Abstract: Vortex rings are known to emerge in a variety of flows relevant to astrophysics, high energy density physics, and inertial confinement fusion, where they can significantly affect the flow through the transport of vorticity. We systematically study the generation and scaling of such rings utilizing a numerical platform involving a shock passing through an interface separating two dissimilar fluids along which there is a hole filled with the heavier fluid. As the shock passes through the interface, it deposits baroclinic vorticity that induces a complex phase inversion process ultimately resulting in the ejection of a ring from the hole. By modulating the aspect ratio of the hole, the amount of vorticity in the flow available to the ring is controlled. Based on the aspect ratio of the ring, we find that two distinct flow regimes emerge. For small aspect ratios, a single ring is generated that contains the majority of the vorticity deposited by the shock. Beyond a critical hole aspect ratio, however, the circulation of the ejected ring saturates, and the additional vorticity in the flow accumulates in a jet that trails the leading ring. This behavior suggests the existence of a fundamental formation number governing the scaling of rings generated from shock-accelerated interfaces, including those in Richtmyer-Meshkov flows.

This work is funded by the U.S. Department of Energy (DOE) NNSA Center of Excellence under cooperative agreement number DE-NA0003869 and by the U.S. DOE NNSA Stewardship Science Graduate Fellowship under grant DE-NA0003960.