On the linkage between the k ^{–5/3} spectral and k ^{–7/3} cospectral scaling in highReynolds number turbulent boundary layers
Connections between the “–5/3” spectral and “–7/3” cospectral scaling exponents characterizing the inertial subranges of the wallnormal energy spectrum and the turbulent momentum flux cospectrum are explored in the equilibrium layer of highReynolds 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 F _{uw}(k) commences at lower wavenumbers (around kz = 3) than the “–5/3” scaling in the wallnormal energy spectrum E _{ww}(k) (around kz = 6), where k is the streamwise wavenumber and z is the distance from the surface. A satisfactory explanation as to why F _{uw}(k) attains its “–7/3” inertial subrange scaling earlier than E _{ww}(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 Rottalike pressure decorrelation term with a prescribed wavenumberdependent relaxation time scale. It predicts the “–7/3” scaling for F _{uw}(k) from the “–5/3” scaling in E _{ww}(k), thereby recovering earlier results derived from dimensional considerations. A finite flux transfer term was previously proposed to explainmore »
 Authors:

^{[1]};
^{[2]}
 Boston Univ., Boston, MA (United States)
 Duke Univ., Durham, NC (United States)
 Publication Date:
 Grant/Contract Number:
 SC0011461
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Fluids
 Additional Journal Information:
 Journal Volume: 29; Journal Issue: 6; Journal ID: ISSN 10706631
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Duke Univ., Durham, NC (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC23)
 Country of Publication:
 United States
 Language:
 English
 OSTI Identifier:
 1474284
Li, Dan, and Katul, Gabriel G. On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in highReynolds number turbulent boundary layers. United States: N. p.,
Web. doi:10.1063/1.4986068.
Li, Dan, & Katul, Gabriel G. On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in highReynolds number turbulent boundary layers. United States. doi:10.1063/1.4986068.
Li, Dan, and Katul, Gabriel G. 2017.
"On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in highReynolds number turbulent boundary layers". United States.
doi:10.1063/1.4986068. https://www.osti.gov/servlets/purl/1474284.
@article{osti_1474284,
title = {On the linkage between the k–5/3 spectral and k–7/3 cospectral scaling in highReynolds 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 wallnormal energy spectrum and the turbulent momentum flux cospectrum are explored in the equilibrium layer of highReynolds 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 wallnormal 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 Rottalike pressure decorrelation term with a prescribed wavenumberdependent 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 slowcomponent 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 = {2017},
month = {6}
}