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.

• Received 11 December 2001

DOI:https://doi.org/10.1103/PhysRevE.65.066303