ANOMALOUS DIFFUSION IN ASYMMETRIC RANDOM-WALKS WITH A QUASI-GEOSTROPHIC FLOW EXAMPLE

We present a model of one-dimensional symmetric and asymmetric random walks. The model is applied to an experiment studying fluid transport in a rapidly rotating annulus. In the model, random walkers alternate between flights (steps of constant velocity) and sticking (pauses betw een flights). Flight time and sticking time probability distribution f unctions (PDFs) have power law decays: P(t) similar to t(-mu) and t(-n u) for flights and sticking, respectively. We calculate the dependence of the variance exponent gamma (sigma(2) similar to t(gamma)) on the PDF exponents mu and nu. For a broad distribution of flight times (mu < 3), the motion is superdiffusive (1 < gamma < 2), and the PDF has a divergent second moment, i.e., it is a Levy distribution. For a broad distribution of sticking times (nu < 3), either superdiffusion or subd iffusion (gamma < 1) can occur, with qualitative differences between s ymmetric and asymmetric walks. For narrow PDFs (mu 3, nu > 3), normal diffusion (gamma = 1) is recovered. Predictions of the model are relat ed to experimental observations of transport in a rotating annulus. Th e Eulerian velocity field is chaotic, yet it is still possible to dist inguish between well-defined sticking events (particles trapped in vor tices) and flights (particles making long excursions in a jet). The di stribution of flight lengths is well described by a power law with a d ivergent second moment (Levy distribution). The observed transport is strongly asymmetric and is well described by the proposed model.