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

Konstantinos Papadopoulos; Vladimir Nikora; Stuart Cameron; Mark Stewart; Christopher Gibbins

doi:10.1080/00221686.2018.1555559

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

^*Corresponding author for this work

University of Nottingham Malaysia Campus

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

20 Downloads (Pure)

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 language	English
Pages (from-to)	133-151
Number of pages	19
Journal	Journal of Hydraulic Research
Volume	58
Issue number	1
Early online date	18 Jan 2019
DOIs	https://doi.org/10.1080/00221686.2018.1555559
Publication status	Published - 31 Jan 2020

Bibliographical note

This study was part of the research project ‘Hydrodynamic Transport in Ecologically Critical Heterogeneous interfaces’ (HYTECH), the support of which, under the European Union’s Seventh Framework Programme (Marie Curie Actions FP7PEOPLE-2012-ITN, European Commission [grant agreement number 316546]),is gratefully acknowledged. Financial support was also provided by the Engineering and Physical Sciences Research Council (EPSRC)/UK grant “Bed friction in roughbed free-surface ﬂows: a theoretical framework, roughness regimes, and quantiﬁcation” [grant EP/K041088/1].

Keywords

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

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10.1080/00221686.2018.1555559Licence: CC BY

Papadopolous_etal_JHR_Spatially_Averaged_VOR
© 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Final published version, 1.16 MBLicence: CC BY

Cite this

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

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.",

keywords = "double averaging methodology, form-induced stress, mobile-boundary flows, second-order hydrodynamic equations, spatially-averaged turbulent stress, turbulence",

author = "Konstantinos Papadopoulos and Vladimir Nikora and Stuart Cameron and Mark Stewart and Christopher Gibbins",

note = "This study was part of the research project {\textquoteleft}Hydrodynamic Transport in Ecologically Critical Heterogeneous interfaces{\textquoteright} (HYTECH), the support of which, under the European Union{\textquoteright}s Seventh Framework Programme (Marie Curie Actions FP7PEOPLE-2012-ITN, European Commission [grant agreement number 316546]),is gratefully acknowledged. Financial support was also provided by the Engineering and Physical Sciences Research Council (EPSRC)/UK grant “Bed friction in roughbed free-surface ﬂows: a theoretical framework, roughness regimes, and quantiﬁcation” [grant EP/K041088/1]. ",

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AU - Gibbins, Christopher

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N2 - 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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Spatially-averaged flows over mobile rough beds: equations for the second-order velocity moments

Abstract

Bibliographical note

Keywords

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Mark Stewart

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

Abstract

Bibliographical note

Keywords

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Mark Stewart

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