Kr. Sreenivasan et B. Dhruva, IS THERE SCALING IN HIGH-REYNOLDS-NUMBER TURBULENCE, Progress of theoretical physics. Supplement, (130), 1998, pp. 103-120
Turbulence velocity measurements have been made in the surface layer o
f the atmosphere at Taylor microscale Reynolds numbers between 10,000
and 20,000. Even at these high Reynolds numbers, the structure functio
ns do not scale unambiguously. It is shown that the scaling improves s
ignificantly by implementing a plausible correction due to the mean sh
ear. For second and fourth order structure functions, the exponents fo
r the corrected data are close to those determined by extended self-si
milarity (ESS). ESS improves scaling enormously for all orders, and is
used to obtain exponents for moment orders between -0.08 and 10. Anom
aly prevails even for very low orders. A major qualitative conclusion
is that it is difficult to discuss the scaling effectively without fir
st understanding quantitatively the effects of finite shear and finite
Reynolds numbers.