Stokes flow in a two-dimensional cavity with moving end walls

Abstract

When fluid in a two-dimensional, rectangular cavity is driven by moving end walls, the resulting flow consists of a pattern of one or more eddies depending on the aspect ratio (ratio of depth to width) of the cavity. For aspect ratios less than 1, the flow pattern consists of a single eddy that fills the entire cavity. As the aspect ratio increases, this eddy pinches off in the center, forming two eddies. Then small eddies form at the center of the side walls, grow toward the center, and finally coalesce into a central, counterrotating eddy.