NUMERICAL AVERAGING AND FAST HOMOGENIZATION

In previous work, a homogenized theory presenting effective enhanced d iffusion coefficients on large scales and long times for a passive sca lar diffusing in the presence of an incompressible, periodic, two-dime nsional, steady fluid flow has been developed which predicts sensitive mean wind dependence in the Peclet dependence of the enhanced diffusi on matrix. Specifically, it has been rigorously demonstrated that the enhanced diffusion coefficients possess a discontinuity on a dense set of mean wind directions in the limit of large Peclet number. Addition ally, at finite Peclet number, the enhanced diffusivities have been sh own numerically to admit complex Peclet dependence sensitively depende nt upon the mean wind direction. Here, we demonstrate that this renorm alized, complex, finite Peclet scaling behavior is quantitatively obse rvable in finite time using highly resolved, and carefully benchmarked Monte Carlo simulations of the underlying stochastic process through comparison of the mean-squared particle displacement with the renormal ized diffusion coefficients, and further exhibit striking agreement wi th the predictions of homogenization theory including sensitive mean w ind dependence.