THE FLOW-FIELD DUE TO A BODY IN IMPULSIVE MOTION

An asymptotic analysis for the long-time unsteady laminar far wake of a bluff body due to a step change in its travelling velocity from U-1 to U-2 is presented. For U-1 greater than or equal to 0 and U-2 > 0, t he laminar wake consists of a new wake of volume flux Q(2) correspondi ng to the current velocity U-2, an old wake of volume flux Q(1) corres ponding to the original velocity U-1, and a transition zone that conne cts these two wakes. The transition zone acts as a sink (or a source) of volume flux (Q(2)-Q(1)) and is moving away from the body at speed U -2. Streamwise diffusion is negligible in the new and old wakes but a matched asymptotic expansion that retains the streamwise diffusion is required to determine the vorticity transport in the transition zone. A source of volume flux Q(2) located near the body needs to be superpo sed on the unsteady wake to form the global flow field around the body . The asymptotic predictions for the unsteady wake velocity, unsteady wake vorticity, and the global flow field around the body agree well w ith finite difference solutions for flow over a sphere at finite Reyno lds numbers. The long-time unsteady flow structures due to a sudden st op (U-2 = 0) and an impulsive reverse (U-1 U-2 < 0) of the body are an alysed in detail based on the asymptotic solutions for the unsteady wa kes and the finite difference solutions. The elucidation of the long-t ime behaviour of such unsteady flows provides a framework for understa nding the long-time particle dynamics at finite Reynolds number.