Variational Modelling of Wave-Structure Interactions for Offshore Wind Turbines

We consider the development of a mathematical model of water waves interacting with the mast of an offshore wind turbine. A variational approach is used for which the starting point is an action functional describing a dual system comprising a potential-flow fluid, a solid structure modelled with (linear) elasticity, and the coupling between them. The variational principle is applied and discretized directly using Galerkin finite elements that are continuous in space and dis/continuous in time. We develop a linearized model of the fluid-structure or wave-mast coupling, which is a linearization of the variational principle for the fully coupled nonlinear model. Our numerical results indicate that our variational approach yields a stable numerical discretization of a fully coupled model of water waves and a linear elastic beam. The energy exchange between the subsystems is seen to be in balance, yielding a total energy that shows only small and bounded oscillations whose amplitude tends to zero as the timestep goes to zero.