On the internal wave generation in Boussinesq and mild-slope equations

The literature contains empirical knowledge on whether the wave celerity or the group velocity should be used in the line source function for internal wave generation for at given set of Boussinesq or mild-slope equations. Theoretical derivations that confirm and explain these empirical findings are devised. For Boussinesq equations with, e.g. Padé[2,2]-type of dispersion relation some procedures for internal wave generation are affected by their excitation of an evanescent mode. This has some undesirable consequences, but the evanescent-mode excitation can be avoided by the use of an “internal flux boundary”.