泥石流能量传递机制与耦合数学模拟

Debris flows are typical unsteady water-sediment flows, involve highly complicated interactions between water and sediment, and may feature substantial mass, momentum and energy exchanges with the bottom boundaries. However, current understanding of the mechanism of the generation, development and recession of debris flows remains far from complete, and generally applicable mathematical models for debris flows are still missing. This project sets out to develop a two-phase coupled modelling theory for debris flows based on mass, momentum and energy conservations laws, in which the mixture of water and sufficiently fine sediments is considered as quasi-fluid phase, and coarse sediments is regarded as "solid" phase, and the interactions between debris flows and erodible bottom boundary are properly incorporated. It also aims to unravel how energy is transferred in debris flows, especially the relationships between the fluctuation and mean energy components of the solid phase of coarse sediments, the counterparts of the fluid phase and energy dissipation. The threshold conditions for the occurrence of self-reinforcement of debris flows will also be established. The project will contribute to the progress of the fundamental theory and enhanced understanding of the physical mechanism of debris flows, and therefore facilitate physically improved computational modelling for debris flood risk management.

泥石流是一类典型的非恒定水沙流动，涉及极其复杂的水沙相互作用，并可能与底部边界发生质量、动量和能量交换。然而，迄今对泥石流形成、演化和消退的物理机制的理解远没有完善，还缺少普遍适用的数学模拟理论以预报泥石流致灾过程。本项目将泥石流中水与细颗粒混合物视作粘性流体、将粗颗粒作为固相连续介质，充分考虑泥石流与可冲积底部边界之间的交换，从湍流运动模式理论和质量、动量、能量守恒律出发建立泥石流两相耦合动力学数学模拟理论；揭示泥石流形成、演化与消退过程中能量传递的行为、规律与物理机制，特别是粗颗粒脉动动能、平均运动动能及其与流体相湍流能量产生与耗散之间的关系，进而建立泥石流自增强机制发生的临界条件。该项研究将发展泥石流运动的基础理论，增进对泥石流物理机制的理解，并为泥石流灾害的防御提供新的数值模拟技术。

长期以来，对泥石流形成、演化和消退的物理机制的理解远没有完善，缺少具备健全物理基础、普遍适用的数学模拟理论以预报泥石流。本项目基于两相流质量、动量和能量守恒律，考虑水沙两项脉动应力以及泥石流与床面之间的交换，建立了一个新的（深度积分平均）全耦合泥石流拟单相流模式和一个新的（深度积分平均）全耦合泥石流两相流模式。应用所建立的模式，对美国USGS全系列大尺度、动床和定床泥石流实验进行了深入、细致的数学模拟研究。在不需要对模型参数进行实质性调整的前提下，两相流模式所解析的泥石流演化过程（泥石流深度、前锋传播速度、床面冲刷、应力等等）与实验观测数据之间的吻合程度超过迄今为止公开发表的数学模型。同时，揭示了流体相湍流与固相颗粒运动影响泥石流演化的规律。最主要的，流体相湍流受高含沙量泥沙所抑制，其应力的作用有限；但是，固相颗粒脉动应力超过流体相湍流应力的作用，对泥石流演化的作用不可忽略；并且，固相颗粒湍流应力与流体相湍流应力之间并非简单的代数关系所能表达，从而需要应用具有良好物理基础的湍流封闭模式。以此为基础，研究了定床、动床条件下泥石流能量关系及其与泥石流效率之间的关系。研究结果显示：泥石流高效率（长距离传播）并非如人们所猜测的、由固相泥沙颗粒内能所能决定，也并非由冲刷床面泥沙所具备的初始势能所决定，而是由水、沙两相之间和泥沙颗粒之间的相互作用导致的。另外，为实际应用之目的，研究了暴雨山洪浅水动力学数值模型和（深度积分平均）水沙耦合动力学数值模拟的自适应网格技术，为将来进一步建立流域暴雨山洪－泥石流耦合数学模型奠定了技术基础。迄至本项目结题日，已正式发表SCI学术期刊论文6篇，另已投稿2篇、完成1篇（尚待发表的SCI学术期刊）论文，共计9篇。