Lagrangian analysis of fluid transport in empirical vortex ring flows

TLDR

Measurements of mechanically generated vortex rings show lobe dynamics during entrainment and detrainment that agree with theory, and the authors suggest extending the analysis to more complex flow geometries. The study applies dynamical systems analyses and computational tools to investigate fluid transport in both mechanically generated vortex rings and the wake of a free‑swimming jellyfish. The authors use dynamical systems techniques and computational modeling to analyze empirically measured vortex ring flows, including the jellyfish wake, to elucidate lobe dynamics. The Lagrangian framework yields entrainment rates that agree with previous Eulerian analyses for mechanical rings, but more accurately captures transport geometry in unsteady flows such as the jellyfish wake.

Abstract

In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested.