Logarithmic scaling for higher-order temperature moments in the atmospheric surface layer

Analogous to the generalized log law derived for high-order moments of the turbulent longitudinal velocity, expressions for the logarithmic variations of passive scalar moments with vertical distance from a boundary in the inertial layer are derived by the random sweeping decorrelation hypothesis and the attached eddy hypothesis. The proposed theory, which includes a piecewise model spectrum for the temperature field, is tested using highly resolved measurements of temperature and streamwise velocity fluctuations obtained in the first meter of the atmospheric surface layer under unstable, near-neutral, and stable thermal stratification. The logarithmic dependence with distance from the surface within the inertial sublayer is observed in both the temperature and velocity moments, with good agreement to the predictions from the random sweeping decorrelation hypothesis. The proposed theory appears to be as, if not more, valid for transported scalars than for the velocity field under certain stability conditions.