On the vortex dynamics of flow past a sphere at Re = 3700 in a uniformly stratified fluid

Vortex dynamics in the flow past a sphere in a linearly stratified environment is investigated numerically. Simulations are carried out for a flow with Reynolds number of Re = 3700 and for several Froude numbers ranging from the unstratified case with Fr=∞ to a highly stratified wake with Fr = 0.025. Isosurface of Q criterion is used to elucidate stratification effects on vortical structures near the sphere and in the wake. Vortical structures in the unstratified case are tube-like and show no preference in their orientation. Moderate stratification alters the orientation of vortical structures to streamwise preference but does not change their tube-like form. In strongly stratified cases with Fr≤0.5, there is strong suppression in vertical motion so that isotropically oriented vortex tubes of approximately circular cross section are replaced by flattened vortex tubes that are horizontally oriented. At Fr = 0.025, pancake eddies and surfboard-like inclined structures emerge in the near wake and have a regular streamwise spacing that is associated with the frequency of vortex shedding from the sphere. Enstrophy variance budget is used to analyze the vortical structure dynamics. Increasing stratification generally decreases enstrophy variance for Fr≥O(1) cases. The flow enters a new regime in strongly stratified cases with Fr≤ 0.25: increasing the stratification increases enstrophy variance, especially near the body. Stratification distorts the cross-sectional distribution of enstrophy variance from a circular isotropic shape in the unstratified wake into different shapes, depending on Fr and distance from the sphere, that include (1) elliptical distribution, (2) twin peaks suggestive of two-dimensional vortex shedding, and (3) triple-layer distribution where a relatively low enstrophy layer is sandwiched between the upper and the lower layers with high enstrophy. In the near wake, vortex stretching by fluctuating and mean strain are both responsible for enhancing vorticity. Increasing stratification (decreasing Fr) to O(1) values tends to suppress vortex stretching. Upon further reduction of Fr below 0.25, the vortex stretching takes large values near the sphere and, consequently, enstrophy variance in the near wake increases. The increase in vortex stretching is associated with unsteady, intermittent shedding of the boundary layer from the sides of the sphere in highly stratified wakes with Fr<0.25.