Lagrangian transport through surfaces in volume-preserving flows

TL;DR

This paper introduces a Lagrangian framework for calculating scalar transport through surfaces in volume-preserving flows, applicable in complex, aperiodic fluid dynamics without relying on surface assumptions.

Contribution

It develops a novel Lagrangian method for quantifying transport through surfaces in high-dimensional, aperiodic flows, independent of surface dynamics.

Findings

Provides a new Lagrangian approach for transport calculation

Applicable to high-dimensional, aperiodic flows

Does not require assumptions on surface dynamics

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 integral of the flux density. 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 from the (Lagrangian) material perspective. We present a Lagrangian framework for calculating transport of conserved quantities through a given surface in $n$-dimensional, fully aperiodic, volume-preserving flows. Our approach does not involve any dynamical assumptions on the surface or its boundary.