Vortex structure in the wake of a sphere

Abstract

Results showing the three-dimensional vortex shedding structure when a sphere is towed at a constant velocity through a stratified fluid are presented. It is found that for small Richardson numbers (weak stratification) and Reynolds numbers in the range from 4×103 to 2×104 the vortex is shed three-dimensionally. However, stratification quickly and effectively inhibits the vertical motion and the initially turbulent wake collapses and reveals the vertically oriented portion of the vortex structure, reminiscent of a two-dimensional vortex street behind a circular cylinder when viewed from above. The structure is, however, distinctly three-dimensional. It is also found that the estimated vortex shedding frequency is in reasonable agreement with previously published results for a sphere in a homogeneous fluid. It is suggested that a weak stratification is an excellent means for revealing the vortex structure of a three-dimensional body in a homogeneous fluid, and that the vortex tube in the wake of a sphere in a homogeneous fluid has a closed-end double helical structure. Two branches of the double helix are continuously unwinding in an opposite sense from the formation region. Moreover, the present double helical model satisfies Thompson’s circulation theorem in contrast to previously proposed helical models.