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

The issue of energy backscatter in decaying three-dimensional incompressibl e 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) proportional to k(s0) as k --> 0 with s(0) = 4, LES display a non-negligible k(4) energy backscatter at subsequent times: E(k, t) proportional to t(gamma4)k(4). The value of gamma (4), superior to the 0.16 eddy-damped quasi-normal Markovian (EDQNM) value, depends upon the res olution 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. How ever, the infrared energy spectrum does not develop the k(4) component pred icted 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 spectru m is observed. Attention is also paid to the energy decay laws. For s(0) = 4, energy decays as t(-1.4) in the 256(3) LES, which is intermediate betwee n the EDQNM t(-1.38) law and Kolmogorov's t(-10/7) approximate to t(-1.43) prediction. For s(0) = 3.5 and s(0) = 3, the LES energy decay law is also c ompared with the theoretical predictions based upon self-similarity.