General Unsteady Circulatory Flow outside a Porous Circular Cylinder with Suction or Injection

An exact solution of the Navier-Stokes equations is established for a general initial/boundary-value problem which describes the development of an incompressible circulatory flow outside an infinite circular cylinder with uniform suction or injection. An asymptotic evaluation of the solution, valid after a long time, reveals the effects of suction or injection upon the ultimate flow behavior; for R>2, the circulation at infinity remains unchanged throughout the process if it is finite initially; for R≤1, all of the vorticity, even if its amount is infinite, is blown away to infinity and the flow becomes irrotational in the final state; intermediate between them is the case of 1<R≤2. Here R=Va/v, with V, a and v being the suction velocity, radius of the cylinder and the kinematic viscosity, respectively.