Chaotic advection in point vortex models and two-dimensional turbulence

Abstract

The dynamics of passively advected particles in either integrable or chaotic point vortexsystems 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 vortexmotion, but rather by pure Lagrangian quantities, such as the distance of an advected particle from the vortex centers. In fact, each point vortex turns out to be surrounded by a regular island, where the advected particles are trapped and their Lagrangian Lyapunov exponent is zero, even though the vortex itself may perform a chaotic trajectory. In the field between the vortices, passive particles undergo chaotic advection with an associated positive Lyapunov exponent. For well‐separated vortices, even at large times, the advected 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 trapped in the interior of the coherent structures have a null Lagrangian Lyapunov exponent, while those in the background turbulent sea move chaotically. This gives clear evidence of the important role played by chaotic advection, even in complex Eulerian flows.