The distribution of "time of flight" in three dimensional stationary chaotic advection

TL;DR

This paper investigates the distribution of 'time of flight' in 3D stationary chaotic mixers, revealing two distinct tail behaviors—exponential with slipping walls and power-law with no-slip walls—linked to flow fixed points.

Contribution

It provides a detailed analysis of 'time of flight' distributions in 3D chaotic flows, highlighting the impact of wall conditions on tail behavior and proposing a model relating decay types to flow fixed points.

Findings

Exponential decay in slipping wall conditions, independent of Lyapunov exponent.

Power-law tail with exponent near -3 in no-slip wall conditions.

Flow fixed points influence the tail behavior of 'time of flight' distributions.

Abstract

The distributions of "time of flight" (time spent by a single fluid particle between two crossings of the Poincar\'e section) are investigated for five different 3D stationary chaotic mixers. Above all, we study the large tails of those distributions, and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically dfferent, with a very large tail following a power law with an exponent close to -3.