Asymptotic Solutions for Three-Dimensional Low Reynolds Number Flow around an Impulsively Started Sphere

The unsteady flow field of an incompressible viscous fluid around an impulsively started sphere with slow motion is analyzed in detail using the method of matched asymptotic expansions. First, integral expressions are derived from the nonlinear Oseen-type vorticity equation and then they are solved asymptotically by an approach proposed by one of the authors. In the present paper we show that to complete the matching process, five local regions are necessary, unlike earlier theories, and the essential feature of these regions is similar to the flow around a two-dimensional circular cylinder analyzed by the present authors. Furthermore, the present paper demonstrates that the present approach leads to unique asymptotic solutions without matching with respect to the time coordinate.