Joyce Lin, University of North Carolina at Chapel Hill


A Falling Sphere in a Stratified Fluid

Abstract:  To model the behavior of a sphere falling under gravity through a sharply stratified fluid, we began with a Stokes approximation. This approximation is appropriate in the limit of small Reynolds numbers. Using the familiar Stokes equations, we followed the deformation of the stratification interface and found an expression for the buoyancy force on the combined system of the sphere and displaced fluid. We then refined the volume calculation using Oseen corrections and proposed a possible model, which we simulated numerically. Currently, we are working to improve the model in the low Reynolds number regime by casting the stratified version of the Stokes approximation in a form that affords efficient numerical integration of the equations of motion. A parallel experimental study is also in progress to examine the sedimentation of quasi-neutrally buoyant spheres through stratified, highly viscous fluids.


Advisors: Roberto Camassa and Rich McLaughlin (UNC)