Fluctuations of Lyapunov Exponents in homogeneous and isotropic turbulence

TL;DR

This paper investigates the stability and fluctuations of finite-time Lyapunov exponents in homogeneous isotropic turbulence through direct numerical simulations, revealing their robustness and relation to Reynolds number and other variables.

Contribution

It demonstrates the stability of FTLE-based Lyapunov exponents across simulation parameters and clarifies previous discrepancies regarding Reynolds number dependence.

Findings

FTLE method yields stable Lyapunov exponents under parameter variations.

Lyapunov exponents reach stability faster than energy and dissipation rate.

Lyapunov exponent scaling differs in MHD flows compared to hydrodynamic flows.

Abstract

In the context of the analysis of the chaotic properties of homogeneous and isotropic turbulence, direct numerical simulations are used to study the fluctuations of the finite time Lyapunov exponent (FTLE) and its relation to Reynolds number, lattice size and the choice of the steptime used to compute the Lyapunov exponents. The results show that using the FTLE method produces Lyapunov exponents that are remarkably stable under the variation of the steptime and lattice size. Furthermore, it reaches such stability faster than other characteristic quantities such as energy and dissipation rate. These results remain even if the steptime is made arbitrarily small. A discrepancy is also resolved between previous measurements of the dependence on the Reynolds number of the Lyapunov exponent. The signal produced by different variables in the steady state is analyzed and the self decorrelation time is used to determine the run time needed in the simulations to obtain proper statistics for each variable. Finally, a brief analysis on MHD flows is also presented, which shows that the Lyapunov exponent is still a robust measure in the simulations, although the Lyapunov exponent scaling with Reynolds number is significantly different from that of magnetically neutral hydrodynamic fluids.