Lagrangian stochastic modeling of anomalous diffusion in two-dimensional turbulence

It is shown that at intermediate times, the Langevin equation corresponding to the nonlinear Fokker-Planck equation with exponents mu=1 and nu>1 produces trajectories with multifractal scaling and anomalous power-law dispersion, in common with observations of drifters in the ocean and numerical simulations of tracer particles in two-dimensional turbulence. The extent of this regime and the occurrence of anomalously large normal diffusion at much later times are shown to be in close agreement with dispersion data from numerical simulations of two-dimensional turbulence. In analogy with the dynamics of point vortices in two-dimensional turbulence, the modeled dynamics are nonergodic and effectively comprise of a background Ornstein-Uhlenbeck process punctuated by occasional fast long flights. It is shown that these dynamics optimize the nonextensive (Tsallis) entropy. It is tentatively suggested that the anomalous dispersion in two-dimensional turbulence is a consequence of smaller than average Lagrangian accelerations in regions of the flow with faster than average velocities. (C) 2002 American Institute of Physics.