Abstract
The generalized log law for the high-order moments of longitudinal velocity with distance from a boundary in the inertial region is derived from the following assumptions: that the random sweeping decorrelation hypothesis applies; that the velocity statistics are near-Gaussian; and that the longitudinal velocity spectrum scales as ${k}^{\ensuremath{-}1}$ in the intermediate region. Measurements of longitudinal velocity collected within the first meter from the surface in the western deserts of Utah show good agreement with the proposed theory even under mild thermal stratification.
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