Chaima, MammeriSupervisor: Abdelkader, Gasmi2025-07-152025-07-152025-06-15https://repository.univ-msila.dz/handle/123456789/47209This work deals with the study of a free surface flow of an ideal, two-dimensional, steady and, irrotational fluid inside a horizontal channel huid is assumed to be incompressible, and surface tension effects are neglected, while channel with an obstacle on the bottom. The gravity is taken into is based on the long-wave approximation, using a small parameter : 0 < epsilon = (H/l) ^ 2 << 1 The bottom profile function y = b(x) and the free surface by y = H + eta(x, t) where 7 is the main unknown of our problem.enfluidpotential flowfree surfaceincompressible fluidsupercritical flowThesis