Surface and internal signatures of organized vortex motions in stratified fluids

Abstract

Internal vortex patterns and the corresponding free surface signatures generated in the late wakes by a submerged sphere moving in a stratified fluid are numerically simulated by a three-dimensional time-dependent model. The flow is assumed to be incompressible and hydrostatic with the Boussinesq approximation. A free surface is included to admit barotropic modes and to investigate the surface signature of internal vortices. 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. A split-explicit method is used to separately integrate the fast barotropic modes and the slow baroclinic 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. Sensitivity studies are performed to examine how the depth of submerged objects, the depth of channel floors, and the size of moving objects affect the evolution of the horizontal vortices. 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. The vorticity stretching thus produced in the direction of stratification is responsible for the generation and evolution of concentrated 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 they exist only in stratified fluids but not in homogeneous media. In view of the proposed mechanism, the horizontal vortices are buoyancy-induced and a model with the stratification properly represented is required to adequately describe the organized vortex motion in stratified wakes.