Scale disparity and spectral transfer in anisotropic numerical turbulence

To study the effect of cancelations within long-range interactions on local isotropy at the small scales (Waleffe, 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 find 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 influences of more local energy-cascading triadic interactions. Nevertheless, the local-to-nonlocal triadic group persists as an anisotropizing influence at later times. We find 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 influences of long range interactions should persist to higher Reynolds numbers. The residual effect of the forced distant triadic group in this low-Reynolds number simulation is found to be forward cascading, on average.