  A generalized logarithmic law for high-order moments of passive scalars is
proposed for turbulent boundary layers. This law is analogous to the
generalized log law that has been proposed for high-order moments of the
turbulent longitudinal velocity and is derived by combining the random sweeping
decorrelation hypothesis with a spectral model informed by the attached eddy
hypothesis. The proposed theory predicts that the high-order moments of passive
scalar fluctuations within the inertial sublayer will vary logarithmically with
wall-normal distance ($z$). The proposed theory is evaluated using high
frequency time-series measurements of temperature and streamwise velocity
fluctuations obtained in the first meter of the atmospheric surface layer (ASL)
under near-neutral thermal stratification. The logarithmic dependence with $z$
within the inertial sublayer is observed in both the air temperature and
velocity moments, with good agreement to the predictions from the proposed
theory. Surprisingly, the proposed theory appears to be as, if not more, valid
for transported passive scalars than for the longitudinal velocity.
