Scaling of structure functions

In a recent paper, Benzi et al. [ Università di Roma, Report No. ROM 2F/92/54 (unpublished)] proposed that an extensive scaling region can be observed—even at moderate Reynolds numbers—when the structure functions of arbitrary order are plotted against the third-order structure function, and that the scaling region in such plots encompasses both inertial and dissipative ranges. This notion of extended self-similarity is analyzed here, and it is found that the concept is valid when it entails low-order structure functions, but that the scaling in the inertial and dissipation regions differs clearly for high orders. The same is true also for moments of the absolute value of velocity increments.