The role of thermal stratification on the longitudinal heat flux co-spectrum

The longitudinal heat flux is necessary to the description of momentum and energy transport in stratified atmospheric boundary layers, yet its spectral scaling behavior remains uncertain in comparison to better-studied quantities such as the vertical momentum and heat fluxes. Here, the scaling laws of the longitudinal heat flux co-spectrum in the atmosphere near the surface as a function of wall normal distance and thermal stratification are experimentally evaluated. Measurements were conducted under varying stability regimes (ranging from slightly unstable to slightly stable) using high-resolution velocity and temperature sensors. This analysis is conducted by first examining the Reynolds Averaged Navier-Stokes formulations and similarity theory to identify the dominant balance in the budget equation, which then informs the cospectral budget used to determine the appropriate scaling laws. The proposed theory reconciles discrepancies reported across field, laboratory, and numerical studies, and highlight the importance of non- conserved flux transfer mechanisms unique to longitudinal heat flux in turbulent flows.