The motion of a cylinder of fluid released from rest in a cross-flow

Abstract

The two-dimensional motion of a cylinder of fluid released from rest into a flow that is uniform far upstream of the cylinder is studied. We consider cases where the cylinder is initially of circular cross-section and the fluid is either inviscid or viscous. For the inviscid fluid, we use analytical methods to determine the motion for small and large times after release and three numerical methods, the vortex-sheet method, the vortex-blob method and the vortex-in-cell method, to determine the intermediate-time motion. For the viscous-fluid problem we use the vortex-in-cell method with random walks to compute both the initial flow around the cylinder and the motion of the released fluid at a Reynolds number of 484. In the inviscid case, the released fluid deforms into a structure that resembles a vortex pair that propagates down stream at a speed less than the onset flow speed. In the viscous case, after a wake representative of a Kármán vortex street has developed, the released fluid usually deforms into an elongated horseshoe shape that travels downstream at a speed greater or less than the incident flow speed (depending on when in the vortex-shedding cycle the cylinder is released). The results of the numerical calculations are compared with some simple experiments in a water channel.