Performance of a Boussinesq model for shoaling and breaking waves : a comparison with large scale laboratory data
In this thesis, a nonlinear model predicting hydrodynamics data for waves shoaling and breaking on a beach is reproduced and extensively tested with laboratory data. The model is based on the 1D Boussinesq equations as derived by Madsen et al. (1991) and Madsen and Sorensen (1992), with the free surface elevation and the depth-integrated velocity as variables. It allows slowly varying bathymetries and contains additional high order terms to improve the frequency dispersion for shorter wave periods, and thus also to improve the shoaling properties of the model. Wave breaking is modelled using the concept of a surface roller as formulated by Schäffer et al. (1993). It is assumed that bottom friction is negligible. A large scale laboratory experiment (Supertank), designed in particular to obtain data to test the validity of wave propagation models, provides the wave and current data. Wave evolution over a complex bathymetry is examined for 4 cases. The data include conditions for long and short waves, and regular and irregular waves. During the model evaluation, emphasis is put on the study of parameters of importance to sediment transport, including (orbital) velocity, undertow and wave shape prediction. The latter encompasses velocity and elevation skewness, kurtosis and asymmetry. It is found that, despite an overestimation of the depth-averaged horizontal velocity in some cases, the predicted velocity moments and undertow are in good agreement with the data. Using a bispectral analysis, it is shown that the nonlinear transfers of energy amongst the low order harmonics are well reproduced, but that errors are introduced in the treatment of the high order super-harmonics. As a result, the short waves tests are found to yield better results than those for long waves. A sensitivity analysis on the free parameters introduced in the simulation of wave breaking is carried out. It appears that the results are mostly sensitive to the critical xv avve fi-ont slope OB , and in particular that the elevation and velocity skewness and kurtosis predictions are very sensitive to this parameter.