Spatially-averaged flows over mobile rough beds: equations for the second-order velocity moments

Konstantinos Papadopoulos (Corresponding Author), Vladimir Nikora, Stuart Cameron, Mark Stewart, Christopher Gibbins

Research output: Contribution to journal › Article

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Abstract

The double-averaging methodology is used in this paper for deriving equations for the second-order velocity moments (i.e. turbulent and dispersive stresses) that emerge in the double-averaged momentum equation for incompressible Newtonian flows over mobile boundaries. The starting point in the derivation is the mass and momentum conservation equations for local (at a point) instantaneous variables that are up-scaled by employing temporal and spatial averaging. First, time-averaged conservation equations for mass, momentum, and turbulent stresses for mobile bed conditions are derived. Then, the double-averaged hydrodynamic equations obtained by spatial averaging the time-averaged equations are proposed. The derived second-order equations can serve as a basis for the construction of simplified mathematical and numerical models and for interpretation of experimental and simulation data when bed mobility is present. Potential applications include complex flow situations such as free-surface flows over vegetated or mobile sedimentary beds and flows through tidal and wind turbine arrays.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalJournal of Hydraulic Research
Early online date18 Jan 2019
DOIs
Publication statusE-pub ahead of print - 18 Jan 2019

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Momentum
Conservation
Newtonian flow
momentum
Wind turbines
Numerical models
Hydrodynamics
Mathematical models
free surface flow
wind turbine
hydrodynamics
methodology
simulation

Keywords

  • double averaging methodology
  • form-induced stress
  • mobile-boundary flows
  • second-order hydrodynamic equations
  • spatially-averaged turbulent stress
  • turbulence
  • Double averaging methodology

Cite this

Spatially-averaged flows over mobile rough beds : equations for the second-order velocity moments. / Papadopoulos, Konstantinos (Corresponding Author); Nikora, Vladimir; Cameron, Stuart; Stewart, Mark; Gibbins, Christopher.

In: Journal of Hydraulic Research, 18.01.2019, p. 1-19.

Research output: Contribution to journal › Article

Papadopoulos, K, Nikora, V, Cameron, S, Stewart, M & Gibbins, C 2019, 'Spatially-averaged flows over mobile rough beds: equations for the second-order velocity moments' Journal of Hydraulic Research, pp. 1-19. https://doi.org/10.1080/00221686.2018.1555559
Papadopoulos K, Nikora V, Cameron S, Stewart M, Gibbins C. Spatially-averaged flows over mobile rough beds: equations for the second-order velocity moments. Journal of Hydraulic Research. 2019 Jan 18;1-19. https://doi.org/10.1080/00221686.2018.1555559
Papadopoulos, Konstantinos ; Nikora, Vladimir ; Cameron, Stuart ; Stewart, Mark ; Gibbins, Christopher. / Spatially-averaged flows over mobile rough beds : equations for the second-order velocity moments. In: Journal of Hydraulic Research. 2019 ; pp. 1-19.
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abstract = "The double-averaging methodology is used in this paper for deriving equations for the second-order velocity moments (i.e. turbulent and dispersive stresses) that emerge in the double-averaged momentum equation for incompressible Newtonian flows over mobile boundaries. The starting point in the derivation is the mass and momentum conservation equations for local (at a point) instantaneous variables that are up-scaled by employing temporal and spatial averaging. First, time-averaged conservation equations for mass, momentum, and turbulent stresses for mobile bed conditions are derived. Then, the double-averaged hydrodynamic equations obtained by spatial averaging the time-averaged equations are proposed. The derived second-order equations can serve as a basis for the construction of simplified mathematical and numerical models and for interpretation of experimental and simulation data when bed mobility is present. Potential applications include complex flow situations such as free-surface flows over vegetated or mobile sedimentary beds and flows through tidal and wind turbine arrays.",
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