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

## Abstract

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.

- Authors:

- Duke Univ., Durham, NC (United States). Nicholas School of the Environment; Duke Univ., Durham, NC (United States). Dept. of Civil and Environmental Engineering
- 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

- Publication Date:

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

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

- OSTI Identifier:
- 1467882

- Alternate Identifier(s):
- OSTI ID: 1322414

- Grant/Contract Number:
- SC0006967; SC0011461; NSF-EAR-1344703

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Fluids

- Additional Journal Information:
- Journal Volume: 28; Journal Issue: 9; Journal ID: ISSN 1070-6631

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Katul, Gabriel G., Banerjee, Tirtha, Cava, Daniela, Germano, Massimo, and Porporato, Amilcare.
```*Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis*. United States: N. p., 2016.
Web. doi:10.1063/1.4961963.

```
Katul, Gabriel G., Banerjee, Tirtha, Cava, Daniela, Germano, Massimo, & Porporato, Amilcare.
```*Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis*. United States. doi:10.1063/1.4961963.

```
Katul, Gabriel G., Banerjee, Tirtha, Cava, Daniela, Germano, Massimo, and Porporato, Amilcare. Wed .
"Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis". United States.
doi:10.1063/1.4961963. https://www.osti.gov/servlets/purl/1467882.
```

```
@article{osti_1467882,
```

title = {Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis},

author = {Katul, Gabriel G. and Banerjee, Tirtha and Cava, Daniela and Germano, Massimo and Porporato, Amilcare},

abstractNote = {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 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 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.},

doi = {10.1063/1.4961963},

journal = {Physics of Fluids},

number = 9,

volume = 28,

place = {United States},

year = {Wed Sep 07 00:00:00 EDT 2016},

month = {Wed Sep 07 00:00:00 EDT 2016}

}