Shallow mixing layers are commonly observed in compound/composite channels, at the confluence of two rivers, between rivers and harbor entrances, between main channels and groyne fields, etc. The growth of shallow mixing layers determines the lateral exchange of pollutants and sediments and has great practical importance. The development (growth/decay) of a mixing layer is the combined result of the transverse velocity shear and the bottom friction. This thesis is devoted to the devising of reliable a mathematical model for shallow flows, and improvement of knowledge in the physics of the shallow mixing layers. Based on the BGK Boltzmann equation, a high resolution numerical scheme for horizontal shallow water flows, which is capable of capturing both wave and diffusion, is formulated,...[ Read more ]

Shallow mixing layers are commonly observed in compound/composite channels, at the confluence of two rivers, between rivers and harbor entrances, between main channels and groyne fields, etc. The growth of shallow mixing layers determines the lateral exchange of pollutants and sediments and has great practical importance. The development (growth/decay) of a mixing layer is the combined result of the transverse velocity shear and the bottom friction. This thesis is devoted to the devising of reliable a mathematical model for shallow flows, and improvement of knowledge in the physics of the shallow mixing layers. Based on the BGK Boltzmann equation, a high resolution numerical scheme for horizontal shallow water flows, which is capable of capturing both wave and diffusion, is formulated, verified and evaluated. This model is applied to shallow mixing layers. The applicability of the model to shallow mixing layers is investigated. Linear stability analysis as an initial value problem is applied to shallow mixing layers to investigate the validity of the traditional normal mode analysis for shallow mixing layers. Finally, the BGK Boltzmann model is extended to shallow flows in the vertical plane.