From the group movement of the bed load within the bottom layer,details of the nonlinear dynamic characteristics of bed load movement are discussed in this paper.Whether the sediment is initiated into motion corresponds to whether the constant term in the equation is equal to zero.If constant term is zero and no dispersive force is considered,the equation represents the traditional Shields initiation curve,and if constant term is zero without the dispersive force being considered,then a new Shields curve which is much lower than the traditional one is got.The fixed point of the equation corresponds to the equilibrium sediment transport of bed load.In the mutation analysis,we have found that the inflection point is the demarcation point of breaking.In theory,the breaking point corresponds to the dividing boundary line,across which the bed form changes from flat bed to sand ripple or sand dune.Compared with the experimental data of Chatou Hydraulic Lab in France,the conclusions are verified.
The flow instability is related to many engineering problems and belongs to a wide-ranging research field. When the problem on the transition from the laminar to the turbulence caused by the instability of the laminar is studied,the "neutral line" and the critical Reynolds number are always taken as the criterion to judge whether a certain kind of flow is stable,whose corresponding flow medium is the clear water,that is,the single-phase Newtonian fluid. And it is not studied in the traditional in-stability theory that the hyper-concentration flow widely exists in rivers. This shortage can be covered by this research. Study shows that the instability of non-Newtonian fluid such as hyper-concentration fluid,compared with Newtonian fluid such as clear water,is influenced by not only Reynolds number,the ratio of the inertia force and the viscous force,but also many other factors such as the sediment concentration,the concentration distribution,the grain size,the volu-metric weight of the sediment and so on,which make the mechanical principle even more complex. So the results of the research can supply the scientific basis for the explanations of "slurrying river",the turbulence intensity of the flow carrying sediment and the variance of the turbulence structure.
Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.
