Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows

V I Nikora (Corresponding Author), Thorsten Stroesser, Stuart M Cameron, Mark Stewart, Konstantinos Papadopoulos, Pablo Ouro Barba, Richard McSherry, Andrea Zampiron, Ivan Marusic, Roger A. Falconer

Research output: Contribution to journalArticle

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Abstract

A theoretically based relationship for the Darcy–Weisbach friction factor for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.
Original languageEnglish
Pages (from-to)626-664
Number of pages39
JournalJournal of Fluid Mechanics
Volume872
Early online date13 Jun 2019
DOIs
Publication statusPublished - 10 Aug 2019

Fingerprint

open channel flow
wall flow
Open channel flow
Wall flow
friction factor
beds
Friction
roughness
Decomposition
decomposition
Surface roughness
Reynolds number
Geometry
Induced currents
high Reynolds number
Large eddy simulation
large eddy simulation
geometry
nonuniformity
friction

Keywords

  • hydraulics
  • turbulent flows
  • waves/free-surface flows
  • waves
  • TURBULENCE STATISTICS
  • SQUARE
  • REYNOLDS
  • MODEL
  • LARGE-EDDY SIMULATION
  • PREDICT
  • free-surface flows
  • DYNAMICS
  • BED OPEN-CHANNEL
  • SKIN FRICTION

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Friction factor decomposition for rough-wall flows : theoretical background and application to open-channel flows. / Nikora, V I (Corresponding Author); Stroesser, Thorsten; Cameron, Stuart M; Stewart, Mark; Papadopoulos, Konstantinos; Barba, Pablo Ouro ; McSherry, Richard; Zampiron, Andrea; Marusic, Ivan; Falconer, Roger A.

In: Journal of Fluid Mechanics, Vol. 872, 10.08.2019, p. 626-664.

Research output: Contribution to journalArticle

Nikora, VI, Stroesser, T, Cameron, SM, Stewart, M, Papadopoulos, K, Barba, PO, McSherry, R, Zampiron, A, Marusic, I & Falconer, RA 2019, 'Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows', Journal of Fluid Mechanics, vol. 872, pp. 626-664. https://doi.org/10.1017/jfm.2019.344
Nikora, V I ; Stroesser, Thorsten ; Cameron, Stuart M ; Stewart, Mark ; Papadopoulos, Konstantinos ; Barba, Pablo Ouro ; McSherry, Richard ; Zampiron, Andrea ; Marusic, Ivan ; Falconer, Roger A. / Friction factor decomposition for rough-wall flows : theoretical background and application to open-channel flows. In: Journal of Fluid Mechanics. 2019 ; Vol. 872. pp. 626-664.
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abstract = "A theoretically based relationship for the Darcy–Weisbach friction factor for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.",
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note = "Financial support was provided by the EPSRC/UK project ‘Bed friction in rough-bed free-surface flows: a theoretical framework, roughness regimes, and quantification’ (grants EP/K041088/1 and EP/K04116/1). I.M. acknowledges the support of the Australian Research Council (grant FL120100017). The large-eddy simulations were carried out at Cardiff University’s high performance computer, which is part of the Supercomputing Wales project. Useful and stimulating discussions with M. Fletcher (Arup), P. Samuels (HR Wallingford), T. Schlicke (Scottish Environment Protection Agency) and J. Wicks (Jacobs) have been instrumental for this project and are gratefully acknowledged. The editor and three reviewers provided insightful comments and helpful suggestions that have been gratefully incorporated in the final version.",
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AU - Cameron, Stuart M

AU - Stewart, Mark

AU - Papadopoulos, Konstantinos

AU - Barba, Pablo Ouro

AU - McSherry, Richard

AU - Zampiron, Andrea

AU - Marusic, Ivan

AU - Falconer, Roger A.

N1 - Financial support was provided by the EPSRC/UK project ‘Bed friction in rough-bed free-surface flows: a theoretical framework, roughness regimes, and quantification’ (grants EP/K041088/1 and EP/K04116/1). I.M. acknowledges the support of the Australian Research Council (grant FL120100017). The large-eddy simulations were carried out at Cardiff University’s high performance computer, which is part of the Supercomputing Wales project. Useful and stimulating discussions with M. Fletcher (Arup), P. Samuels (HR Wallingford), T. Schlicke (Scottish Environment Protection Agency) and J. Wicks (Jacobs) have been instrumental for this project and are gratefully acknowledged. The editor and three reviewers provided insightful comments and helpful suggestions that have been gratefully incorporated in the final version.

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N2 - A theoretically based relationship for the Darcy–Weisbach friction factor for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.

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KW - TURBULENCE STATISTICS

KW - SQUARE

KW - REYNOLDS

KW - MODEL

KW - LARGE-EDDY SIMULATION

KW - PREDICT

KW - free-surface flows

KW - DYNAMICS

KW - BED OPEN-CHANNEL

KW - SKIN FRICTION

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