Energy backscatter in large-eddy simulations of three-dimensional incompressible isotropic turbulence

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Abstract
The issue of energy backscatter in decaying three-dimensional incompressible isotropic turbulence is studied by means of large-eddy simulations (LES). For each set of initial parameters, multiple realizations are performed to improve the statistical convergence of the infrared modes. For an initial energy spectrum E(k, 0) ∝ k s 0 as k → 0 with s 0 = 4, LES display a non-negligible k 4 energy backscatter at subsequent times: E(k,t) ∝ t γ4 k 4. The value of γ4, superior to the 0.16 eddy-damped quasi-normal Markovian(EDQNM) value, depends upon the resolution of the simulation and the integration time. In the LES initialized with s 0 = 3.5, a weak energy growth is observed at small wavenumbers. However, the infrared energy spectrum does not develop the k 4 component predicted by Eyink and Thomson (2000 Phys. Fluids 12 477–9). With s 0 = 3, on the other hand, an almost perfect invariance of the infrared energy spectrum is observed. Attention is also paid to the energy decay laws. For s 0 = 4, energy decays as t −1.4 in the 2563 LES, which is intermediate between the EDQNM t −1.38 law and Kolmogorov's t −10/7 ≈ t −1.43 prediction. For s 0 = 3.5 and s 0 = 3, the LES energy decay law is also compared with the theoretical predictions based upon self-similarity.

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