Experimental studies of coherent structures in an advection-reaction-diffusion system

Velocity and geometry of propagating fronts in complex convective flow fields

We numerically study the propagation of reacting fronts through three-dimensional flow fields composed of convection rolls that include time-independent cellular flow, spatiotemporally chaotic flow, and weakly turbulent flow. We quantify the asymptotic front velocity and determine its scaling with system parameters including the local angle of the convection rolls relative to the direction of front propagation. For cellular flow fields, the orientation of the convection rolls has a significant effect upon the front velocity and the front geometry remains relatively smooth. However, for chaotic and weakly turbulent flow fields, the front velocity depends upon the geometric complexity of the wrinkled front interface and does not depend significantly upon the local orientation of the convection rolls. Using the box counting dimension we find that the front interface is fractal for chaotic and weakly turbulent flows with a dimension that increases with flow complexity.

Barriers to front propagation in laminar, three-dimensional fluid flows

We present experiments on one-way barriers that block reaction fronts in a fully three-dimensional (3D) fluid flow. Fluorescent Belousov-Zhabotinsky reaction fronts are imaged with laser-scanning in a laminar, overlapping vortex flow. The barriers are analyzed with a 3D extension to burning invariant manifold (BIM) theory that was previously applied to two-dimensional advection-reaction-diffusion processes. We discover tube and sheet barriers that guide the front evolution. The experimentally determined barriers are explained by BIMs calculated from a model of the flow.

Front tracking velocimetry in advection-reaction-diffusion systems

In advection-reaction-diffusion systems, the spreading of a reactive scalar can be significantly influenced by the flow field in which it grows. In systems with sharp boundaries between reacted and unreacted regions, motion of the reaction fronts that lie at those boundaries can quantify spreading. Here, we present an algorithm for measuring the velocity of reaction fronts in the presence of flow, expanding previous work on tracking reaction fronts without flow. The algorithm provides localized measurements of front speed and can distinguish its two components: one from chemical dynamics and another from the underlying flow. We validate that the algorithm returns the expected front velocity components in two simulations and then show that in complex experimental flows, the measured front velocity maps fronts from one time step to the next self-consistently. Finally, we observe a variation of the chemical speed with flow speed in a variety of experiments with different time scales and length scales.

Optimal stretching in the reacting wake of a bluff body

We experimentally study spreading of the Belousov-Zhabotinsky reaction behind a bluff body in a laminar flow. Locations of reacted regions (i.e., regions with high product concentration) correlate with a moderate range of Lagrangian stretching and that range is close to the range of optimal stretching previously observed in topologically different flows [T. D. Nevins and D. H. Kelley, Phys. Rev. Lett. 117, 164502 (2016)]. The previous work found optimal stretching in a closed, vortex dominated flow, but this article uses an open flow and only a small area of appreciable vorticity. We hypothesize that optimal stretching is common in advection-reaction-diffusion systems with an excitation threshold, including excitable and bistable systems, and that the optimal range depends on reaction chemistry and not on flow shape or characteristic speed. Our results may also give insight into plankton blooms behind islands in ocean currents.

Front tracking for quantifying advection-reaction-diffusion

We present an algorithm for measuring the speed and thickness of reaction fronts, and from those quantities, the diffusivity and the reaction rate of the active chemical species. This front-tracking algorithm provides local measurements suitable for statistics and requires only a sequence of concentration fields. Though our eventual goal is front tracking in advection-reaction-diffusion, here we demonstrate the algorithm in reaction-diffusion. We test the algorithm with validation data in which front speed and thickness are prescribed, as well as simulation results in which diffusivity and reaction rate are prescribed. In all tests, measurements closely match true values. We apply the algorithm to laboratory experiments using the Belousov-Zhabotinsky reaction, producing speed, diffusivity, and reaction rate measurements that are statistically more robust than in prior studies. Finally, we use thickness measurements to quantify the concentration profile of chemical waves in the reaction.

Optimal Stretching in Advection-Reaction-Diffusion Systems

We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted by the same optimal range of the local advective stretching, but stronger stretching causes reaction blowout and can hinder reaction from spreading. We hypothesize that optimal stretching and blowout occur in many advection-diffusion-reaction systems, perhaps creating ecological niches for phytoplankton in the ocean.

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

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 et al. [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."