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

McColl, Kaighin A.; Katul, Gabriel G.; Gentine, Pierre; Entekhabi, Dara

doi:10.1063/1.4943599

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

Journal Article · Wed Mar 16 00:00:00 EDT 2016 · Physics of Fluids

DOI:https://doi.org/10.1063/1.4943599· OSTI ID:1437155

^[1]; Katul, Gabriel G. ^[2]; Gentine, Pierre ^[3]; Entekhabi, Dara ^[4]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Civil and Environmental Engineering
Duke Univ., Durham, NC (United States). Nicholas School of the Environment, and Dept. of Civil and Environmental Engineering
Columbia Univ., New York, NY (United States). Dept. of Earth and Environmental Engineering
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

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 layer 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.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Duke Univ., Durham, NC (United States)

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

Grant/Contract Number:: SC0006967; SC0014203; SC0011461

OSTI ID:: 1437155

Journal Information:: Physics of Fluids, Vol. 28, Issue 3; ISSN 1070-6631

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

Country of Publication:: United States

Language:: English

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Cited by: 17 works

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