Homogenization Driven by a Fractional Brownian Motion: The Shear Layer Case
Tomasz Komorowski, Alexei Novikov, Lenya Ryzhik · Multiscale Modeling and Simulation · 2014
We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent $H\in(0,1)$. We establish a diffusive homogenization limit for the tracer when the Hurst exponent $H\in(0,1/2)$. We also identify an intermediate range of times when the tracer behaves diffusively even when $H\in(1/2,1)$. The proof is based on an auxiliary limit theorem for an additive functional of a fractional Brownian motion.