Circular Far-Wake Flow behind a Sphere: Solutions to the Second Order

Abstract

The theory of hydrodynamic phenomenon of the axisymmetric circular far-wake flow behind a sphere is revisited in this study by the generalized similarity solution of the governing momentum equations to obtain the solutions to the second order in respect of the inverse distance from the sphere center. In case of a laminar wake, the nonlinear equation is derived from the Navier–Stokes equations; while in case of a turbulent wake, it is obtained from the Reynolds averaged Navier–Stokes (RANS) equations and the eddy viscosity concept. The first-order Oseen-type linearization yields solutions well known in the literature, but the second-order solutions obtained in this study are novel.