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This paper is devoted to the study of the asymptotic behaviors of the minimalspeed of propagation of pulsating traveling fronts solving the Fisher-KPPreaction-advection-diffusion equation within either a large drift, a mixture oflarge drift and small reaction, or a mixture of large drift and largediffusion. We consider a periodic heterogenous framework and we use the formulaof Berestycki, Hamel and Nadirashvili \cite{bhn2} for the minimal speed ofpropagation to prove the asymptotics in any space dimension $N.$ We express thelimits as the maxima of certain variational quantities over the family of"first integrals" of the advection field. Then, we perform a detailed study inthe case N=2 which leads to a necessary and sufficient condition for thepositivity of the asymptotic limit of the minimal speed within a large drift.

The speed of propagation for KPP reaction-diffusion equations within large drift