NONLINEAR LONG WAVES GENERATED BY A MOVING PRESSURE DISTURBANCE

The evolution of long waves generated by a pressure disturbance acting on an initially unperturbed free surface in a channel of finite depth is analysed. Both off-critical and transcritical conditions are consi dered in the context of the fully nonlinear inviscid problem. The solu tion is achieved by using an accurate boundary integral approach and a time-stepping procedure for the free-surface dynamics. The discussion emphasizes the comparison between the present results and those provi ded by both the Boussinesq and the related Korteweg-de Vries model. Fo r small amplitudes of the forcing, the predictions of the asymptotic t heories are essentially confirmed. However, for finite intensities of the disturbance, several new features significantly affect the physica l results. In particular, the interaction among different wave compone nts, neglected in the Korteweg-de Vries approximation, is crucial in d etermining the evolution of the wave system. A substantial difference is indeed observed between the solutions of the Korteweg-de Vries equa tion and those of both the fully nonlinear and the Boussinesq model. F or increasing dispersion and fixed nonlinearity the agreement between the Boussinesq and fully nonlinear description is lost, indicating a r egime where dispersion becomes dominant. Consistently with the long-wa ve modelling, the transcritical regime is characterized by an unsteady flow and a periodic emission of forward-running waves. However, also in this case, quantitative differences are observed between the three models. For larger amplitudes, wave steepening is almost invariably ob served as a precursor of the localized breaking commonly detected in t he experiments. The process occurs at the crests of either the trailin g or the upstream-emitted wave system for Froude numbers slightly sub- and super-critical respectively.