A crude upper bound for the ensemble-averaged speed of a reaction front in a fully developed turbulent shear flow has been derived from the Kolmogorov-Petrovskii-Piskunov equation modified by the convection term with Gaussian velocity field exhibiting long range correlations and infrared divergence in the limit of large Reynolds number. The analysis involves a singular perturbation for small values of the ratio of the Kolmogorov length scale to the integral length scale of turbulent flow; the principal tools used are a functional integral technique and a renormalization procedure. The basic physical result is that the infrared divergence of a random velocity field may lead to the acceleration of a coarse-grained reaction front.
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