Super‐diffusion via Lévy lagrangian velocity processes

Super‐diffusive mixing in geophysics occurs in atmospheric turbulence, near surface currents in oceans, and macro‐pore flow in the subsurface to name three of many areas. Models of super‐diffusion have been around for almost a century, yet here we put forth a new perspective on the topic which clarifies and substantially expands on classical approaches. Eighty years after it was introduced, we trivially derive Richardson's scaling law for atmospheric super‐diffusion, where the mean square separation of two tracer particles goes as t3, by assuming the Lagrangian velocity can be represented as a Brownian process. Next we generalize in the spirit of Mandelbrot's intermittency to other types of flows by employing Lagrangian velocities represented as α‐stable Lévy processes. For a specific flow field, we show how to obtain the stability parameter, α, from tracer experiments and the finite‐size Lyapunov exponent.