Strongly stratified flow past a sphere at moderate Reynolds numbers

초록

Wake downstream of a sphere in the stratified flow has been of long-standing interest in fluid dynamics. Previous experimental studies have shown that planar vortex shedding is developed in the flow confined to horizontal planes behind the sphere under strong stratification; however, initiation mechanism of the vortex shedding has not been clearly understood, in particular its dependency on Reynolds and internal Froude numbers, Re and Fr. This paper presents numerical reproductions of the planar vortex shedding by solving Navier-Stokes equation for linearly stratified flow past a sphere under Boussinesq approximation. Computed results show that stationary wake on horizontal planes behind the sphere develops into a wave-like wake followed by unsteady, planar vortex shedding as the stratification increases. The effects of two-dimensionality on unsteadiness were shown by initiation of the vortex shedding found at Re as low as 150, which confirms Squire's theorem considering that three-dimensional unsteadiness initiates at about Re=300 in non-stratified flow past a sphere. The present results also show that drag increase relative to nonstratified cases is attributable to the increase of stagnation pressure on windward side due to stratification.