Surface And Internal Signatures Of Organized Vortex Motions In Stratified Fluid

Internal vortex patterns and the corresponding free surface signatures generated by a submerged sphere moving in a stratified fluid are numerically simulated by a three-dimensional time-dependent computer model. The flow is assumed to be incompressible and hydrostatic, and the Boussinesq approximation is applied. The turbulent mixing is modeled using the Smagorinsky formula for horizontal fluxes and a Richardson number closure for vertical fluxes. The numerical techniques include a second-order finite difference scheme with a staggered and stretched grid system. To efficiently handle the slow baroclinic and the fast barotropic modes in the flow, a split-explicit method is used to separately integrate the two modes in time. This method allows us to economically simulate the time history of the slowly evolving vortices. Preliminary results for the velocity field, the flow pattern, the density distribution, and the induced surface signature are presented. They consistently reveal the existence of coherent structures in the stratified flow field. A mechanism based on the interaction of the wake vorticity and the buoyancy induced oscillation is proposed for the generation and growth of the horizontal vortices in stratified fluids. This mechanism explains why the horizontal vortices appear long after the initial disturbances generated by a submerged moving body have dissipated, and why these vortices exist only in stratified fluids but not in homogenous media. In a forthcoming paper, we will examine how the density distribution, the depth of the moving object, and the depth of the channel floor affect the organized vortex structures and the corresponding surface signatures.