CHAOTIC ADVECTION IN POINT VORTEX MODELS AND 2-DIMENSIONAL TURBULENCE

The dynamics of passively advected particles in either integrable or c haotic point vortex systems and in two-dimensional (2-D) turbulence is studied. For point vortices, it is shown that the regular or chaotic nature of the particle trajectories is not determined by the Eulerian chaoticity of the vortex motion, but rather by pure Lagrangian quantit ies, such as the distance of an advected particle from the vortex cent ers. In fact, each point vortex turns out to be surrounded by a regula r island, where the advected particles are trapped and their Lagrangia n Lyapunov exponent is zero, even though the vortex itself may perform a chaotic trajectory. In the field between the vortices, passive part icles undergo chaotic advection with an associated positive Lyapunov e xponent. For well-separated vortices, even at large times, the advecte d particles do not cross the boundary between the chaotic sea and the regular islands surrounding the vortices. A similar situation holds in the case of forced-dissipative 2-D turbulence, where particles trappe d in the interior of the coherent structures have a null Lagrangian ly apunov exponent, while those in the background turbulent sea move chao tically. This gives clear evidence of the important role played by cha otic advection, even in complex Eulerian flows.