Log-normality of temperature dissipation in a turbulent boundary layer

Using measurements of all three components of the temperature dissipation χ in a laboratory boundary layer, the measured probability density p(χ_r) of χ_r, or χ averaged over a distance r, is found to be closely log-normal over a significant range of r. The variance σ² of lnχ_r 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 χ_r 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(χ_r) but are consistent with the bounds given by Novikov's theory. It is suggested that the observed close agreement with log-normality of p(χ_r) may be misleading when sufficiently high order moments of χ_r are considered.