Scaling hypothesis leading to extended self-similarity in turbulence

A scaling hypothesis leading to extended self-similarity (ESS) for structure functions (the qth order moments of the magnitude of the longitudinal component velocity differences) in isotropic, homogeneous turbulence is proposed. This is done by generalizing the scale variable r to rg(r/L), with a crossover function g. By extending the refined self-similarity, it is shown that the presented scaling also leads to ESS for structure functions of the energy dissipation rate fluctuations, and to ESS bridging relations between velocity and dissipation rate moments. Extended self-similarity on the basis of a universal crossover function g strictly holds toward the outer scale (L) range only. Yet we find at least approximate ESS toward the viscous, inner scale (l) range. Furthermore, the probability densities for the velocity differences and the energy dissipation rate fluctuations which are compatible with this ESS are offered.