Scaling of Lyapunov exponents in homogeneous isotropic turbulence

Prakash Mohan, Nicholas Fitzsimmons, and Robert D. Moser
Phys. Rev. Fluids 2, 114606 – Published 16 November 2017

Abstract

Lyapunov exponents measure the average exponential growth rate of typical linear perturbations in a chaotic system, and the inverse of the largest exponent is a measure of the time horizon over which the evolution of the system can be predicted. Here, Lyapunov exponents are determined in forced homogeneous isotropic turbulence for a range of Reynolds numbers. Results show that the maximum exponent increases with Reynolds number faster than the inverse Kolmogorov time scale, suggesting that the instability processes may be acting on length and time scales smaller than Kolmogorov scales. Analysis of the linear disturbance used to compute the Lyapunov exponent, and its instantaneous growth, show that the instabilities do, as expected, act on the smallest eddies and that at any time, there are many sites of local instabilities.

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  • Received 20 July 2017

DOI:https://doi.org/10.1103/PhysRevFluids.2.114606

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid Dynamics

Authors & Affiliations

Prakash Mohan* and Nicholas Fitzsimmons

  • Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA

Robert D. Moser

  • Institute for Computational Engineering and Sciences and the Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA

  • *prakash@ices.utexas.edu
  • Present address: Applied Research Laboratories, the University of Texas at Austin, Austin, TX 78758; nfitz@arlut.utexas.edu
  • rmoser@ices.utexas.edu

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Issue

Vol. 2, Iss. 11 — November 2017

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