Finite-time barriers to front propagation in two-dimensional fluid flows

TL;DR

This paper introduces a new method to identify one-way reaction front barriers in complex, time-dependent fluid flows using finite-time velocity data, extending the concept of invariant manifolds to more realistic scenarios.

Contribution

It develops a variational approach to detect burning Lagrangian coherent structures (bLCSs) based solely on finite-time velocity data, applicable to arbitrary time-dependent flows.

Findings

The method accurately identifies barriers in simulated flows.

bLCSs closely match BIMs in test cases.

Applicable to complex, time-varying fluid flows.

Abstract

Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear", introduced by Farazmand, Blazevski, and Haller [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind".