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In this paper we build models for short-term, mean-term and long-termdynamics of dune and megariple morphodynamics. They are models that aredegenerated parabolic equations which are, moreover, singularly perturbed. We,then give an existence and uniqueness result for the short-term and mean-termmodels. This result is based on a time-space periodic solution existence resultfor degenerated parabolic equation that we set out. Finally the short-termmodel is homogenized.

Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment