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利用突变理论中的尖点突变模式研究河型分类及其转化趋势。通过选取适当的控制变量与状态参量,在尖点突变模式下进行坐标变换,推求得到了河道状态的平衡方程,并绘制出3维坐标下的平衡曲面图;依据该平衡方程选取相应的临界状态参数,对控制参平面进行2维投影,得到不同河型的判别条件。通过对100多条天然河流及试验河段资料的计算判定其河流所处状态及其河型。结果表明:基于尖点突变模式所建立的河道状态平衡曲面及河型分类判别条件能够判定现有河流所处的状态及河型,从而为实际工程中的河流整治提供参考。
Study on river classification and its transformation tendency by using cusp catastrophe model in catastrophe theory. By choosing the appropriate control variables and state parameters, coordinate transformation is performed under the cusp catastrophe mode, the equilibrium equation of the river state is deduced, and the equilibrium surface map is drawn under the three-dimensional coordinates. According to the equilibrium equation, the corresponding critical state Parameters, two-dimensional projection of the control parameters plane, get the discriminant conditions of different river type. Through the calculation of the data of more than 100 natural rivers and experimental river sections, the state of the river and its river type are determined. The results show that the state of the existing river and the river pattern can be judged based on the state balance surface of the river channel and the river classification and discerning conditions established by the cusp catastrophe mode, so as to provide a reference for the river regulation in practical engineering.