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Expressions for the logarithmic variations of the normalized turbulent longitudinal velocity ($$\overline{u^2p}^+$$)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 ($$\overline{u^2p}^+$$)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 E_u(k) is discussed, where k is the wavenumber. Using velocity time series sampled above a uniform ice sheet, an E_u(k) ~ k-1 scaling is confirmed for kz < 1 and kδ > 1. The data were then used tomore » analyze assumptions required for the utility of the random sweeping decorrelation (RSD) hypothesis connecting the k-1 power-law with log-scaling in ($$\overline{u^2p}^+$$)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 and kδ > 1, significant interactions among high-order turbulent velocity and velocity increments lead to the conclusion that the RSD hypothesis cannot be exactly valid. Lastly, its operational utility stems from the observations that some of the interaction terms among the high-order velocity and velocity increments act in opposite directions thereby canceling their additive effects in RSD.« less