REFINED SIMILARITY HYPOTHESES FOR TURBULENT VELOCITY AND TEMPERATURE-FIELDS

The refined similarity hypothesis of Kolmogorov [J. Fluid Mech. 13, 82 (1962)] is extended to a scalar field. These hypotheses are tested us ing measurements in a circular jet and the atmospheric ; surface layer . Over a significant part of the inertial range, statistics of the nor malized stochastic variables for velocity and temperature indicate a d ependence on the separation r. This dependence is also quantified thro ugh the probability density functions of the stochastic variables and the correlation between the velocity (or temperature) increment and th e local energy (or temperature) dissipation rates. Probability density functions of the stochastic variables are conditioned on the local Re ynolds number Re-r based on r and the local energy dissipation rate. T hese functions depend on Re-r when the latter is small and are approxi mately universal when Re-r is very large. This behaviour is consistent with the refined similarity hypothesis. There is however a slight dif ference between the shapes of the conditional probability density func tions in the two hows, implying a weak dependence on the turbulence Re ynolds number R(lambda) and flow conditions. (C) 1995 American Institu te of Physics.