Slow Viscous Flow Past a Cavity

The problem of a viscous shear flow past a two-dimensional cavity of infinite depth is treated analytically by the use of the Stokes approximation. The flow pattern near the mouth of the cavity is examined with special interest in the location of a dividing streamline between the outer flow and the inner “cavity flow”. It is shown that the outer flow penetrates to a considerable depth into the cavity, and that the separation (or reattachment) of the flow occurs on the cavity wall (not at the cavity corner). A brief mention is also made of the nature of the cavity flow.