Is The First Wave Really The Largest ?

Until now analytical approaches of long wave runup on a plane beach were focused on finding its maximum value, failing to capture the existence of resonant regimes. One dimensional numerical simulations, for the Nonlinear Shallow Water Equations (NSWE), are employed in order to investigate the Boundary Value Problem (BVP) for plane and non-trivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the BVP. Resonant phenomena controlled by the incident wavelength and the beach slope are found to occur, resulting in enhanced runup of non-leading waves. The evolution of energy reveals the existence of a quasi-periodic state for the case of monochromatic waves, the energy level of which, as well as the time required to reach that state depend on the incident wavelength for a given beach slope. Dispersion is found to slightly reduce the value of maximum runup, but does not affect the overall picture. Runup amplification occurs for both leading elevation and depression waves.