The ship-induced hydrodynamics in a canal result in different mechanism of the cross-sectional evolution. However, the ship-induced hydrodynamic factors are not induced in existing studies of cross-sectional stability of a canal. In this paper, the minimum rate of energy dissipation equations for a canal are derived based on the theory of thermodynamics, introducing the ship wave factors, and variational equation is adopted to establish the stable cross-sectional shape equations. Then, the measured results in Changzhou segment of the Grand Canal are used to evaluate the performance of the derived equations by comparing with other typical equations without considering ship wave factors. The results show that the derived equations give better prediction of the cross-sectional area, mean water depth, maximum water depth and the bottom width of the stable cross-section with the relative error less than 20%. At last, an application of the derived equations is given for Yan River to predict the stable cross-sectional shape.

船在运河中的水动力导致横截面演化的不同机制。但是，在现有的运河横断面稳定性研究中，没有诱发出船舶引起的水动力因素。本文基于热力学理论，推导了舰船的最小能量耗散率方程，引入了船舶波浪因子，并采用变分方程建立了稳定的断面形状方程。然后，将大运河常州段的测量结果通过与其他典型方程进行比较来评估推导方程的性能，而无需考虑船舶波浪因素。结果表明，导出的方程可以更好地预测横截面积，平均水深，最大水深和稳定断面的底部宽度，相对误差小于20％。最后，给出了推导方程在延河地区的应用，以预测稳定的断面形状。