New approximate solution with resonance modes of Saint-Venant equations by WKB-type method

Exact analytical solutions of linearized Saint-Venant equations remain unknown except for uniform regime but this later configuration is not often encountered in real open-channel hydraulic system. In this paper, an approximate solution of linearized Saint-Venant equations in their general non-uniform shape is proposed. This solution is based on a mathematical method developed in quantum mechanics to handle differential equations with space-varying coefficients. It results in irrational transfer functions between levels or flows and boundary flows at any point of the channel and it captures all resonance modes. The accuracy of the method is illustrated on a case study.