Abstract
In this paper, we are interested in the study of the diffusion of a passive particle with positive mass by a divergence free velocity field. We consider here the very simple turbulent shear flow case, in which we will prove the superdiffusive behaviour of the motion for large enough values of the energy spectrum of the velocity field. For small values, the proof of the diffusive behaviour of the model is also new, and it is shown that this diffusion is strictly greater than the one obtained with a non-massive particle. One interesting point to insist on is that we are able to obtain explicit hydrodynamic equations without even having the stationary measure of the studied processes
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Benabou, G. Superdiffusive Behaviour of a Passive Ornstein–Uhlenbeck Tracer in a Turbulent Shear Flow. J Stat Phys 121, 319–341 (2005). https://doi.org/10.1007/s10955-005-7003-4
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DOI: https://doi.org/10.1007/s10955-005-7003-4