The flux integral revisited: the Lagrangian perspective

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.