Far-wake flows downstream of cylinders: a novel generalized similarity method

Abstract

The nonlinear momentum equation for turbulent far-wake flow downstream of a cylinder is derived from the Reynolds averaged Navier–Stokes equations and solved by iteration and generalized similarity solution. The first-order Oseen-type linearization yields for the wake boundary layer width a series, whose terms vary as x^1/2, x^-1/2, x^-3/2 etc., where x is the streamwise distance from the center of cylinder. The velocity deficit from the free-stream velocity is similarly obtained as a series and the iteration is carried over to a second-order. This method is then applied to the problem of an array of cylinders. Both turbulent and laminar far-wake flow cases are analyzed. The series solutions broadly extend the earlier findings. The first-order solutions agree in form with those stated in the book of Schlichting (1979).