Simulations of short-crested harbour waves with variational Boussinesq modelling

Waves propagating from the deep ocean to the coast show large changes in wave height, wave length and direction. The challenge to simulate the essential wave characteristics is in particular to model the speed and nonlinear interaction correctly. All these physical phenomena are present, but hidden, in the Euler equations, a set of partial differential equations which are Newton’s momentum equation for incompressible fluid. Numerical simulation of the full 3D equations are for present hardware still too demanding. For that reason an equivalent but completely different formulation can be used: a formulation in surface variables only (dimension reduction to 2D), given by a dynamic variational principle leading to a Hamiltonian system. The challenge is then to approximate the kinetic energy; we do this by exploiting a minimization property of this functional, leading to the so-called Variational Boussinesq Model (VBM). In that way we obtain tailor made accurate results with consistent a Finite Element implementation. The VBM software can be used for many important applications in coastal engineering. As one illustration the simulation of short-crested waves entering a harbour will be shown; experimental data from Deltares are available to quantify the simulations. Accurate wave simulations can play an important role in the design of the lay-out of harbours