Scale disparity and spectral transfer in anisotropic numerical turbulence.

To study the e ect of cancelations within long-range interactions on local isotropy at the small scales (Wale e, Phys. Fluids A, 4, 1992), we calculate explicitly the degree of cancelation in distant triadic interactions in the simulations of Yeung & Brasseur (Phys. Fluids A, 3, 1991) and Yeung, Brasseur & Wang (to appear, J. Fluid Mech.) using the single scale disparity parameter \s" developed by Zhou (Phys. Fluids A, 5, 1993). In the simulations, initially isotropic simulated 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. We nd that the marginally distant interactions in the simulation do not cancel out under summation and that the development of small-scale anisotropy is indeed a direct consequence of the distant triadic group, as argued by Yeung et al. A reduction of anisotropy at later times occurs as a result of the isotropizing in uences of more local energy-cascading triadic interactions. Nevertheless, the distant triadic group persists as an anisotropizing in uence at later times. We nd that, whereas long-range interactions, in general, contribute little to net energy transfer into or out of a high wavenumber shell k, the anisotropic transfer of component energy within the shell increases with increasing scale separation s. These results are consistent with results by Zhou, and Brasseur & Wei (Phys. Fluids, 6, 1994), and suggest that the anisotropizing in uences of long range interactions should persist to higher Reynolds numbers. The residual e ect of the forced distant triadic group in this low-Reynolds number simulation is found to be forward cascading, on average. 1This research partially supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), M/S 132C, NASA Langley Research Center, Hampton, VA, 23681-0001 2This research was supported by NSF grant CTS 93-07973. 3This research was supported by AFOSR/URI grant AFOSR-90-0113, ONR grant N00014-92-J-1417 and ARO/URI grant DAAL03-92-G-0117.