A non-Boussinesq vortex ring*

The motion of an axisymmetric buoyant vortex ring is calculated using contour dynamics. An evolution equation for vortex sheet on the interface is obtained to account for additional physics such as buoyancy. In this talk, we will first review the Boussinesq limit. Then an equation for vortex sheet in the non-Boussinesq regime is derived. The evolution of rings using both approaches are compared for Atwood numbers. In the non-Boussinesq case, surface tension can also be introduced through a pressure jump on the interface. We also discuss the relevant dimensionless numbers and explore the dynamics of buoyant vortex rings in parameter space.