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Title: On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in high-Reynolds number turbulent boundary layers

Abstract

Connections between the “–5/3” spectral and “–7/3” cospectral scaling exponents characterizing the inertial subranges of the wall-normal energy spectrum and the turbulent momentum flux cospectrum are explored in the equilibrium layer of high-Reynolds number turbulent boundary layers. Previous laboratory experiments and field measurements featured here in the atmospheric boundary layer show that the “–7/3” scaling in the momentum flux cospectrum Fuw(k) commences at lower wavenumbers (around kz = 3) than the “–5/3” scaling in the wall-normal energy spectrum Eww(k) (around kz = 6), where k is the streamwise wavenumber and z is the distance from the surface. A satisfactory explanation as to why Fuw(k) attains its “–7/3” inertial subrange scaling earlier than Eww(k) in wavenumber space remains elusive. A cospectral budget (CSB) model subject to several simplifications and closure schemes offers one viewpoint. In its simplest form, the CSB model assumes a balance at all k between the production term and a Rotta-like pressure decorrelation term with a prescribed wavenumber-dependent relaxation time scale. It predicts the “–7/3” scaling for Fuw(k) from the “–5/3” scaling in Eww(k), thereby recovering earlier results derived from dimensional considerations. A finite flux transfer term was previously proposed to explain anomalous deviations from the “–7/3” cospectralmore » scaling in the inertial subrange using a simplified spectral diffusion closure. However, this explanation is not compatible with an earlier commencement of the “–7/3” scaling in Fuw(k). An alternative explanation that does not require a finite flux transfer is explored here. By linking the relaxation time scale in the slow-component of the Rotta model to the turbulent kinetic energy (TKE) spectrum, the earlier onset of the “–7/3” scaling in Fuw(k) is recovered without attainment of a “–5/3” scaling in Eww(k). In conclusion, the early onset of the “–7/3” scaling at smaller k is related to a slower than k–5/3 decay in the TKE spectrum at the crossover from production to inertial scales.« less

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Boston Univ., Boston, MA (United States)
  2. Duke Univ., Durham, NC (United States)
Publication Date:
Research Org.:
Duke Univ., Durham, NC (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER)
OSTI Identifier:
1474284
Grant/Contract Number:  
SC0011461
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 29; Journal Issue: 6; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES

Citation Formats

Li, Dan, and Katul, Gabriel G. On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in high-Reynolds number turbulent boundary layers. United States: N. p., 2017. Web. doi:10.1063/1.4986068.
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Li, Dan, & Katul, Gabriel G. On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in high-Reynolds number turbulent boundary layers. United States. https://doi.org/10.1063/1.4986068
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Li, Dan, and Katul, Gabriel G. Wed . "On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in high-Reynolds number turbulent boundary layers". United States. https://doi.org/10.1063/1.4986068. https://www.osti.gov/servlets/purl/1474284.
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@article{osti_1474284,
title = {On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in high-Reynolds number turbulent boundary layers},
author = {Li, Dan and Katul, Gabriel G.},
abstractNote = {Connections between the “–5/3” spectral and “–7/3” cospectral scaling exponents characterizing the inertial subranges of the wall-normal energy spectrum and the turbulent momentum flux cospectrum are explored in the equilibrium layer of high-Reynolds number turbulent boundary layers. Previous laboratory experiments and field measurements featured here in the atmospheric boundary layer show that the “–7/3” scaling in the momentum flux cospectrum Fuw(k) commences at lower wavenumbers (around kz = 3) than the “–5/3” scaling in the wall-normal energy spectrum Eww(k) (around kz = 6), where k is the streamwise wavenumber and z is the distance from the surface. A satisfactory explanation as to why Fuw(k) attains its “–7/3” inertial subrange scaling earlier than Eww(k) in wavenumber space remains elusive. A cospectral budget (CSB) model subject to several simplifications and closure schemes offers one viewpoint. In its simplest form, the CSB model assumes a balance at all k between the production term and a Rotta-like pressure decorrelation term with a prescribed wavenumber-dependent relaxation time scale. It predicts the “–7/3” scaling for Fuw(k) from the “–5/3” scaling in Eww(k), thereby recovering earlier results derived from dimensional considerations. A finite flux transfer term was previously proposed to explain anomalous deviations from the “–7/3” cospectral scaling in the inertial subrange using a simplified spectral diffusion closure. However, this explanation is not compatible with an earlier commencement of the “–7/3” scaling in Fuw(k). An alternative explanation that does not require a finite flux transfer is explored here. By linking the relaxation time scale in the slow-component of the Rotta model to the turbulent kinetic energy (TKE) spectrum, the earlier onset of the “–7/3” scaling in Fuw(k) is recovered without attainment of a “–5/3” scaling in Eww(k). In conclusion, the early onset of the “–7/3” scaling at smaller k is related to a slower than k–5/3 decay in the TKE spectrum at the crossover from production to inertial scales.},
doi = {10.1063/1.4986068},
journal = {Physics of Fluids},
number = 6,
volume = 29,
place = {United States},
year = {Wed Jun 21 00:00:00 EDT 2017},
month = {Wed Jun 21 00:00:00 EDT 2017}
}
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