We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ε (0, 1). We establish a diffusive homogenization limit for the tracer when the Hurst exponent H ε (0, 1/2). We also identify an intermediate range of times when the tracer behaves diffusively even when H ε (1/2, 1). The proof is based on an auxiliary limit theorem for an additive functional of a fractional Brownian motion.
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- Ecological Modeling
- Physics and Astronomy(all)
- Computer Science Applications