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Turbulent diffusion as a random-walk process

W D McComb

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A random-walk type of diffusion coefficient is shown to reduce to the classical, continuum result for turbulence, in the limit of long diffusion times. The analysis is carried out in a Lagrangian frame where the mean-square displacement may be calculated explicitly, and the frequency of such displacements obtained from the Rice-Kac theorem. The further problem of finding the random-walk diffusivity in terms of Eulerian variables is considered.


PACS

05.40.Fb Random walks and Levy flights

45.20.Jj Lagrangian and Hamiltonian mechanics

47.27.nf Flows in pipes and nozzles

MSC

76F20 Dynamical systems approach to turbulence (See also 37-XX)

82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)

82B05 Classical equilibrium statistical mechanics (general)

82B21 Continuum models (systems of particles, etc.)

Subjects

Fluid dynamics

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 17 (21 November 1974)



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