An update on the intermittency exponent in turbulence

Ever since Kolmogorov’ introduced the intermittency exponent, more than a dozen attempts have been made to obtain its numerical value from experiments. The resulting estimates have varied from as low a value as 0.18 to as high as 0.7. (See Ref. 2 for a summary of early measurements, Table IV of Ref. 3 for measurements until about 1975 and Refs. 4-10 for experiments made thereafter.) It is unsatisfactory that this exponent, which plays a moderately important role in the theoretical framework of turbulence, should be known with no better certainty. We present in this Brief Communication a brief critique of the various definitions and experimental techniques used for determining the intermittency exponent, and provide the best estimate for it from recent atmospheric data. Some of this variability is clearly due to differences in the definitions of the intermittency exponent, and it is therefore essential to describe all of them briefly. We find it convenient to adopt different symbols to denote the different definitions of the intermittency exponent. First, there is the constant p1 in Kolmogorov’s lognormal hypothesis’ given by