Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis

Expressions for the logarithmic variations of the normalized turbulent longitudinal velocity (u2p¯+)1/p with normalized distance z/δ from a boundary for high-order (p) moments in the intermediate region of wall bounded flows characterized by thickness δ are derived. The ansatz that (u2p¯+)1/p variation in ln(z/δ) originates from a compound effect of random sweeping and -1 power-law scaling in the longitudinal velocity spectrum Eu(k) is discussed, where k is the wavenumber. Using velocity time series sampled above a uniform ice sheet, an Eu(k) ∼ k−1 scaling is confirmed for kz 1. The data were then used to analyze assumptions required for the utility of the random sweeping decorrelation (RSD) hypothesis connecting the k−1 power-law with log-scaling in (u2p¯+)1/p. It has been found out that while the RSD hypothesis is operationally applicable to scales associated with attached eddies bounded by kz 1, significant interactions among high-order turbulent velocity and velocity incremen...