Transient Stokes Flow in a Channel Driven by Moving Sleeves

A two-dimensional, nonstationary Stokes flow in an infinite channel with plane, parallel walls is considered. The flow is driven by two sleeves forming parts of the walls and moving with a constant velocity starting at t = 0. The exact Laplace transform of the stream function is determined and an approximate inversion, valid for t small, is performed. The resulting approximate formula for the stream function is used to study numerically the nonstationary flow as it approaches the stationary state in which an infinite system of Moffatt eddies is fully developed. The results are presented as a series of streamline plots.