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.