Minimisation principles for the evolution of a soft sea bed interacting with a shallow sea

Abstract

Minimisation principles are used in fluid–structure coupling to model sandy sea beds evolution. The sandy bed is seen as a structure with low stiffness. We start with a model problem featuring the behaviour of the coupling. Then, the water motion in shallow domains is described by the Saint-Venant equations. This coupling bringing the bottom sea changes is based on the assumption that the bed adapts to the flow in order to minimise some energy quantity together with minimal sand transport. The approach is shown being equivalent to the use of an Exner equation for the bed with a non-local expression for the sediment transport flux. Because the choice of the functional permits to include different physical quantities one thinks to play a role in the bottom morphodynamics, the approach is also atool for validating different modelling hypothesis.