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Title: Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage

Abstract

A series of recent studies has shown that a model of the turbulent vertical velocity variance spectrum (F vv) combined with a simplified cospectral budget can reproduce many macroscopic flow properties of turbulent wall-bounded flows, including various features of the mean-velocity profile (MVP), i.e., the "law of the wall". While the approach reasonably models the MVP's logarithmic layer, the buffer layer displays insufficient curvature compared to measurements. The assumptions are re-examined here using a direct numerical simulation (DNS) dataset at moderate Reynolds number that includes all the requisite spectral and co-spectral information. Starting with several hypotheses for the cause of the "missing" curvature in the buffer layer, it is shown that the curvature deficit is mainly due to mismatches between (i) the modelled and DNS-observed pressure-strain terms in the cospectral budget and (ii) the DNS-observed F vv and the idealized form used in previous models. By replacing the current parameterization for the pressure-strain term with an expansive version that directly accounts for wall-blocking effects, the modelled and DNS reported pressure-strain profiles match each other in the buffer and logarithmic layers. Forcing the new model with DNS-reported F vv rather than the idealized form previously used reproduces the missing buffer layermore » curvature to high fidelity thereby confirming the "spectral link" between F vv and the MVP across the full profile. A broad implication of this work is that much of the macroscopic properties of the flow (such as the MVP) may be derived from the energy distribution in turbulent eddies (i.e., F vv) representing the microstate of the flow, provided the link between them accounts for wall-blocking.« less

Authors:
ORCiD logo [1];  [2];  [3];  [4]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Civil and Environmental Engineering
  2. Duke Univ., Durham, NC (United States). Nicholas School of the Environment, and Dept. of Civil and Environmental Engineering
  3. Columbia Univ., New York, NY (United States). Dept. of Earth and Environmental Engineering
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Civil and Environmental Engineering; Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Earth, Atmospheric and Planetary Sciences
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); 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:
1437155
Grant/Contract Number:  
SC0006967; SC0014203; SC0011461
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 28; Journal Issue: 3; 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; 54 ENVIRONMENTAL SCIENCES

Citation Formats

McColl, Kaighin A., Katul, Gabriel G., Gentine, Pierre, and Entekhabi, Dara. Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage. United States: N. p., 2016. Web. doi:10.1063/1.4943599.
McColl, Kaighin A., Katul, Gabriel G., Gentine, Pierre, & Entekhabi, Dara. Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage. United States. doi:10.1063/1.4943599.
McColl, Kaighin A., Katul, Gabriel G., Gentine, Pierre, and Entekhabi, Dara. Wed . "Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage". United States. doi:10.1063/1.4943599. https://www.osti.gov/servlets/purl/1437155.
@article{osti_1437155,
title = {Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage},
author = {McColl, Kaighin A. and Katul, Gabriel G. and Gentine, Pierre and Entekhabi, Dara},
abstractNote = {A series of recent studies has shown that a model of the turbulent vertical velocity variance spectrum (Fvv) combined with a simplified cospectral budget can reproduce many macroscopic flow properties of turbulent wall-bounded flows, including various features of the mean-velocity profile (MVP), i.e., the "law of the wall". While the approach reasonably models the MVP's logarithmic layer, the buffer layer displays insufficient curvature compared to measurements. The assumptions are re-examined here using a direct numerical simulation (DNS) dataset at moderate Reynolds number that includes all the requisite spectral and co-spectral information. Starting with several hypotheses for the cause of the "missing" curvature in the buffer layer, it is shown that the curvature deficit is mainly due to mismatches between (i) the modelled and DNS-observed pressure-strain terms in the cospectral budget and (ii) the DNS-observed Fvv and the idealized form used in previous models. By replacing the current parameterization for the pressure-strain term with an expansive version that directly accounts for wall-blocking effects, the modelled and DNS reported pressure-strain profiles match each other in the buffer and logarithmic layers. Forcing the new model with DNS-reported Fvv rather than the idealized form previously used reproduces the missing buffer layer curvature to high fidelity thereby confirming the "spectral link" between Fvv and the MVP across the full profile. A broad implication of this work is that much of the macroscopic properties of the flow (such as the MVP) may be derived from the energy distribution in turbulent eddies (i.e., Fvv) representing the microstate of the flow, provided the link between them accounts for wall-blocking.},
doi = {10.1063/1.4943599},
journal = {Physics of Fluids},
number = 3,
volume = 28,
place = {United States},
year = {2016},
month = {3}
}

Journal Article:
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Cited by: 10 works
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Figures / Tables:

FIG. 1 FIG. 1: Modeled (red, dotted-dashed) and DNS (black, solid) mean velocity profiles (MVPs) for four different model variants. (a) The original model used in KM14. Inset: The idealized form for the scaled vertical velocity variance spectrum Fvv+ used in KM14, plotted on a log-log axis (solid line), where C0 ismore » the Kolmogorov constant and kα+= 1/y+ is the cutoff wavenumber (dashed line). (b) Same model as in (a), but forced with the DNS dissipation rate ϵ. Inset: Profile of the ratio between DNS TKE production P+ and dissipation rate ϵ+ (solid line), and the value assumed in KM14 (dashed line). (c) Same model as in (b), but forced with the DNS vertical velocity variance spectra Fvv+. (d) Same model as in (c), but using the new pressure-strain parameterization given in Equation (11).« less

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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.