二维河网系统分形动力学研究

Study of Two-dimentional Rivernetwork Fractal Dynamics

河网系统是一个远离平衡态的、开放的复杂系统。现阶段认为河流的演变机理包括外在宏观形状表现以及内在微观动力学机制,而河流的演变也是二者之间的平衡转化。目前,使用分形理论对河流的特征及河床的演变发展研究已经成为一种重要的手段。鉴于分形理论运用的局限性,特别是算法有宏观形状而无微观机制的弊病,应用线宽和线面积这两个可以直接与河流动力学衔接的概念,推导了可以直接用绘制图形(河流)的线宽计算维数的线维数和线面积计算维数的面维数,实现了维数计算由点到线、面的突破,为河网分形发育程度与河流动力学及最小能耗等理论衔接提供了可能,即为构建河网外在形状和内在动力学的新理论,以及最终实现河流的宏观外在特征和微观内在特征的衔接提供了两种理论途径。

River network is in a state of far-from-equilibrium and is an open complex system. So far one has reasons to believe that the external macroscopic form and innate microcosmic dynamics mechanism form the mechanism of river＇s evolvement. The fractal analysis is an important method to analyze river＇s characteristics and river＇s evolution. There are limitations of fractal analysis, especially in its algorisms, so two concepts are proposed about the line dimension with line （river） width and the area dimension with line （river） area to establish the links between river dynamics and width or area, so dimension calculation can go from point to line or area and make it possible to analyze the development degree of river network and dynamics or minimum energy consumption. The next phase of focus is to establish a link between line dimension or area dimension and dynamics, then a new method of dimension can be finally developed as the theoretical basis in the exploitation, governance, sustainable development of rivers.