A Fractional PDE Approach to Turbulent Mixing; Part II: Numerical Simulation

We propose a generalizing fractional order transport model of advection-diffusion kind with fractional time- and space-derivatives, governing the evolution of passive scalar turbulence. This approach allows one to incorporate the nonlocal and memory effects in the underlying anomalous diffusion i.e., \textit{sub-to-standard} diffusion to model the trapping of particles inside the eddied, and \textit{super-diffusion} associated with the sudden jumps of particles from one coherent region to another. For this nonlocal model, we develop a high order numerical (spectral) method in addition to a fast solver, examined in the context of some canonical problems.