Lagrangian and Eulerian analysis of transport and mixing in the three dimensional, time dependent Hill’s spherical vortex

Abstract

In this paper, we extend the notion of Eulerian indicators (EIs), previously developed for two dimensional time dependent flows, to three dimensional time dependent flows, where the time dependence can be arbitrary. These are applied to a study of transport and mixing in the Hill’s spherical vortex subject to a linear strain rate field. We consider the axisymmetric case and the fully three dimensional case with different types of time dependence. We develop a Lagrangian characterization of transport and mixing appropriate for open three dimensional flows and we show that the EIs provide a detailed description of the flow structure that can be correlated with the Lagrangian transport and mixing results. The EIs yield results consistent with the dynamics of the Hill’s vortex flow characteristics, correlation with transverse shear, and anti-correlation with transversality.