Structure-function based study on the logarithmic region in atmospheric surface layer with and without sand

In the logarithmic layer of boundary-layer turbulence, velocity structure functions scale as power and logarithmic functions of displacement at small and large scales, respectively. Using measured clear-air and sand-laden data from the atmospheric surface layer with friction Reynolds number up to 10⁶, we justify the balance between the third-order structure function divergence and shear production in the K\'arm\'an-Howarth-Monin equation in the logarithmic regime. The relative ranges of the two regimes depend on the ratio between the energy production and dissipation rate, which captures the relative strength between the anisotropic wall effect and near-isotropic dissipation.