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We have confirmed the validity of Chatwin and Sullivan's alpha-beta model using our experimental results in a thermal wake. Using the same data set, we have also examined and validated Derksen and Sullivan's maximum entropy formulation to approximate the probability density function of a turbulent contaminant fluctuation when only the fourth and the lower order moments are known. In addition, the paper provides evidence to suggest the kurtosis is quadratically dependent on skewness. The measurements were made in a thermal wake created by a heated cylinder in a fully developed turbulent pipe flow, at 7 stations from 16.7 to 58.3 cylinder diameters downstream of the source. The Reynolds number is 180,000 based on the centreline mean velocity and the pipe diameter (or 11,000 based on the cylinder diameter). The resultspresented in this paper include the cross-stream distributions of the mean and root mean square velocity and temperature as well as the probability density functions of the temperature fluctuations. (c) 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]