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 here 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 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 here are novel.