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.
Brownian Motion Random Walk Fractal Brownian Motion Persistence Length Homogeneous Turbulence
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