### Vortex Ring Interaction with a Density Interface

In this calculation, we study the motion of axisymmetric vortex rings in a
sharply stratified, viscous fluid (1). Such flows are common in nature and
technology. Examples are the interaction of a ship or submarine wake with the ocean
surface, the interaction of a buoyant thermal with a temperature inversion, and turbulent
coherent structures interacting with a flame front.

The Navier-Stokes equations are solved by means of a second-order projection method
(2). Special treatment of the nonlinear terms ensures that the interface is resolved
in a robust and accurate manner.

The conditions are for a relatively stiff interface. The data was reflected across the
symmetry axis; vorticity is shown on the left, density on the right.

As the ring approaches the interface, it begins to expand, and a layer of counter-sign vorticity is formed. The ring peels vorticity from the interface, and secondary and
tertiary rings are formed which orbit around the primary ring, causing it to rebound. The
counter-sign vorticity pulls fluid back towards the symmetry axis. Eventually, a strong
backflow jet is created, and the original ring is almost completely annhialated.

(1) Daniel L. Marcus and John B. Bell, "Numerical Simulation of a Viscous Vortex
Ring Interaction with a Density Interface," *Physics of Fluids*, **6**(4),1505-1515,
1994

(2) John B. Bell and Daniel L. Marcus, "A Second-Order Projection Method for
Variable-Density Flows," *Journal of Computational Physics *., **101**,
334-348, 1992