Embedded wave generation for dispersive surface wave models

This paper generalizes previous research on embedded wave generation in Boussinesq-type of equations for multi-directional surface water waves; the generation takes place by adding a suitable source term to the equations. Accurate generation is important to prevent influx errors in simulated waves downstream. For numerical implementations it may be a useful alternative to boundary influx methods since it is relatively easy to implement and will account accurately for the dispersive properties of the model. The source functions are unique only when the spatial and temporal constituents satisfy the dispersion relation of the model; this ambiguity can be used to choose the spatial extent over which the generation is applied by adjusting the given input signal. Elevation and velocity type of generation can then produce waves running forward or partly forward and partly backward as desired. The sources, derived for linear models, can also generate high waves in nonlinear equations provided an adjustment zone in which the nonlinearity grows gradually is used. Results of simulations are shown for various cases, including a focusing wave and oblique wave interaction.