Lévy dynamics of enhanced diffusion: Application to turbulence
1987; American Physical Society; Volume: 58; Issue: 11 Linguagem: Inglês
10.1103/physrevlett.58.1100
ISSN1092-0145
AutoresMichael F. Shlesinger, Bruce J. West, J. Klafter,
Tópico(s)Advanced Thermodynamics and Statistical Mechanics
ResumoWe introduce a stochastic process called a L\'evy walk which is a random walk with a nonlocal memory coupled in space and in time in a scaling fashion. L\'evy walks result in enhanced diffusion, i.e., diffusion that grows as ${\mathrm{t}}^{\mathrm{\ensuremath{\alpha}}}$,\ensuremath{\alpha}>1. When applied to the description of a passive scalar diffusing in a fluctuating fluid flow the model generalizes Taylor's correlated-walk approach. It yields Richardson's ${\mathrm{t}}^{3}$ law for the turbulent diffusion of a passive scalar in a Kolmogorov -(5/3) homogeneous turbulent flow and also gives the deviations from the (5/3) exponent resulting from Mandelbrot's intermittency. The model can be extended to studies of chemical reactions in turbulent flow.
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