Application of nonlinear dynamics to hydro-geomorphology

建立了考虑交错杆件和双排杆件干涉的弱非线性分析方法。研究结果表明，当两个模式处于同一阶次时，模式交叉干涉控制着每个波的发展过程，它们不能同时增长。模式交叉干扰对杆件的发展过程有很大的影响。通过水工试验和弱非线性分析，通过设置交替条形和双列条形两种不同的水力条件，阐明了平时洪水时沙坝形状的变化过程。研究了河道水流非恒定特性和植被生长对河道数量和河道时间稳定性的影响。结果表明，在非恒定流条件下，植被使河流数量减少，抑制了河流的时间变化。在此基础上，研究了非均匀泥沙床上沙洲的动力特性。结果表明，非均匀沙床面沙坝几何形状随时间发生变化，不能达到平衡状态。通过回顾已有的沙地与平床过渡的弱非线性稳定性分析，提出了一个新的模型，该模型适当考虑了弗劳德数与屏蔽数之间的函数关系。分析发现，在较小的平均床坡和较大的流速系数范围内，沙丘-平底过渡具有亚临界分叉的特点。此外，Izumi将现有的渠道初始模型扩展到基态坡度剖面为任意给定的更一般情况。分析表明，渠道间距约为坡面流水深的一千倍。

A weakly nonlinear analysis considering the interference between alternate bar and double-row bar has been developed. Findings show that when the two modes are on the same order, the mode cross interference controls development process of each wave and they cannot grow simultaneously. The development process of bars is strongly influenced of the mode cross interference. Hydraulic experiments and the weakly nonlinear analysis, by setting several hydraulic conditions under which either alternate bars or double-row bars formed, have been conducted to clarify a changing process of bar shape formed during flood at usual time. It is found that the channel shape at usual time is strongly affected by the bar shape during flood.Effect of unsteady characteristics of flow and vegetation growth on number of braided streams and temporal stability of streams has been studied. The results show that the number of streams decreases and temporal change of streams is suppressed with vegetation under unsteady flow conditions. Furthermore, dynamic characteristics of bars on bed with non-uniform sediment have been studied. The results show that bar geometry on bed with non-uniform sediment has been changed with time and does not approach equilibrium state.A new model was proposed taking proper account of the functional relation between the Froude number and the Shields number by revisiting the existing weakly nonlinear stability analysis of the transition of dune and flat bed regimes. It is found that, from the analysis, the dune-flat bed transition is characterized by subcritical bifurcation in the range of relatively small average bed slopes, and large velocity coefficient. In addition, Izumi extended the existing model of the inception of channels to the more general cases in which the base state slope profile is arbitrary given. The analysis shows that the spacing of channels is approximately one thousand times the depth of surface flow on slopes.