Scaling Laws for the Longitudinal Structure Function in the Atmospheric Surface Layer

Scaling laws for the longitudinal structure function in the atmospheric surface layer (ASL) are studied using dimensional analysis and matched asymptotics. Theoretical predictions show that the logarithmic scaling for the scales larger than those of the inertial subrange recently proposed for neutral wall-bounded flows also holds for the shear-dominated ASL composed of weakly unstable, neutral, and all stable conditions (as long as continuous turbulence exists). A 2/3 power law is obtained for buoyancy-dominated ASLs. Data from the Advection Horizontal Array Turbulence Study (AHATS) field experiment confirm these scalings, and they also show that the length scale formed by the friction velocity and the turbulent kinetic energy dissipation rate consistently outperforms the distance from the ground z as the relevant scale in all cases regardless of stability. With this new length scale, the production range of the longitudinal structure function collapses for all measurement heights and stability conditions. A new variable to characterize atmospheric stability emerges from the theory: namely, the ratio between the buoyancy flux and the TKE dissipation rate.