Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow

TL;DR

This paper investigates the differences between short- and long-time transport structures in three-dimensional, time-dependent flows using dynamical systems tools, revealing the presence of regular or slowly evolving chaotic regions at short times.

Contribution

It introduces a comprehensive analysis combining classical and alternative dynamical systems tools to distinguish short- and long-time transport structures in complex flows.

Findings

Short-time transport structures include regular and slowly evolving chaotic regions.

Long-time structures differ significantly, with more developed chaotic mixing.

Tools like finite time Lyapunov exponents effectively identify these differences.

Abstract

Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this paper, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time.