Crossover model for the scaling exponents of intermittent fully developed turbulence

Abstract

We consider the distribution of the velocity difference between two points separated by an inertial range distance in a high Reynolds number turbulent flow. The pth moment of this distribution is assumed to vary as the ((1/3)p)+$y_p$ power of the separation. We propose a new one-parameter model for the dependence of $y_p$ on p based on a dynamical scaling argument. We find that $y_p$=0 for p$p_c$, and is proportional to (p-$p_c$) for p>$p_c$. The model fits experiment reasonably well for $p_c$≊5, suggesting that the Kolmogorov (5/3) law for the energy spectrum is exact.