Persistence of Logarithmic Temperature Profile in Unstably Stratified Atmospheric Boundary Layers with and Without Sand

Monin-Obukhov similarity theory (MOST) is a widely used framework in atmospheric boundary layer (ASL) research. MOST predicts that the mean potential temperature profile deviates from the logarithmic law in buoyancy-dominated turbulence. However, recent studies show that the logarithmic profile remains intact in unstably stratified atmospheric boundary layers. Using data from the Qingtu Lake Observation Array(QLOA) with Reynolds number up to O(106), we investigate the similarity functions and mean temperature profile with different stability parameters and sand-bearing conditions. By assessing the accuracy of the logarithmic profile and the MOST-based empirical expressions obtained by Hogstrom and Wilson, we discover that the logarithmic law is a better fit than the MOST expressions. The Von Kármán constant of the potential temperature profile has a power function dependences on the stability parameter. In sand-laden ASLs, it is remarkable to find that the logarithmic law still holds, and the error of the MOST expressions amplifies. The von Kármán constant of potential temperature increases in sandiness conditions. Still, a quantitative theory that describes the sand effect on the mean temperature profile remains to be studied.