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Scale-dependent error growth in Navier-Stokes simulations

Nazmi Burak Budanur* and Holger Kantz

  • Max Planck Institute for the Physics of Complex Systems (MPIPKS) Nöthnitzer Straße 38, 01187 Dresden, Germany

  • *nbudanur@pks.mpg.de
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Phys. Rev. E 106, 045102 – Published 5 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.045102

Abstract

We estimate the maximal Lyapunov exponent at different resolutions and Reynolds numbers in large eddy simulations (LES) and direct numerical simulations of sinusoidally driven Navier-Stokes equations in three dimensions. Independent of the Reynolds number when nondimensionalized by Kolmogorov units, the LES Lyapunov exponent diverges as an inverse power of the effective grid spacing showing that the fine scale structures exhibit much faster error growth rates than the larger ones. Effectively, i.e., ignoring the cutoff of this phenomenon at the Kolmogorov scale, this behavior introduces an upper bound to the prediction horizon that can be achieved by improving the precision of initial conditions through refining of the measurement grid.

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Phys. Rev. E 106, 045102– Published 5 October, 2022
  • Received 22 February 2022
  • Accepted 12 September 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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