Cross-Sectional Stability of a Canal under the Action of Ship Waves Based on Minimum Energy Hypothesis

Abstract

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.