蜿蜒河流的数学刻画及其自组织

Mathematical Characterization of Winding River and Its Self- organization

为探讨蜿蜒河流河床演变中的自组织,应用微分几何方法建立了河道基本单元的数学模型,并通过求解数学模型得到了拐点坐标。根据实测资料和数学模型,绘制了下荆江在近500年间的5次河道轴线变化趋势及拐点分布,观察其变化趋势发现拐点的平面坐标是慢弛豫变量,拐点间距分布具有赫斯特效应,河道平面形态具有分形特征。由此探讨了河床演变中的自组织临界性及河型转换的内外部根源。

To explore self- organization in bed evolution of winding rivers,differential geometry method is applied to establish the mathematical model of basic unit,solving mathematical model to get inflection point coordinates. The Lower reach of Jingjiang in nearly 500 years with five axis change trend and inflection point distribution is drawn according to the mathematical model and the measured data. Observing its change trend,the author finds out that plane coordinate of the turning point is slow relaxation variables,inflection point distribution shows the Hurst effect,and channel plane morphology has fractal characteristics. Thus the author discusses the self- organized criticality of riverbed evolution and river pattern conversion of internal and external causes.