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

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.

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.