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

TL;DR

This paper introduces a generalized logarithmic law for high-order moments of passive scalars in turbulent boundary layers, validated with atmospheric measurements, revealing a logarithmic variation with height that aligns well with theoretical predictions.

Contribution

The paper develops and validates a new generalized logarithmic law for high-order passive scalar moments in turbulent boundary layers, combining theoretical modeling with atmospheric data.

Findings

High-order temperature moments vary logarithmically with height in the inertial sublayer.

The proposed theory accurately predicts temperature and velocity moments in the atmospheric surface layer.

The theory is more valid for passive scalars than for velocity fluctuations.

Abstract

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.