Chaotic Jets

In chaotic Hamiltonian flows, nearby trajectories often separate exponentially, but some regions are almost regular and can trap particles for long times. Trapping produces heavy-tailed, non-Gaussian transport that is not described by ordinary diffusion. The authors revisit the idea of a 'chaotic jet' as a local region where this trapping happens, and they introduce a diagnostic to detect it.

The diagnostic is based on the local stretching rate. A tiny pair of tracer particles is followed until their separation grows from a small scale delta to a larger scale epsilon. The time needed for this growth, delta t, defines the local rate sigma_L = ln(epsilon/delta)/delta t, a finite-time Lyapunov exponent. The authors compute many such rates for passive tracers advected by a flow generated by point vortices, a standard Hamiltonian model of two-dimensional fluids. They find that the distribution of exit times delta t has a power-law tail with exponent gamma about 2.82, the hallmark of anomalous transport, while the distribution of local rates sigma_L has an exponential tail with characteristic value sigma_L0 about 0.4. Small values of sigma_L correspond to long trapping, so the exponential tail of local stretching rates appears to be connected to the heavy tail of trapping times.

The practical value is a local indicator: instead of running very long global simulations to measure transport exponents, one might estimate the statistics of local stretching to identify the regions responsible for anomalous transport. The main caveat is that sigma_L and delta t are linked by definition, so the explanation is not fully independent of the quantity being explained.