Asymptotic solutions for three-dimensional low Reynolds number flow aroundan impulsively started sphere

The unsteady flow field of an incompressible viscous fluid around an impuls ively started sphere with slow motion is analyzed in detail using the metho d 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 presen t paper we show that to complete the matching process, five local regions a re necessary, unlike earlier theories, and the essential feature of these r egions is similar to the flow around a two-dimensional circular cylinder an alyzed by the present authors. Furthermore, the present paper demonstrates that the present approach leads to unique asymptotic solutions without matc hing with respect to the time coordinate.