Abstract
We introduce a novel stochastic process, called a Lévy Walk, to provide a statistical description of motion in a turbulent fluid. The Lévy Walk describes random (but still correlated) motion in space and time in a scaling fashion and is able to account for the motion of particles in a hierarchy of coherent structures. When Kolmogorov's -5/3 law for homogeneous turbulence is used to determine the memory of the Lévy Walk, then Richardson's 4/3 law of turbulent diffusion follows in the Mandelbrot absolute curdling limit. If, as suggested by Mandelbrot, that turbulence is isotropic, but fractal, then intermittency corrections follow in a natural fashion.
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© 1987 Springer-Verlag
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Shlesinger, M.F., West, B.J., Klafter, J. (1987). Diffusion in a turbulent phase space. In: Kim, Y.S., Zachary, W.W. (eds) The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function. Lecture Notes in Physics, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17894-5_323
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DOI: https://doi.org/10.1007/3-540-17894-5_323
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