Scale-dependent Error Growth in Navier--Stokes Simulations

Abstract

We estimate the maximal Lyapunov exponent at different resolutions and Reynolds numbers in large eddy (LES) and direct numerical simulations (DNS) 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 cut-off 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.

arXiv comment13 pages, 4 figures

References in corpus (5)

• Growth of non-infinitesimal perturbations in turbulence
• Chaos and predictability of homogeneous-isotropic turbulence
• Chaotic properties of a turbulent isotropic fluid
• Scaling of Lyapunov Exponents in Homogeneous Isotropic Turbulence
• Coarse graining the state space of a turbulent flow using periodic orbits

Cited by in corpus (3)

• Characterizing Data Assimilation in Navier-Stokes Turbulence with Transverse Lyapunov Exponents
• Synchronisation in two-dimensional damped-driven Navier-Stokes turbulence: insights from data assimilation and Lyapunov analysis
• Intrinsic relationship between synchronisation thresholds and Lyapunov vectors: evidence from large eddy simulations and shell models