Front dynamics in turbulent media

Abstract

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.

Front speed enhancement in cellular flows

“…In particular, introducing the Damköhler number Da = L/(U τ ) (the ratio of advective to reactive time scales) and the Péclet number P e = U L/D (the ratio of diffusive to advective time scales), we seek for an expression of the front speed as an adimensional function v f /v 0 = φ(Da, P e) ≥ 1. We will see that a crucial role in determining such a function is played by the renormalization of the diffusion constant and chemical time scale induced by the advection [14,15].…”

Front propagation in laminar flows

“…We will provide a detailed analysis of these two regimes, highlighting their differences. In the context of the thin front regime we can mention, among the many contributions, the works on the G-equation approximation and its relation with the "geometrical optics" regime [19,20], the work on turbulent flows [10,11] and the numerical study of front propagation in synthetic turbulence [23].…”

Reaction front propagation in a turbulent flow

“…In another recent work [19] rigorous bounds for FKPP front propagation speeds in simple flow geometries have been derived. More closely related to the present study are the investigations of front propagation in a two-dimensional stochastic field generated by integration of a stochastic differential equation [20,21] and meant to represent a synthetic turbulent velocity field. This work uses a source representing a cubic autocatalytic reaction k 2 ͑1−͒ and focuses primarily on qualitative properties of reaction fronts generated by synthetic velocity fields.…”