Vertical diffusion of the far wake of a sphere moving in a stratified fluid

Abstract

The far wake of a sphere towed horizontally in a linearly stratified fluid with Froude numbers F ∈ (0.25,12.7) and Reynolds numbers Re ∈ [150,30 000] is investigated. Regardless of the initial Froude number, the wake becomes quasi two dimensional at times large compared with the Brunt–Väisälä period. For F≤4.5, the horizontal motions are coherent over the whole depth of the wake. The wake takes the form of a regular von Kármán street for F≤1.5 but is irregular at larger F. For F≥4.5 the far wake consists of, vertically incoherent, horizontal motions in several layers. The transition occurs smoothly by a vertical decorrelation of the horizontal motion in the depth of the far which starts at F=4.5. The most novel result is that the horizontal velocity and vertical vorticity diffuse vertically in a time much shorter than predicted by a viscous diffusion law. The ratio of the observed diffusion time to the viscous diffusion time is expected to depend on Reynolds number as is indicated by a simple model.