浊流是一种发生在水下、含低浓度泥沙、并沿床面运动的自然流动现象，地表和海洋中的浊流非常普遍。一般认为其是控制海底地形地貌的主要因素。此外，浊流沉积物不仅是海底油气资源的重要产生及储存场所，其高速和超大范围运动的特性也导致其对海底工程设施具有极强的破坏性。浊流的运动是一个重力驱动、湍流支撑、涉及与环境有强烈物质交换的复杂过程。通过对环境水体的卷入以及与床面泥沙的动态交换，浊流可以在很小的平均坡度下将大量泥沙输运至极远的（上千公里）距离，而其中物理机制的认识还很不充分。因此，研究浊流运动具有很重要的科学意义和工程价值。

本文建立了新的垂向积分模型体系。从一般的分散两相湍流理论入手，证明了在一般情形下使用混合物不可压缩流动近似的合理性。通过对浊流沿深度方向进行分区，得到了能够考虑环境水体影响的浊流运动-泥沙冲淤-床面变形相耦合的新模型，从而能更合理地考虑水体卷入、侵蚀沉积、环境水体沿程压力梯度及约化重力这四个对浊流最为重要的影响因素，并能够考虑环境水体密度变化及其流动对于浊流运动和演化过程的影响。

针对以密度为主变量的系统，构造了满足保平衡性质的数值格式，并证明了该数值格式守正性。另外，针对泥沙浓度与运动耦合的浊流黎曼问题，本文求解了其精确解，得到了适用于浊流的双稀疏波近似公式，发现了有别于明渠流动的浊流黎曼问题的特殊结构。同时，分析指出了在环境水体密度变化时，浊流黎曼问题可能出现新的解结构。

利用新模型探索了环境水体的密度变化和流动对浊流定常平衡态产生的影响。通过对典型特例的模拟和分析，发现在本文所取条件下，单纯的环境水体密度变化或流动均不会对新模型的定常平衡态的远处渐近性质产生影响，但会影响浊流上游的流动特性，并会改变浊流的自加速条件。

最后，本文以阿加迪尔峡谷浊流为背景，进行了真实尺度的浊流数值模拟研究。通过模拟结果与地学资料的对比研究，推断出了当地发生的真实浊流的规模上限；模拟结果表明，该浊流全局总侵蚀体积与初始泥沙总体积近似成幂次关系。

另外，作为笔者转博之前硕士阶段研究成果的核心部分，本文附录总结了对液滴高速冲击薄液层的数值模拟研究结果。针对液滴冲击后形成的皇冠状水花的运动规律，以及粘性在其中发挥的作用，通过CLSVOF方法进行了数值模拟研究。模拟结果和理论分析表明，在冲击后的不同阶段中，粘性引起的能量耗散在量级上有变化。在冲击初期，粘性引起的耗散主要发生在液滴与液层相接的颈部，且量级小至可忽略；在皇冠状水花形成之后，粘性引起的耗散主要发生在壁面附近，因而可以使用前人基于浅水系统的理论推导；而两者之间的第二阶段，能量的主要耗散区从液滴颈部向壁面移动，耗散量级在冲击形成皇冠及皇冠运动的整个过程中占主要部分。

Turbidity currents are turbulent underflows with low sediment concentration. It can involve water from the environment, roll up sediment from and deposit sediment to the bed. In these mechanics of dynamic equilibrium, a large amount of sediment can be transported at a very large distance. In the process of sediment transport, turbidity currents become the controlling factor of the seabed topography and landform. The high-speed movement of turbidity currents is also very destructive and can pose a great threat to submarine facilities. Sediment deposited from turbidity currents is an important source and storage site for offshore oil and gas resources. Therefore, the study for the movement of turbidity currents has very important scientific significance and engineering value. So far, studies of turbidity currents can be inversions based on sediment deposits, laboratory experiments, and mechanical models. The first two methods are limited by the uniqueness and scaling problem so that their research reliability is limited.

There are still many conceptual problems in mechanical models for turbidity current, a more general theory is developed and a new vertical-averaged model is established through strict derivation. Starting from the general dispersed two-phase turbulence theory, the compressibility of turbidity currents is deduced theoretically. The region of turbidity currents is divided into several zones along the vertical direction. Thus, the model can distinguish flows of environmental water, turbidity currents and flows near the sea bed. A more rigorous bed deformation model coupled with turbidity currents is proposed, the four important factors affecting turbidity current are considered in the model, including water entrainment, erosion and deposition, the static pressure gradient along the upper attached water body and reduced gravity.

After the hyperbolic property of the model is confirmed, a numerical scheme for the new model is constructed with the Well-Balanced property and integrity being proved for the first time. The exact solution of the Riemann Problem for turbidity current is gotten for the first time, and a formula in double-rarefactions form for turbidity current is obtained, a special structure of turbidity current problem different from the open channel flow is obtained and a new structure of solution to the Riemann Problem for turbidity current is suggested when the density of the environmental water varies.

Then, numerical experiments are carried out for the important law of a steady equilibrium of turbidity current. The influence of density and flow of steady water on the steady-state equilibrium of turbidity current is explored by using the new model. The results show that in a few special cases considered, the variation of density or only flows of environmental water will not affect the remotely asymptotic property of the steady equilibrium state of the new model, but do affect the upstream solution and will change the self acceleration criterion of turbidity currents.

Finally, a real-scale turbidity current event (Agadir Canyon turbidity current) is numerically simulated using a widely used coupled model (FCM). The results show that a limited-scaled event may happen, otherwise it will not meet the limited erosional area near the canyon mouth shown by the marine geologist. A dimensionless parameter scheme for the global erosion volume is also suggested by the results.

Besides, as part of the research results for my Ph.D. program during the master stage, an extra chaper that summarizes the numerical simulation results of droplets impacting a thin liquid layer at high speed is attached at the end of the thesis. Focusing on the control law of the movement of the splashing crown spray formed by droplet impact, and further, the role of viscosity in it, the CLSVOF method was used to simulate this process. The simulation results and analysis show that the dissipation level of viscous material varies during the three stages after impact. Viscous dissipation occurs mainly in the neck of the droplet and the liquid layer at the initial stage of impact, and the magnitude can be neglected; after the crown spray formation, viscous dissipation is mainly on the wall; and in the second stage, the main dissipation zone moves from the neck of the droplet to the wall, and the dissipation magnitude is the main part of the whole impact process.