Numerical simulations and experimental measurements of dense-core vortex rings in a sharply stratified environment

Abstract

We present three-dimensional direct numerical simulations of a vortex ring settling in sharply stratified miscible ambient fluids for near two-layer configurations, and comparisons of these simulations with the results from laboratory experiments. The core fluid of the vortex rings has density higher than both the top and the bottom layers of the ambient fluid, and is fully miscible in both layers. This setup ensures a rich parameter space that we partially explore in this study. In particular, a critical (bifurcation) phenomenon is identified that distinguishes the long-time behavior of the settling vortex ring as either being fully trapped at the ambient density layer or continuing through the layer in its downward motion. This critical behavior is determined by the initial conditions (e.g. the size and speed of the vortex ring, the initial distance to the layer, etc). The numerical simulations are able to provide evidence for this in qualitative agreement with an experimental phase diagram. Our setup isolates essential elements of mixing, trapping and escape through stratified fluids in a variety of situations, such as the mixing and dispersion of pollutants and plankton in the ocean.