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Cospectral budget of turbulence explains the bulk properties of smooth pipe flow.

Publication ,  Journal Article
Katul, GG; Manes, C
Published in: Physical review. E, Statistical, nonlinear, and soft matter physics
December 2014

Connections between the wall-normal turbulent velocity spectrum E(ww)(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 E(ww)(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 E(ww)(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.

Duke Scholars

Published In

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

December 2014

Volume

90

Issue

6

Start / End Page

063008

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Katul, G. G., & Manes, C. (2014). Cospectral budget of turbulence explains the bulk properties of smooth pipe flow. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 90(6), 063008. https://doi.org/10.1103/physreve.90.063008
Katul, Gabriel G., and Costantino Manes. “Cospectral budget of turbulence explains the bulk properties of smooth pipe flow.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 90, no. 6 (December 2014): 063008. https://doi.org/10.1103/physreve.90.063008.
Katul GG, Manes C. Cospectral budget of turbulence explains the bulk properties of smooth pipe flow. Physical review E, Statistical, nonlinear, and soft matter physics. 2014 Dec;90(6):063008.
Katul, Gabriel G., and Costantino Manes. “Cospectral budget of turbulence explains the bulk properties of smooth pipe flow.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 90, no. 6, Dec. 2014, p. 063008. Epmc, doi:10.1103/physreve.90.063008.
Katul GG, Manes C. Cospectral budget of turbulence explains the bulk properties of smooth pipe flow. Physical review E, Statistical, nonlinear, and soft matter physics. 2014 Dec;90(6):063008.

Published In

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

December 2014

Volume

90

Issue

6

Start / End Page

063008

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences