Lagrangian Chaos: Transport, Mixing, and Diffusion in Fluids

摘要

The problem of Lagrangian chaos (of the chaotic motion of fluid particles) isreviewed using methods and tools borrowed from the theory of dynamical systems. The main subject is the behavior of fluid particles which move according to regular velocity fields, that is, in the absence of Eulerian chaos or turbulence. In this framework, particular attention is given to the relation with mixing, transport, and diffusion phenomena in fluids. A possible general mechanism for the onset of Lagrangian chaos in two dimensional fluids is discussed. Evidence that the presence of a chaotic velocity field (Eulerian chaos) is not relevant for many properties of the particle motion is provided. Similar methods are applied to the analysis of the properties of the small scale statistics of passive scalar and magnetic fields. The long time diffusion features of contaminant particles, which show the importance of the combined effect of the molecular diffusion and the geometrical structures of the velocity field, are also studied.