Super-diffusion via Lévy lagrangian velocity processes

Details Super-diffusion via Lévy lagrangian velocity processes Super-diffusion via Lévy lagrangian velocity processes

Oct 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005georl..3219816c&link_type=abstract

Geophysical Research Letters, Volume 32, Issue 19, CiteID L19816

Physics

Geophysics

8

Atmospheric Composition And Structure: Aerosols And Particles (0345, 4801, 4906), Atmospheric Composition And Structure: Middle Atmosphere: Constituent Transport And Chemistry (3334), Atmospheric Composition And Structure: Pollution: Urban And Regional (0305, 0478, 4251), Biogeosciences: Modeling, Global Change: Oceans (1616, 3305, 4215, 4513)

Scientific paper

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.

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