Scaling and renormalization for the Kolmogorov-Petrovskii-Piskunov equation with turbulent convection

The problem of determining the upper bounds for the ensemble-averaged reaction front position and speed in a fully developed three-dimensional turbulent flow has been examined, in which the reaction is of Kolmogorov-Petrovskii-Piskunov type and turbulent velocity is a Gaussian random field exhibiting long-range correlations and infrared divergence in the limit of large Reynolds number. An asymptotic method has been developed that gives the general formalism for determining the upper bounds for reaction front in the longtime, large-distance Limit. Two anomalous scaling regimes and corresponding scaling functions have been determined by the use of exact renormalization procedure.