Stochastic approaches to Lagrangian coherent structures

Abstract

This Note discusses a connection between deterministic Lagrangian coherent structures (robust fluid parcels which move coherently in unsteady fluid flows according to a deterministic ordinary differential equation), and the incorporation of noise or stochasticity which leads to the Fokker–Planck equation (a partial differential equation governing a probability density function). The link between these is via a stochastic ordinary differential equation. It is argued that a closer investigation of the stochastic differential equation offers additional insights to both the other approaches, and in particular to uncertainty quantification in Lagrangian coherent structures.