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This paper describes the classification of the water surface profiles observed in open channel flows over an obstacle. The analytical solution of linearized equation based on the Boussinesq equation is firstly derived theoretically and the water surface profiles of the solution are classified using the non-dimensional hydraulic parameters. It is shown that the profiles are mainly categorized into the patterns such as concave profiles with and without undular part and convex profiles around an obstacle. Using the perturbation method, the second order non-linear solutions are derived to investigate the nonlinearity of Boussinesq equation. It is pointed out that the prominent anti-symmetric profiles with transition from subcritical to super critical flow are observed near the resonance relation between obstacle and water surface.

Classification of Water Surface Profiles in Open Channel Flows over an Obstacle