Abstract
We study a model of turbulent transport described by the motion in a Gaussian random velocity field with Kolmogorov spectrum. The field is assumed to be divergence-free, homogeneous in time and space, and Markovian in time. The molecular viscosity defines the cutoff in the Fourier space, thus regularizing the vector field of the pure infinite-Reynolds-number Kolmogorov spectrum by vector fields with smooth realizations. We provide an asymptotic bound on the effective diffusivity of the finite-Reynolds number fields as R→∞. Namely, with macroscopic parameters of the system fixed and the viscosity tending to zero, the effective diffusivity is bounded above by a constant which does not depend on the Reynolds number.
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Koralov, L. Transport by Vector Fields with Kolmogorov Spectrum. Journal of Statistical Physics 98, 405–418 (2000). https://doi.org/10.1023/A:1018691325820
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DOI: https://doi.org/10.1023/A:1018691325820