Log-normality of temperature dissipation in a turbulent boundary layer

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Abstract
Using measurements of all three components of the temperature dissipation χ in a laboratory boundary layer, the measured probability density p (χr) of χr, or χ averaged over a distance r, is found to be closely log‐normal over a significant range of r. The variance σ2 of lnχr follows the relation σ2=A+μln(L/r), with μ=0.35, where L is an integral scale of turbulence. High order moments, up to order 5, of χr show a power‐law variation with r/L. With increasing order of the moment, the power‐law exponents become increasingly smaller than the corresponding values implied by assumed log‐normality of p (χr) but are consistent with the bounds given by Novikov’s theory. It is suggested that the observed close agreement with log‐normality of p (χr) may be misleading when sufficiently high order moments of χr are considered.