Velocity distribution around a sphere descending in a salt-stratified water

When a sphere descends at constant speed in a salt-stratified water, a thin and high-speed jet is often generated above the sphere. The phenomenon has first been observed by shadowgraph and then has been investigated numerically. In this study, a systematic measurement by particle image velocimetry (PIV) has been performed for a wide range of Froude number $Fr$ and Reynolds number $Re$, to actually observe the numerically simulated velocity distributions and confirm the accuracy of the numerical simulations for a very high Schmidt (Prandtl) number of $Sc=(Pr=)700$. The results show that the radius of the jet is proportional to both $Fr^{1/2}$ and $Re^{-1/2}$, meaning that it is proportional to $\sqrt{Fr/Re}$ (when $F < 1$). The boundary layer on the sphere surface has a thickness comparable to the jet radius, and it is also proportional to $\sqrt{Fr/Re}$. These results are in agreement with the recent numerical simulations and a simple dimensional analysis. Typical diverging internal-wave patterns, whose vertical wavelength has been predicted to be proportional to $Fr$, could also be observed.