Y. Zhou et al., SCALE DISPARITY AND SPECTRAL TRANSFER IN ANISOTROPIC NUMERICAL TURBULENCE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(1), 1996, pp. 1261-1264
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.