Chaotic dynamics of super-diffusion revisited

Details Chaotic dynamics of super-diffusion revisited Chaotic dynamics of super-diffusion revisited

Apr 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009georl..3608812c&link_type=abstract

Geophysical Research Letters, Volume 36, Issue 8, CiteID L08812

Physics

Geophysics

1

Atmospheric Processes: Turbulence (4490), Mathematical Geophysics: Stochastic Processes (3235, 4468, 4475, 7857), Atmospheric Processes: Theoretical Modeling

Scientific paper

Super-diffusive mixing in geophysics occurs in atmospheric turbulence, near surface currents in the oceans, and fracture flow in the subsurface to name a few examples. Models of super-diffusion have been around since L. F. Richardson's pioneering work in the 1920's. Here we construct a family of super-diffusive stochastic processes X α (t), 0 < α, with independent, nonstationary increments, but a priori defined mean-square displacement given by t α+1. The case α = 2 corresponds to Richardson super-diffusion. The family of processes is a nonstationary extension of Brownian motion and hence completely characterized by its first two moments. The Fokker-Planck equation for X α (t) is classical diffusive with time dependent diffusion coefficient given by t α /2. In contrast to what is found in fractional Brownian motion, where the fractal dimension depends on the Hurst exponent, here the fractal dimension and hence complexity of the process is the same for all exponents α as that of classical Brownian motion. An analytical expression is developed for the finite-size Lyapunov exponent and numerical examples presented.

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