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

壁面流动中的水力阻力问题是理论流体力学和应用流体力学中最热门的研究课题之一，也是最长期存在的水力学问题之一。研究人员继续探索各种经验和概念性方法来解决这一问题，特别是将重点放在控制水位、洪水淹没程度、流速、深度和水流速度的床面摩擦力的参数化上。目前用于量化床面摩擦的方法大多是经验性的，因此应该被认为是其他相当复杂的设计和建模方法中最薄弱的部分。尽管世界各地都在努力提高自由水面水位的预测和控制能力，特别是在洪水期间，水利工程师仍然使用经验或半经验关系来表示“粗糙度”或“摩擦”系数。这些阻力系数以简单的形式包含了复杂流体动力过程的综合影响，便于实际应用。人们普遍认为，这些阻力系数取决于水流参数、河床物质、河床和河道形态以及河流和岸边植被。尽管这种相关性的定量形式已经被几代水力学工作者所关注，但将阻力系数与水流和粗糙度参数联系起来的现有关系仍然主要是经验上的，而不是理论上合理的。因此，陆上水流、运河、水道、河流和河口的水力模型的不确定性水平仍然很高，经常超过20%-40%。因此，该项目的中心目标是开发先进的预测能力，以量化粗糙床明渠水流的水力阻力，并提出一种方法，将这项研究的理论和物理见解纳入与最终用户最相关的应用水力模型。为了实现这一目标，项目组将建立一个严格的理论框架，明确地揭示粘性、湍流和形状诱导的应力、二次流、不均匀和不稳定对总床面摩擦的贡献，并将这些贡献与流动物理联系起来。这一理论分析将为阿伯丁的复杂实验室实验和加的夫的大涡模拟数值研究奠定基础，以澄清明渠水流中床面摩擦的性质，完善粗糙度区域的定义，并识别和量化主要摩擦产生机制对总体摩擦的贡献。将理论分析与试验和数值研究相结合，将得到适用于应用水力模型的摩阻系数的概化关系式。拟议的研究将带来的好处的例子包括：水位和洪水淹没程度预测的不确定性显著减少；本研究打算开发的基于摩擦控制/减少能力的更好的城市规划和新的设计理念(例如，作为“绿色城市”概念的一部分的“减少摩擦”的城市规划和更有效的排水系统)；以及改进的溪流恢复设计和实施等。除水工程外，该项目的理论和方法发展也将适用于航空航天和机械工程等其他领域，在这些领域，阻力控制研究特别重要，而且还在不断增长。陆上径流和土壤侵蚀、仿生学和生态系统(陆地和水生生态系统)等跨学科领域是可以直接应用该项目成果的其他例子。

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.