A VORTICITY MODEL FOR VISCOUS-FLOW PAST A CYLINDER

A mathematical model is proposed for the steady two-dimensional flow of a viscous incompressible fluid past a cylinder which incorporates the details of the structure of the vorticity in this case where its behaviour is known. The model is constructed to be consistent both with boundary-layer theory for sufficiently large Reynolds numbers and with the asymptotic solution at large distances from the cylinder. The governing Navier-Stokes equations are transformed to a set of equations which we refer to as the modified Navier-Stokes equations and are then solved numerically. Solutions have been obtained for the cases of flow past a stationary and a rotating circular cylinder and flow past an inclined elliptic cylinder. Good agreement is found with existing results.