Extended self-similarity and hierarchical structure in turbulence.
We show that a generalization of the She-Leveque hierarchical structure [Z.S. She and E. Leveque, Phys. Rev. Lett. 72, 336 (1994)] together with a constant maximum magnitude of the velocity difference give rise to the extended self-similarity (ESS) [R. Benzi et al., Phy. Rev. E 48, R29 (1993)]. Our analysis thus suggests that the ESS measured in turbulent flows is an indication of the most intense structures being shocklike. Analyses of velocity measurements in a turbulent pipe flow support our conjecture.
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong.
Emily S C
ES
Ching
Zhen-Su
ZS
She
Weidong
W
Su
Zhengping
Z
Zou