Joyce Lin, University of North Carolina
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, which is appropriate in the limit of small Reynolds numbers. We explored various models, simulating them numerically and discussing them analytically. The simplest model uses the familiar Stokes equations with variable density. Following the deformation of the interface, we also developed a model that includes the buoyancy force on the combined system of the sphere and displaced fluid. Yet another model uses the Maxey and Riley derivation for unsteady motion of a sphere with variable density.
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. Parallel experiments are in progress to examine the sedimentation of spheres through stratified, highly viscous fluids.
Advisor: Roberto Camassa and Rich McLaughlin (UNC)