Refined similarity hypotheses for turbulent velocity and temperature fields

Abstract

The refined similarity hypothesis of Kolmogorov [J. Fluid Mech. 13, 82 (1962)] is extended to a scalar field. These hypotheses are tested using measurements in a circular jet and the atmospheric surface layer. Over a significant part of the inertial range, statistics of the normalized stochastic variables for velocity and temperature indicate a dependence on the separation r. This dependence is also quantified through the probability density functions of the stochastic variables and the correlation between the velocity (or temperature) increment and the local energy (or temperature) dissipation rates. Probability density functions of the stochastic variables are conditioned on the local Reynolds number Rer based on r and the local energy dissipation rate. These functions depend on Rer when the latter is small and are approximately universal when Rer is very large. This behaviour is consistent with the refined similarity hypothesis. There is however a slight difference between the shapes of the conditional probability density functions in the two flows, implying a weak dependence on the turbulence Reynolds number Rλ and flow conditions.