Integral Approach of Asymptotic Expansions for Low Reynolds Number Flow Past an Arbitrary Cylinder

An incompressible stationary flow past an arbitrary two-dimensional cylindrical body at low Reynolds number is analyzed by an asymptotic approach. First, the integral formulations are derived from the vorticity equation and the continuity equation. Second, simple integral equations with only one variable are derived from them. From these integral equations, asymptotic integral equations on the Stokes and Oseen regions are finally obtained by using the concept of both the significant integral operator given by Kida and the generalized expansions given by Skinner. Furthermore, using analytical results given by Kida, it is shown that no other local region exists.