $O\left ( {\lambda ^{ - 1/2}} \right )$ is required to ensure that the velocity conditions at infinity are satisfied. The flow close to the cylinder is quasi-steady except for a time of length $O\left ( 1 \right )$ about the time of separation; most of the action takes place in the outer domain where the dominant transient behaviour extends over a time that is $O\left [ {{{\left \{ {ln\left ( {\lambda ^{ - 1}} \right )} \right \}}^{ - 1}}} \right ]$ of a complete cycle.