Bed friction in rough-bed free-surface flows: a theoretical framework, roughness regimes, and quantification

Lead Research Organisation: University of Aberdeen
Department Name: Engineering


The problem of hydraulic resistance in wall-bounded flows remains among the hottest research topics in theoretical and applied fluid mechanics in spite of also being one of the most long-standing hydraulic problems. Researchers continue exploring a wide variety of empirical and conceptual approaches to resolve this problem, particularly focusing on the parameterisation of the bed friction that controls water levels, flood inundation extent, flow rates, depths, and water velocities. The approach currently used for quantifying bed friction is mostly empirical and thus should be considered the weakest component of otherwise quite sophisticated design and modelling methodologies. Despite world-wide efforts to advance capabilities for prediction and control of water levels in free surface flows, especially during flood events, hydraulic engineers still use empirical or semi-empirical relationships for 'roughness' or 'friction' factors. These resistance coefficients subsume the combined effects of complex hydrodynamic processes in simple forms making them convenient for practical applications. There is a general agreement that these resistance coefficients depend on parameters of the flow, bed material, bed and channel forms, and in-stream and bank vegetation. Although the quantitative form of this dependence has been targeted by several generations of hydraulicians, available relationships linking the resistance coefficients to flow and roughness parameters are still largely empirical rather than theoretically justified. As a result, the level of uncertainties of hydraulic models of overland flows, canals, waterways, rivers, and estuaries remains high, often exceeding 20-40%. The central goal of the project is therefore to develop advanced predictive capabilities for quantification of hydraulic resistance in rough-bed open-channel flows and propose a methodology for incorporation of the theoretical and physical insights from this study into applied hydraulic models that are most relevant to the end-users. To achieve this goal, the project team will build a rigorous theoretical framework to explicitly reveal contributions to the total bed friction from viscous, turbulent, and form-induced stresses, secondary currents, non-uniformity, and unsteadiness, and link these contributions to the physics of the flow. This theoretical analysis will underpin sophisticated laboratory experiments in Aberdeen and Large Eddy Simulation numerical studies in Cardiff to clarify the nature of bed friction in open-channel flows, refine the definitions of the roughness regimes, and identify and quantify the contributions to the overall friction from the dominant friction-generated mechanisms. The combination of the theoretical analysis with laboratory and numerical studies will lead to the generalised relationships for the friction coefficients suitable for applied hydraulic models. The examples of benefits that the proposed research will bring include significantly reduced uncertainties in predictions of water levels and flood inundation extent; better urban planning and new design philosophies based on friction control/reduction aptitudes that this research intends to develop (e.g., 'friction-reduced' urban planning as part of 'green cities' concept and more efficient drainage systems); and improved stream restoration design and implementation, among many others. The theoretical and methodological developments of the project will be also applicable, in addition to water engineering, to other areas such as aerospace and mechanical engineering, where drag control studies are particularly important and continue to grow. The interdisciplinary fields of overland flow and soil erosion, biomimetics, and ecosystems (both terrestrial and aquatic), represent other examples where the outcomes of this project can be directly employed.

Planned Impact

The design, maintenance, prediction, and control of any waterway, either natural or constructed, are essential elements of water and waterway engineering that determine safety, security, efficiency, and cost of urban and rural infrastructure. These activities require accurate knowledge of the bed friction, which is necessary to predict water levels, flow rates, or pressure gradients. The approach, currently used for quantifying bed friction, is mostly empirical and thus should be considered the weakest component of otherwise quite sophisticated design and modelling methodologies. The proposed research will eliminate, or at least significantly reduce, this weakness by addressing the fundamentals of the problem and developing ways of incorporating the gained theoretical and physical insights into applied numerical modelling tools for the prediction of open-channel flows. The main beneficiaries of this research thus include: (1) central and regional government agencies dealing with waterway management, flood risk reduction, water quality control, and protection of ecosystem services (e.g., Environment Agency, Scottish Environment Protection Agency); (2) water companies responsible for the management, collection, treatment, and distribution of water; (3) civil engineering and environmental consultancies developing and/or applying hydro-environmental modelling tools (e.g., Arup, Halcrow, HR Wallingford); and (4) other end-users, indirectly related to traditional hydraulic engineering and ranging from aerospace to micro-fluidics applications that may take advantage of the project findings.

The key benefits that the proposed research will provide include: (1) significantly reduced uncertainties in predictions of water levels, flood inundation extent, flow rates, depths, and velocities; (2) better urban planning and new design philosophies based on friction control/reduction aptitudes that this research intends to develop (e.g., 'friction-reduced' urban planning as part of 'green cities' concept, more efficient drainage systems); (3) minimised energy consumption in waterway use by a better control of water levels (e.g., in waterway navigation); (4) improved stream restoration design and implementation; (5) new environmentally friendly fish passages (e.g., novel design of unstructured block ramps for improved fish habitats via enhanced water depth control and bed stabilisation); (6) reduced construction and maintenance costs for waterways and associated structures such as bank protection, intakes, and outfalls (as a result of improved predictive and control capabilities); and (7) increased reliability of assessments of climate change effects on aquatic systems.

Overall, the advanced knowledge on the bed friction nature, a theoretical framework, and quantitative measures, provided through this project, will contribute to the long-term maintenance of national water systems by improving their design, particularly related to flood prevention and control. The improved modelling and drag control capabilities will also help the UK and regional government agencies and engineering consultancies to maintain competitive advantage in the global market for water engineering and management projects.


