An inertial range crossover in structure functions

Abstract

Experimental and numerical data within the traditional inertial subrange defined by the third-order structure function is used to study higher-order scaling exponents for the longitudinal and transverse structure functions. For 262<Rλ<3200, these exponents converge only over larger scales, r>rS, where rS is between η and λ and has an Rλ dependence. Below these scales, scaling exponents cannot be determined for any of the structure functions without resorting to procedures such as extended self-similarity (ESS). With ESS, different longitudinal and transverse higher-order exponents are obtained that are consistent with earlier results. The relationship of these statistics to derivative and pressure statistics, to turbulent structures and to length scales is discussed.