Approach to the four-fifths law for grid turbulence

Estimates of [(deltau)(3)], where deltau is the longitudinal velocity incre ment, are derived from the generalized Kolmogorov equation and measured val ues of [(deltau)(2)] in decaying grid turbulence over a range of values for the Taylor microscale Reynolds number R-lambda. These estimates are then u sed to describe the approach to the '4/5' behaviour with less ambiguity tha n the measured values of [(deltau)(3)]. Extrapolation to large values of R- lambda is implemented with the use of a Batchelor-like parametrization of [ (deltau)(2)]. The results suggest that the '4/5' behaviour is first reached , to 1% accuracy, when R-lambda exceeds about 4 x 10(4). A similar value of R-lambda is needed for [(deltau)(delta theta)(z)], where delta theta is th e temperature increment, to attain the '4/3' behaviour predicted by Yaglom.