The problem of flame propagation in a random velocity field: weak turbulence limit

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Abstract
The problem of thin flame front propagation with curvature-dependent speed in a weak turbulent flow has been considered, and its connection with classical problems in the physics of disordered systems such as polymers in a random medium, growing interfaces and n-body interaction problems has been discussed. By a path-integral approach, an explicit formula for the randomly moving flame front in terms of the fluctuating velocity field has been derived. The steepest-descent approximation has been used to find the random configuration of the flame surface in the limit of small Markstein diffusivity. New expressions for the turbulent burning velocity (the overall propagation rate of a flame surface subject to a random velocity field) involving the random velocity field along the Lagrangian trajectories have been derived.

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