Turbulent front speed in the Fisher equation: Dependence on Damköhler number

Brandenburg, Axel; Haugen, Nils Erland L.; Babkovskaia, Natalia

doi:10.1103/physreve.83.016304

Cited by 11 publications

(29 citation statements)

References 24 publications

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“…The term [49], where a reactive front propagation in a turbulent flow was studied using the Kolmogorov-Petrovskii-Piskunov-Fisher equation. To describe the interaction with a turbulent velocity field an advection term was added to this equation, so that advection-reaction-diffusion equation reads [49]:…”

Section: Turbulent Transport Of Admixtures and Temperaturementioning

confidence: 99%

“…This equation has also been amended by an advection term to describe the interaction with a turbulent velocity field [52,53]. In MFS of [49] memory effects of turbulent diffusion have been taken into account to determine the front speed in the case when the turbulent time, τ 0 , is much larger than the characteristic chemical time, τ c . It was found that the memory effects saturate the front speed to values of the turbulent speed, while the nonlinearity of the reaction term increases the front speed.…”

Section: Introductionmentioning

confidence: 99%

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Turbulent diffusion of chemically reacting gaseous admixtures

2014

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We study turbulent diffusion of chemically reacting gaseous admixtures in a developed turbulence. In our previous study [Phys. Rev. Lett. 80, 69 (1998)] using a path-integral approach for a delta-correlated in time random velocity field, we demonstrated a strong modification of turbulent transport in fluid flows with chemical reactions or phase transitions. In the present study we use the spectral tau approximation, that is valid for large Reynolds and Peclet numbers, and show that turbulent diffusion of the reacting species can be strongly depleted by a large factor that is the ratio of turbulent and chemical times (turbulent Damköhler number). We have demonstrated that the derived theoretical dependence of turbulent diffusion coefficient versus the turbulent Damköhler number is in a good agreement with that obtained previously in the numerical modelling of a reactive front propagating in a turbulent flow and described by the Kolmogorov-Petrovskii-Piskunov-Fisher equation. We have found that turbulent cross-effects, e.g., turbulent mutual diffusion of gaseous admixtures and turbulent Dufour-effect of the chemically reacting gaseous admixtures, are less sensitive to the values of stoichiometric coefficients. The mechanisms of the turbulent cross-effects are different from the molecular cross effects known in irreversible thermodynamics. In a fully developed turbulence and at large Peclet numbers the turbulent cross-effects are much larger than the molecular ones. The obtained results are applicable also to heterogeneous phase transitions.

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Section: Turbulent Transport Of Admixtures and Temperaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Turbulent diffusion of chemically reacting gaseous admixtures

2014

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“…From our numerical simulations, we find that H is negligible. We further assume: (a) the turbulence time scales are smaller than the scales associated with the front so that the time variation of the turbulent fluctuations in the velocity field can be ignored in the evolution equation for F ; (b) isotropic velocity field vv = v 2 I; and (c) the τ approximation vv · ∇c = vc /τ [17]. Then from Eq.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…Using the procedure outlined in Ref. [17], we now briefly describe the methodology to obtain the eddy diffusivity for model A. Assuming very small variations of the concentration field perpendicular to the direction of front propagation, we decompose these as c(x, y) = c(x) + c (x, y).…”

Section: Acknowledgmentsmentioning

confidence: 99%

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Front structure and dynamics in dense colonies of motile bacteria: Role of active turbulence

2016

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We study the spreading of a bacterial colony undergoing turbulent like collective motion. We present two minimalistic models to investigate the interplay between population growth and coherent structures arising from turbulence. Using Direct Numerical Simulation (DNS) of the proposed models we find that turbulence has two prominent effects on the spatial growth of the colony: (a) the front speed is enhanced, and (b) the front gets crumpled. Both these effects, which we highlight by using statistical tools, are markedly different in our two models. We also show that the crumpled front structure and the passive scalar fronts in random flows are related in certain regimes.

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Dependence of advection-diffusion-reaction on flow coherent structures

Tang

Luna

2013

Physics of Fluids

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A study on an advection-diffusion-reaction system is presented. Variability of the reaction process in such a system triggered by a highly localized source is quantified. It is found, for geophysically motivated parameter regimes, that the difference in bulk concentration subject to realizations of different source locations is highly correlated with the local flow topology of the source. Such flow topologies can be highlighted by Lagrangian coherent structures. Reaction is relatively enhanced in regions of strong stretching, and relatively suppressed in regions where vortices are present. In any case, the presence of a divergence-free background flow helps speed up the reaction process, especially when the flow is time-dependent. Probability density of various quantities characterizing the reaction processes is also obtained. This reveals the inherent complexity of the reaction-diffusion process subject to nonlinear background stirring.

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Turbulent front speed in the Fisher equation: Dependence on Damköhler number

Cited by 11 publications

References 24 publications

Turbulent diffusion of chemically reacting gaseous admixtures

Turbulent diffusion of chemically reacting gaseous admixtures

Front structure and dynamics in dense colonies of motile bacteria: Role of active turbulence

Dependence of advection-diffusion-reaction on flow coherent structures

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