The flux integral revisited: the Lagrangian perspective

Abstract: 

Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known flux integral. The recent development of highly accurate semi-Lagrangian methods for solving scalar conservation laws and of Lagrangian approaches to coherent structures in turbulent (geophysical) fluid flows necessitate a new approach to transport, i.e. accumulated (over time) flux, from the (Lagrangian) material perspective.

In my talk, I will present a Lagrangian framework for calculating transport of conserved quantities through a given (hyper-)surface in n-dimensional, fully aperiodic, volume-preserving flows.