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Cameron S (2017) Very-large-scale motions in rough-bed open-channel flow in Journal of Fluid Mechanics

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Mulahasan S (2017) Effect of Floodplain Obstructions on the Discharge Conveyance Capacity of Compound Channels in Journal of Irrigation and Drainage Engineering

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Stewart M (2018) Hydraulic resistance in open-channel flows over self-affine rough beds in Journal of Hydraulic Research

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McSherry R (2018) Free surface flow over square bars at intermediate relative submergence in Journal of Hydraulic Research

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Witz M (2018) Bed particle dynamics at entrainment in Journal of Hydraulic Research

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Sokoray-Varga B (2018) Self-similarity and Reynolds number invariance in Froude modelling in Journal of Hydraulic Research

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Cameron S (2020) Entrainment of sediment particles by very large-scale motions in Journal of Fluid Mechanics

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Zampiron A (2020) Effects of Streamwise Ridges on Hydraulic Resistance in Open-Channel Flows in Journal of Hydraulic Engineering

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Zampiron A (2021) Momentum and energy transfer in open-channel flow over streamwise ridges in Journal of Fluid Mechanics

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Cameron S (2022) Theoretical description of PIV measurement errors in Acta Geophysica

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Stewart M (2023) High-resolution measurements of swordfish skin surface roughness. in Bioinspiration & biomimetics

Description Key findings of this project include: (1) discovery of very large scale motions in rough-bed turbulent open-channel flows (JFM, 2017, 884); (2) significant effect of spectral structure of the rough bed topography on the overall hydraulic resistance; (3) significant effects of secondary currents on the flow turbulence structure and hydraulic resistance and a way of their control to minimize or maximize the total drag; (4) theoretical decomposition of the friction factor into constituents due to viscous, turbulent, dispersive stresses, flow non-uniformity, and unsteadiness and their quantitative assessment.
Exploitation Route The project findings have been extensively published and can be used to improve friction modules in the current hydraulic models and in the assessment of turbulence effects on mixing of substances and sediment dynamics.
Sectors Aerospace

Defence and Marine




Description The outcomes of this project have opened new avenues in assessing and prediction of hydraulic resistance in turbulent open-channel flows over complex rough beds. The theoretical approach developed and extensively tested in this project has created a basis for multiple follow-up studies in other wall-bounded flows such as turbulent boundary layers, conduits, and pipes. As part of this project, the rough surface of the sailfish skin, the fastest fish in the world, has been assessed to identify possibilities for its mimicking on open-channel beds to achieve drag reduction and reduce hydraulic resistance. The project outcomes underpinned 6 PhD studies and led to a further advanced study of secondary currents generated by bed heterogeneities (EP/V002414/1).
First Year Of Impact 2019
Sector Aerospace, Defence and Marine,Energy,Environment
Impact Types Societal

Description Aquaculture
Geographic Reach National 
Policy Influence Type Participation in a guidance/advisory committee
Description Field Stereoscopic Particle Image Velocimetry (FSPIV) system for high-resolution in-situ studies of freshwater and marine ecosystems
Amount £289,054 (GBP)
Funding ID NE/T009004/1 
Organisation Natural Environment Research Council 
Sector Public
Country United Kingdom
Start 09/2019 
End 03/2020
Description Secondary currents in turbulent flows over rough walls
Amount £735,380 (GBP)
Funding ID EP/V002414/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 01/2021 
End 12/2024
Title A Robotic Particle Image Velocimetry System for studies of open-channel flows 
Description A robotic Particle Image Velocimetry System has been developed to be used in the experiments within this project and in general forlaboratory studies of turbulent flows over smooth and rough beds. 
Type Of Material Improvements to research infrastructure 
Year Produced 2017 
Provided To Others? No  
Impact The robotic Particle Image Velocimetry system allows automatic calibration and measurements of flow fields where multiple measurement planes are required. 
Description Melbourne 
Organisation University of Melbourne
Country Australia 
Sector Academic/University 
PI Contribution Our group shares experimental data on fixed and mobile bed granular flows in water channels to support physical interpretation of wind-tunnel experiments conducted by Professor Ivan Marusic and his group. This is ongoing collaboration within EP/K041088/1 "Bed friction in rough-bed free-surface flows: a theoretical framework, roughness regimes and quantification".
Collaborator Contribution Professor Ivan Marusic and his group helped with planning, methodology, and interpretations, contributing at all project stages for EP/K041088/1 "Bed friction in rough-bed free-surface flows: a theoretical framework, roughness regimes, and quantification". The collaboration is ongoing.
Impact Two successful EPSRC research proposals have resulted from discussions with Professor Ivan Marusic (EP/K041088/1 "Bed friction in rough-bed free-surface flows: a theoretical framework, roughness regimes, and quantification"; EP/V002414/1 "Secondary currents in turbulent flows over rough walls").
Start Year 2014
Description Shallow turbulent flows and mixing layers 
Organisation French National Institute of Agricultural Research
Department INRA Versailles
Country France 
Sector Academic/University 
PI Contribution Data analysis and interpretation in relation to turbulence structure
Collaborator Contribution Extensive laboratory experiments, data handling, analysis and interpretation
Impact Proust, S., Nikora, V. Compound open-channel flows: effects of transverse currents on the flow structure. Journal of Fluid Mechanics, 2020, 885, A24 3. Proust, S., Berni, C., Nikora, V. Shallow mixing layers over hydraulically smooth bottom in a tilted open channel. Journal of Fluid Mechanics 2022, 951, A17
Start Year 2016
Description Public lectures 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact The talks have focused on career development of emerging researchers and its enhancement through research publications in specialized peer-reviewed journals

I received feedback from a number of early stage researchers that after my talks their publication style has sharply improved.
Year(s) Of Engagement Activity 2014,2015,2016,2017,2021,2022