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, the laminar wake consists of a new wake of volume flux Q(2) corresponding to the current velocity U-2, an old wake of volume flux Q(1) corresponding to the original velocity U-1, and a transition zone that connects 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 superposed 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 with finite difference solutions for flow over a sphere at finite Reynolds numbers. The long-time unsteady flow structures due to a sudden stop (U-2 = 0) and an impulsive reverse (U-1 U-2 < 0) of the body are analysed in detail based on the asymptotic solutions for the unsteady wakes and the finite difference solutions. The elucidation of the long-time behaviour of such unsteady flows provides a framework for understanding the long-time particle dynamics at finite Reynolds number.