Scaling Laws for the Longitudinal Turbulent Heat Flux in the Atmospheric Surface Layer

Abstract The longitudinal turbulent heat flux is central to the description of vertical momentum and energy transport in stratified atmospheric boundary layers, yet its scaling behavior with respect to thermal stratification remains uncertain in comparison to better‐studied quantities such as the vertical heat flux. Here, the scaling laws of the longitudinal heat flux and its co‐spectrum in the atmosphere close to the surface as a function of wall normal distance and thermal stratification are experimentally evaluated. Measurements were conducted under varying stability regimes ranging from unstable to slightly stable at two sites. The first experiment included five high‐temporal resolution (100 Hz) velocity and temperature sensors as well as a triaxial sonic anemometer all positioned within 2 m above a bare soil surface. The second experiment included a single triaxial sonic anemometer positioned at 5 m above the surface of a grass‐covered forest clearing. The analysis first examines the Reynolds‐averaged Navier‐Stokes equations for the longitudinal heat flux and applies similarity theory to identify the dominant terms. This analysis is then used to inform a co‐spectral budget, which is used to deduce the appropriate scaling laws at large and inertial subrange scales. The proposed theory aims to reconcile discrepancies reported across field, laboratory, and numerical studies, and highlights the importance of non‐conserved scale‐wise flux transfer mechanisms unique to longitudinal heat flux in turbulent flows even when the longitudinal heat flux transport term is small.