An internal splash: Levitation of falling spheres in stratified fluids

We experimentally explore the motion of falling spheres in strongly stratified fluids in which the fluid transitions from low density at the top to high density at the bottom and document an internal splash in which the falling sphere may reverse its direction of motion (from falling, to rising, to falling again) as it penetrates a region of strong density transition. We present measurements of the sphere's velocity and exhibit nonmonotonic sphere velocity profiles connecting the maximum and minimum terminal velocities, matching earlier measurements [J. Fluid Mech. 381, 175 (1999)], but further exhibit the new levitation phenomenon. We give a physical explanation of this motion which necessarily couples the sphere motion with the stratified fluid, and vice versa, and supplement this with a simplified, reduced mathematical model involving a nonlinear system of ordinary differential equations which captures the nonmonotonic transition and agrees with the measured velocity profiles at all depths except those in the vicinity of the sharp transition for which the model deviates from the measured speeds. We repeat the experiments adjusting the distance between the camera and falling sphere thereby reducing the optical blur associated with the change in optical refractive index associated with the strong density transition. By directly measuring the residual optical distortion with a center plane, vertical ruler, we exhibit that the measured velocity profile within the transition layer is strongly sensitive to the details of the measured optical distortion, and show subsequent improved agreement between the measurement and the model. Through direct measurement of the nonlinear mapping between physical and imaged coordinates we document measured velocity error trends which may occur from inaccurately accounting for this optical distortion. We suggest strategies for correcting this localized measurement detail generally. (C) 2004 American Institute of Physics.