Anomalous Transport and Fractal Kinetics

Abstract

An orbit of the passive particle transport is associated with a streamline of a flow, if the flow is inviscid, stationary and incompressible. In a general situation 3D flows have a nontrivial topology of streamlines due to their chaotic behaviour. As a result of the chaos the real space has a complicated structure of islands and stochastic sea of fractal or multifractal nature. Transport of a passive particle can be described as a random walk in a multifractal medium. It is important that the random walk is also fractal in time. Altogether, this produces nontrivial exponents of the asymptotic law of the average particle displacement. A kinetic equation of particle transport is described in many details to draw the attention to new nontrivial aspects of the statistical irreversibility. The multifractal transport creates the possibility of anomalous diffusion due to the Levy process of a particle random walk or due to some analog of the Levy process. Coherent structures in the random walk of a passive particle and its intermittency are features of the fractal or multifractal space-time nature.