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Finite-time barriers to front propagation in two-dimensional fluid flows.
John R Mahoney1, Kevin A Mitchell1
1School of Natural Sciences, University of California, Merced, California 95343.
Chaos (Woodbury, N.Y.)
|September 3, 2015
Summary
Researchers identified a new method to detect one-way dynamical barriers, called burning Lagrangian coherent structures (bLCS), in fluid flows. This technique works even with complex, time-varying fluid velocities, advancing the study of reaction fronts.
Area of Science:
- Fluid dynamics
- Chemical reaction engineering
- Dynamical systems theory
Background:
- Invariant manifolds, known as burning invariant manifolds (BIMs), act as one-way dynamical barriers for reaction fronts in fluid flows.
- Previous methods for identifying these barriers required time-independent or time-periodic fluid velocity fields.
Purpose of the Study:
- To develop a novel approach for identifying one-way dynamical barriers in fluid flows using only finite-time velocity data.
- To introduce the concept of burning Lagrangian coherent structures (bLCS) applicable to arbitrarily time-dependent flows.
Main Methods:
- The study adapts the variational formulation of Lagrangian coherent structures (LCSs) based on stationary Lagrangian shear.
- This method is applied to identify bLCS from fluid velocity data over a finite time interval.
Main Results:
- The developed approach successfully identifies prominent one-way barriers in time-dependent fluid flows.
- Numerical validation shows that the identified bLCS closely tracks the BIM in a double-vortex channel flow with opposing wind.
Conclusions:
- The new bLCS method provides a robust way to detect reaction front barriers in complex, time-varying fluid flows.
- This advancement extends the applicability of invariant manifold theory to more realistic and dynamic scenarios.
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