Velocity distribution around a sphere descending in a linearly stratified fluid

Since the first work on flow around an obstacle moving vertically in a stratified fluid was carried out, it has been over three decades and yet little has been observed regarding the near-wake structure. At first, the descending obstacle simply pulls the originally horizontal isopycnic surface, deforming its shape. However, as time proceeds, density diffusion becomes effective, especially in the density boundary layer around the sphere, and the fluid of non-conserved density is detached from the isopycnic surface and moves upward to return approximately to its original height, generating a buoyant jet. This thin and unique high-speed rear-jet has exceptional characteristics, one of them being that it can reach speeds greater than five times the sphere/particle velocity.  At present, it has been realized that most of the studies developed observe only the descending speed of a freely falling sphere/particle, and do not measure the fluid velocity around it. Therefore, there is need to conduct more systematic velocity measurement in order to verify the parameter dependence of the flow as predicted by the numerical simulations.

Shinya Okino, Shinsaku Akiyama and Hideshi Hanazaki from Kyoto University in Japan measured the velocity distributions around a sphere descending at constant speed. Additionally, they hoped to investigate the Froude number and the Reynolds number dependence of the velocity distributions to examine the recent predictions by numerical simulations of the buoyant jet and the boundary layer of the sphere. Their work is currently published in Journal of Fluid Mechanics.

The researchers commenced the experimental studies by setting up a test tank filled with linearly stratified salt water to a given height using a two tank method. They then used an acrylic sphere of a given radius sustained by steel wires allowing it to span obliquely across the tank. The team then generated vertical light sheet for a planar particle image velocimetry where the images of the seeding particles were photographed by a high resolution charge-coupled device camera. Eventually, the Navier–Stokes equations with a buoyancy term under the Boussinesq approximation, transport equation of density and the divergence free condition for the velocity were utilized in the numerical computations.

The authors observed that the radius of the jet and the thickness of the boundary layer were comparable, and that they decreased for smaller Froude numbers and larger Reynolds numbers. In addition, the researchers noted that the measured velocity distributions around the sphere generally agreed well with the numerical simulation.

The research team has successfully observed the flow around a sphere descending at constant speed in a salt-stratified fluid by particle image velocimetry, with particular attention being paid to its dependence on the Froude number and the Reynolds number. In their work, they have clarified many aspects of  the prediction via numerical simulations and by the linear theory of internal waves which had previously not been identified experimentally.