Unsteady Circulatory Flow about a Circular Cylinder with Suction or Injection

An exact solution of the Navier-Stokes equations is presented for an incompressible circulatory flow about an infinite circular cylinder with uniform suction or injection. An asymptotic evaluation of the solution for large time shows that, starting from a typical initial state, the flow ultimately becomes irrotational for R ≦ 1; for 1 < R ≦ 2, the initial vorticity distribution remains unchanged in the final state of flow; but for R > 2, the initial vorticity distribution changes with the circulation at infinity remaining constant: Here R = Va/v, with V, a and v being the suction velocity, radius of the cylinder and the kinematic viscosity, respectively. The torque on the cylinder has been evaluated for both small and large times.