The Matching Condition for Two-Dimensional Flow at Low Reynolds Number: With Application to the Motion of an Elliptic Cylinder

The problem of the title is treated as a singular perturbation problem. For a body of arbitrary cross-section, a matching condition is obtained from the outer solution in terms of the forces experienced by the body. The problem is then to find a solution of the Stokes equations which satisfies the boundary conditions on the body and is consistent with the matching condition. The technique is illustrated by application to the elliptic cylinder. One of the features of the solution is that it gives an unambiguous result for the lift on an elliptic cylinder at incidence.