Passage rates of propagating interfaces in randomly advected media and heterogeneous media

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Abstract
The mean passage rate of a propagating interface, subject to random advection or random variation of the local propagation speed, is investigated analytically and computationally. A model representing the longitudinal propagation of two points of the interface separated by a fixed transverse distance is formulated and analyzed. In the limit of weak random perturbations, the model predicts several parameter dependences of the mean passage rate. These predictions are evaluated by performing two-dimensional and three-dimensional numerical simulations of interface propagation. The analysis addresses broadband (i.e., multiscale, as in turbulent flow) as well as narrow-band perturbations. In the broadband case, scaling laws governing transient as well as statistically steady propagation are derived. The numerical simulations span a sufficient range of perturbation amplitudes to exhibit the complete amplitude dependence of the mean passage rate, including scaling behaviors governing the weak and strong perturbation limits.

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