Schmidt-number effects on the flow past a sphere moving vertically in a stratified diffusive fluid

The flow generated by a sphere moving vertically in a uniformly stratified fluid is investigated numerically for typical Schmidt numbers (or Prandtl numbers) which would be usually realized. For a high Schmidt number of Sc=700 typical to salt stratification, strong vertical round jet is formed in the lee of the sphere as has been demonstrated previously. On the other hand, with larger molecular diffusion typical to the heat conductivity in the water (Sc=7) and that in the air (Sc=0.7), the jet becomes much broader and the vertical velocity significantly decreases. This shows that the formation of the vertical jet is controlled by the diffusion processes of stratifying agents. Indeed, the thickness of the diffusive boundary layer along the obstacle surface determines the radius of the jet which becomes broader with larger molecular diffusion. The results demonstrate that a strong vertical jet is most likely generated in the high Schmidt-number fluid such as the sea water, suggesting that this phenomenon would be most intimately related to the phenomena in the ocean, such as the vertical movement of zooplanktons and buoys used for the ocean observation.