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

Doan, Minh; Simons, JJ; Lilienthal, Katherine; Solomon, Tom; Mitchell, Kevin

doi:10.1103/physreve.97.033111

Cited by 10 publications

(4 citation statements)

References 30 publications

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“…Reacting fronts that propagate through a moving fluid are important parts of many systems in science and engineering that are of intense current interest [1][2][3]. This includes geophysical problems such as the lock-exchange instability [4,5] of oceanic and atmospheric flows, the buoyancy and surface tension driven flows of chemical fronts [3,[6][7][8][9], the propagation of polymerization fronts [10], the rich spatiotemporal dynamics of forest fires [11,12], and the improved properties of combustion of pre-mixed gases in a turbulent fluid flow [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Propagating fronts in fluids with solutal feedback

Mukherjee

Paul

2020

Phys. Rev. E

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We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counter-rotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit squareroot scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counter-rotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Lastly, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.

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Section: Introductionmentioning

confidence: 99%

“…Significant attention has been paid to the study of propagating fronts through externally generated flow fields in the absence of solutal or thermal feedback (c.f. [8,[32][33][34][35]). In this case, an aspect of interest is the enhancement of the front velocity in the presence of imposed fluid motion.…”

Section: Introductionmentioning

confidence: 99%

Propagating fronts in fluids with solutal feedback

Mukherjee

Paul

2020

Phys. Rev. E

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“…This theory identifies analogs of passive transport barriers, called burning invariant manifolds (BIMs), which are one-way barriers to front propagation. Experiments on front propagation in driven fluid flows [25][26][27][28] demonstrate the physical significance of these theories. Despite this success with reaction fronts, a comparable understanding for more general active systems is lacking.…”

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confidence: 82%

Transport barriers to self-propelled particles in fluid flows

Berman,

Buggeln,

Brantley

et al. 2020

Preprint

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We present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble Bacillus subtilis bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into xy-space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.

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“…In addition, there has been a broad range of work on propagating fronts for flow fields that are not turbulent. Examples include the study of fronts in a shaken layer of liquid exhibiting Faraday waves [18], convective flows [19][20][21], Hele-Shaw flows [22], Marangoni flows [23], and fields of disordered vortices [24,25] to name a few.…”

Section: Introductionmentioning

confidence: 99%

Velocity and geometry of propagating fronts in complex convective flow fields

Mukherjee

Paul

2019

Phys. Rev. E

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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.

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

Cited by 10 publications

References 30 publications

Propagating fronts in fluids with solutal feedback

Propagating fronts in fluids with solutal feedback

Transport barriers to self-propelled particles in fluid flows

Velocity and geometry of propagating fronts in complex convective flow fields

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