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Lattice gas automaton approach to "Turbulent Diffusion"

Jean Pierre Boon·Eric Vanden Eijnden·David Hanon
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Abstract

A periodic Kolmogorov type flow is implemented in a lattice gas automaton. For given aspect ratios of the automaton universe and within a range of Reynolds number values, the averaged flow evolves towards a stationary two-dimensional $ABC$ type flow. We show the analogy between the streamlines of the flow in the automaton and the phase plane trajectories of a dynamical system. In practice flows are commonly studied by seeding the fluid with suspended particles which play the role of passive tracers. Since an actual flow is time-dependent and has fluctuations, the tracers exhibit interesting intrinsic dynamics. When tracers are implemented in the automaton and their trajectories are followed, we find that the tracers displacements obey a diffusion law, with ``super-diffusion'' in the direction orthogonal to the direction of the initial forcing.

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Jean Pierre Boon, Eric Vanden Eijnden, David Hanon. 2001-10-27. Lattice gas automaton approach to "Turbulent Diffusion". https://arxiv.org/abs/cond-mat/0110575

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