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

Katul, Gabriel G.; Banerjee, Tirtha; Cava, Daniela; Germano, Massimo; Porporato, Amilcare

doi:10.1063/1.4961963

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

Journal Article · Wed Sep 07 00:00:00 EDT 2016 · Physics of Fluids

DOI:https://doi.org/10.1063/1.4961963· OSTI ID:1467882

Katul, Gabriel G. ^[1]; Banerjee, Tirtha ^[2]; Cava, Daniela ^[3]; ^[4]; Porporato, Amilcare ^[5]

Duke Univ., Durham, NC (United States). Nicholas School of the Environment; Duke Univ., Durham, NC (United States). Dept. of Civil and Environmental Engineering; Duke University
Karlsruhe Inst. of Technology (KIT) (Germany). Inst. of Meteorology and Climate Research, Atmospheric Environment Research (IMK-IFU)
Istituto di Scienze dell Atmosfera e del Clima, Lecce (Italy). Consiglio Nazionale delle Ricerche
Duke Univ., Durham, NC (United States). Dept. of Civil and Environmental Engineering
Duke Univ., Durham, NC (United States). Nicholas School of the Environment; Duke Univ., Durham, NC (United States). Dept. of Civil and Environmental Engineering

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 to 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.

View Accepted Manuscript (DOE)

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)

Grant/Contract Number:: SC0006967; SC0011461

OSTI ID:: 1467882

Alternate ID(s):: OSTI ID: 1322414

Journal Information:: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 9 Vol. 28; ISSN 1070-6631; ISSN PHFLE6

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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