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We consider a simple model of the evolution of the concentration of a tracer,subject to a background shear flow by a fluid with viscosity $\nu \ll 1$ in aninfinite channel. Taylor observed in the 1950's that, in such a setting, thetracer diffuses at a rate proportional to $1/\nu$, rather than the expectedrate proportional to $\nu$. We provide a mathematical explanation for thisenhanced diffusion using a combination of Fourier analysis and center manifoldtheory. More precisely, we show that, while the high modes of the concentrationdecay exponentially, the low modes decay algebraically, but at an enhancedrate. Moreover, the behavior of the low modes is governed by finite-dimensionaldynamics on an appropriate center manifold, which corresponds exactly todiffusion by a fluid with viscosity proportional to $1/\nu$.

Analysis of enhanced diffusion in Taylor dispersion via a model problem