Kolmogorov’s refined similarity hypotheses

Using velocity data obtained in the atmospheric surface layer, we examine Kolmogorov’s refined hypotheses. In particular, we focus on the properties of the stochastic variable V=Δu(r)/(r${\mathrm{\varepsilon }}_{\mathit{r}}$ ${)}^{1/3}$, where Δu(r) is the velocity increment over a distance r, and ${\mathrm{\varepsilon }}_{\mathit{r}}$ is the dissipation rate averaged over linear intervals of size r. We show that V has an approximately universal probability density function for r in the inertial range and discuss its properties; we also examine the properties of V for r outside the inertial range.