Patchiness: A new diagnostic for Lagrangian trajectory analysis in time-dependent fluid flows

In 2-D time-dependent fluid hows, a patch represents a localized region in space that has a significantly different average velocity compared to its surroundings. We show that one can obtain important information about the Lagrangian particle motion in such flows by studying the nature, long-term evolution, and statistical characteristics of the patchiness behavior. For example, the dispersion of passive tracers at any time is directly related to the distribution of patches in the how. We thoroughly investigate the transport properties of the Lagrangian trajectories associated with a cellular flow previously used as a model for time-dependent Rayleigh-Benard convection, and a kinematic model of a meandering jet (originally due to Bower [1991]). In both cases, we examine the statistical attributes of the patchiness, their relationship with the geometric features of the stable and unstable manifolds, and the effect of noise on the structure of patchiness. We uncover some interesting features associated with the origin of these patches and their influence on Lagrangian transport.