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 between flights). Flight time and sticking time
probability distribution functions (PDFs) have power law decays:
*P(t) ~ t^(-u)* and *t^(-v)* for flights and sticking,
respectively. We calculate the dependence of the variance exponent
*d* (*sigma^2 ~ t^d*) on the PDF exponents *u* and
*v*. For a broad distribution of flight times (*u* <
3), the motion is superdiffusive (1 < *d* < 2), and the
PDF has a divergent second moment, i.e., it is a Levy distribution.
For a broad distribution of sticking times (*v* < 3), either
superdiffusion or subdiffusion (*d* < 1) can occur, with
qualitative differences between symmetric and asymmetric random
walks. For narrow PDFs (*u > 3, v > 3*), normal diffusion
(*d*=1) is recovered. Predictions of the model are related to
experimental observations of transport in a rotating annulus. The
Eulerian velocity field is chaotic, yet it is still possible to
distinguish between well-defined sticking events (particles trapped
in vortices) and flights (particles making long excursions in a
jet). The distribution of flight lengths is well described by a
power law with a divergent second moment (Levy distribution). The
observed transport is strongly asymmetric and is well described by
the proposed model.