Cospectral budget of turbulence explains the bulk properties of smooth pipe flow
Cospectral budget of turbulence explains the bulk properties of smooth pipe flow
Connections between the wall-normal turbulent velocity spectrum Eww (k) at wave number k and the mean velocity profile (MVP) are explored in pressure-driven flows confined within smooth walls at moderate to high bulk Reynolds numbers (Re). These connections are derived via a cospectral budget for the longitudinal (u') and wall-normal (w') velocity fluctuations, which include a production term due to mean shear interacting with Eww (k) , viscous effects, and a decorrelation between u' and w' by pressure-strain effects [=π(k)]. The π(k) is modeled using a conventional Rotta-like return-to-isotropy closure but adjusted to include the effects of isotropization of the production term. The resulting cospectral budget yields a generalization of a previously proposed “spectral link” between the MVP and the spectrum of turbulence. The proposed cospectral budget is also shown to reproduce the measured MVP across the pipe with changing Re including the MVP shapes in the buffer and wake regions. Because of the links between Eww (k) and the MVP, the effects of intermittency corrections to inertial subrange scales and the so-called spectral bottleneck reported as k approaches viscous dissipation eddy sizes (η) on the MVP shapes are investigated and shown to be of minor importance. Inclusion of a local Reynolds number correction to a parameter associated with the spectral exponential cutoff as kη → 1 appears to be more significant to the MVP shape in the buffer region. While the bulk shape of the MVP is reasonably reproduced in all regions of the pipe, the solution to the cospectral budget systematically underestimates the negative curvature of the MVP within the buffer layer.
063008-[8pp]
Manes, Costantino
7d9d5123-4d1b-4760-beff-d82fe0bd0acf
Katul, Gabriel
a7f3c557-0168-42c3-8e53-3e88679bafd0
December 2014
Manes, Costantino
7d9d5123-4d1b-4760-beff-d82fe0bd0acf
Katul, Gabriel
a7f3c557-0168-42c3-8e53-3e88679bafd0
Manes, Costantino and Katul, Gabriel
(2014)
Cospectral budget of turbulence explains the bulk properties of smooth pipe flow.
Physical Review E, 90 (6), .
(doi:10.1103/PhysRevE.90.063008).
Abstract
Connections between the wall-normal turbulent velocity spectrum Eww (k) at wave number k and the mean velocity profile (MVP) are explored in pressure-driven flows confined within smooth walls at moderate to high bulk Reynolds numbers (Re). These connections are derived via a cospectral budget for the longitudinal (u') and wall-normal (w') velocity fluctuations, which include a production term due to mean shear interacting with Eww (k) , viscous effects, and a decorrelation between u' and w' by pressure-strain effects [=π(k)]. The π(k) is modeled using a conventional Rotta-like return-to-isotropy closure but adjusted to include the effects of isotropization of the production term. The resulting cospectral budget yields a generalization of a previously proposed “spectral link” between the MVP and the spectrum of turbulence. The proposed cospectral budget is also shown to reproduce the measured MVP across the pipe with changing Re including the MVP shapes in the buffer and wake regions. Because of the links between Eww (k) and the MVP, the effects of intermittency corrections to inertial subrange scales and the so-called spectral bottleneck reported as k approaches viscous dissipation eddy sizes (η) on the MVP shapes are investigated and shown to be of minor importance. Inclusion of a local Reynolds number correction to a parameter associated with the spectral exponential cutoff as kη → 1 appears to be more significant to the MVP shape in the buffer region. While the bulk shape of the MVP is reasonably reproduced in all regions of the pipe, the solution to the cospectral budget systematically underestimates the negative curvature of the MVP within the buffer layer.
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e-pub ahead of print date: 10 December 2014
Published date: December 2014
Organisations:
Water & Environmental Engineering Group
Identifiers
Local EPrints ID: 372690
URI: http://eprints.soton.ac.uk/id/eprint/372690
ISSN: 1539-3755
PURE UUID: e9b3a622-73fb-4d47-ac59-6299f315bae5
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Date deposited: 17 Dec 2014 11:10
Last modified: 14 Mar 2024 18:41
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Author:
Costantino Manes
Author:
Gabriel Katul
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