SCALE DISPARITY AND SPECTRAL TRANSFER IN ANISOTROPIC NUMERICAL TURBULENCE

To study the effects of cancellations within long-range interactions o n isotropy at small scales, we calculate explicitly the degree of canc ellation in long-range, or ''distant,'' triadic interactions in the si mulations of Yeung and Brasseur [Phys. Fluids A 3, 884 (1991)] and Yeu ng, Brasseur, and Wang [J. Fluid Mech. 283, 43 (1995)] using the singl e scale disparity parameter s developed by Zhou [Phys. Fluids A 5, 109 2 (1993); 5, 2511 (1993)]. In the simulations initially isotropic turb ulence was subjected to coherent anisotropic forcing at the large scal es and the smallest scales were found to become anisotropic as a conse quence of direct large-small scale couplings and then to return toward s isotropy. We verify here that the most nonlocal interactions do not cancel out under summation, that the observed small-scale anisotropy i s indeed a direct result of the distant triadic group, and that the re duction of anisotropy at later times follows from the influences towar ds isotropy of more local energy-cascading triadic interactions. We fi nd that as the scale separation s increases beyond about 10, the net e nergy transfer to or from high-wave-number shells within the distant t riadic group goes asymptotically to zero, while the long-range anisotr opic influences increase monotonically, indicating that long-range dyn amics persists to larger scale separations and hence higher Reynolds n umbers.