PASSAGE RATES OF PROPAGATING INTERFACES IN RANDOMLY ADVECTED MEDIA AND HETEROGENEOUS MEDIA

The mean passage rate of a propagating interface, subject to random ad vection or random variation of the local propagation speed, is investi gated analytically and computationally. A model representing the longi tudinal propagation of two points of the interface separated by a fixe d transverse distance is formulated and analyzed. In the limit of weak random perturbations, the model predicts several parameter dependence s of the mean passage rate. These predictions are evaluated by perform ing two-dimensional and three-dimensional numerical simulations of int erface propagation. The analysis addresses broadband (i.e., multiscale , as in turbulent flow) as well as narrow-band perturbations. In the b roadband case, scaling laws governing transient as well as statistical ly steady propagation are derived. The numerical simulations span a su fficient range of perturbation amplitudes to exhibit the complete ampl itude dependence of the mean passage rate, including scaling behaviors governing the weak and strong perturbation limits.