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