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

Abstract

The effects of the Schmidt number (Sc) on the flow past a sphere descending in a stratified fluid are investigated using high-resolution numerical simulations over a wide range of Sc(0.7≤Sc≤2000). The results indicate that the buoyant jet appearing above the sphere is strongly influenced by density diffusion as well as buoyancy, and it becomes stronger and thinner with increasing Schmidt number. Scaling laws are derived and validated for the radius of the buoyant jet and thickness of the density boundary layer on the sphere. The former, characterized by significant density diffusion, is proportional to Fr/(ReSc), where Re[=W*(2a*)/ν*] is the Reynolds number and Fr[=W*/(N*a*)] is the Froude number (a* is the radius of the sphere, W* is the descending velocity of the sphere, ν* is the kinematic viscosity of the fluid, and N* is the Brunt–Väisälä frequency). The latter is similar to that of the passive scalar with a high Schmidt number (∝Re−1/2Sc−1/3), but a better estimate Re−1/2Fr1/4Sc−3/8 can be obtained by assuming a balance between buoyancy and viscous forces in the velocity boundary layer.