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混沌－分形研究是非线性地貌发育理论，尤其是非线性流水地貌学研究的前沿问题，是当代地貌学深层次研究的一个重要界面，在国内外刚刚起步。本文在概述国内外研究进展基础上，以黄河下游及长江中下游为例，运用粗视化方法，对不同河段、不同河型的河床深泓纵剖面进行了分维量计和检验。初步分析表明，冲积河流的河道纵剖面具有分维特征，可用来刻划河流纵剖面发育的复杂程度，结合河床起伏度的统计对比分析，可将其作为河流纵向消能的另一种量度。河流纵剖面的分维具有时空变化，其微小变化可以体现河型在时空上的分异和偏离。分维数值与某些环境因素及水力条件有关，如分维数值Ｄ与河床纵坡降Ｊ呈负相关。因此，可作为河型演变分析依据的佐证，预测河流纵剖面的发育趋势。
Chaos - fractal research is a nonlinear topography development theory, especially the frontier problem of nonlinear waterlogging geomorphology research. It is an important interface of contemporary geomorphology deep research and has just started at home and abroad. Based on the research progress at home and abroad, taking the downstream of the Yellow River and the middle and lower reaches of the Yangtze River as an example, this paper makes a fractal dimension test of the longitudinal section of the deep riverbed in different river sections and different river types by using the method of rough visualization. The preliminary analysis shows that the river profile of the alluvial river has the fractal dimension, which can be used to characterize the complexity of river profile development. Combined with the statistical analysis of river bed undulation, it can be used as another measure of longitudinal energy dissipation of the river. The fractal dimension of the river longitudinal profile has the spatial and temporal changes, and its small changes can reflect the divergence and deviation of the river patterns in time and space. The value of fractal dimension is related to some environmental factors and hydraulic conditions. For example, the fractal dimension D is inversely related to the longitudinal gradient J of the riverbed. Therefore, it can be used as evidence of river evolution analysis to predict the trend of river longitudinal profile.