Stretching in a model of a turbulent flow

TL;DR

This paper investigates how Lyapunov exponents in a chaotic turbulence model depend on flow characteristics, revealing power-law relations and sensitivities to eddy interactions, with implications for understanding turbulence dynamics.

Contribution

It demonstrates a power law relation between Reynolds number and Lyapunov exponent in the KS turbulence model and explores the influence of eddy advection and stagnation points on chaos.

Findings

Lyapunov exponent scales as a power law with Reynolds number.

Lyapunov exponents are sensitive to small eddy advection by large eddies.

Number of stagnation points correlates linearly with maximum Lyapunov exponent.

Abstract

Using a multi-scaled, chaotic flow known as the KS model of turbulence, we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov exponents are sensitive to the advection of small eddies by large eddies, which can be explained by considering the Lagrangian correlation time of the smallest scales. We also relate the number of stagnation points within a flow to the maximum Lyapunov exponent, and suggest a linear dependence between the two characteristics.