Steady Stokes flow in an annular cavity

This paper addresses a general analytical method of superposition for the study of two-dimensional creeping flows in a wedge-shaped cavity arb, ||0 caused by tangential velocities of its curved walls. The method is illustrated by several numerical examples; the rate of convergence and the accuracy of fulfilling the boundary conditions are investigated. The main objective is to demonstrate the advantages of the method of superposition when analysing streamline patterns and the velocity-field distribution in the whole domain, including the Moffatt eddies near corner points. The equations for the positions of the stagnation and separation points are written analytically. The streamline patterns for uniform velocities at the top and the bottom walls are shown graphically. These patterns represent the transition from the corner eddies into internal eddies.