Scale disparity and spectral transfer in anisotropic numerical turbulence

To study the effects of cancellations within long-range interactions on isotropy at small scales, we calculate explicitly the degree of cancellation in long-range, or ''distant,'' triadic interactions in the simulations of Yeung and Brasseur [Phys. Fluids A 3, 884 (1991)] and Yeung, Brasseur, and Wang [J. Fluid Mech. 283, 43 (1995)] using the single scale disparity parameter s developed by Zhou [Phys. Fluids A 5, 1092 (1993); 5, 2511 (1993)]. In the simulations initially isotropic turbulence was subjected to coherent anisotropic forcing at the large scales and the smallest scales were found to become anisotropic as a consequence of direct large-small scale couplings and then to return towards isotropy. We verify here that the most nonlocal interactions do not cancel out under summation, that the observed small-scale anisotropy is indeed a direct result of the distant triadic group, and that the reduction of anisotropy at later times follows from the influences towards isotropy of more local energy-cascading triadic interactions. We find that as the scale separation s increases beyond about 10, the net energy transfer to or from high-wave-number shells within the distant triadic group goes asymptotically to zero, while the long-range anisotropic influences increase monotonically, indicating that long-range dynamics persists to larger scale separations and hence higher Reynolds numbers.