Stokes flow in a circular arc trough due to surface shear

The fluid motion in a circular arc trough due to constant surface shear is studied. Under the Stokes assumption, the problem is separated into longitudinal flow and transverse flow. Three methods are used: exact solution for the semi-circular trough, perturbation solution for the shallow trough and numerical solution by point match. Maximum velocity occurs at the middle of the top surface. A single recirculating cell exists for transverse flow. Unlike plate-driven flows, no corner singularities in velocity or stress are found.