Importance of second-order wave generation for focused wave group run-up and overtopping

Background: Focused wave groups offer a means for coastal engineers to determine extreme run-up and overtopping events. Research purpose: This work examines numerically the importance of second-order accurate laboratory wave generation for NewWave-type focused wave groups generated by a piston-type paddle generator, and interacting with a plane beach and a seawall in a wave basin. Methods: The numerical wave tank is based on the Boussinesq equations for non-breaking waves, and the nonlinear shallow water equations for broken waves. During the model validation, good agreement is achieved between the numerical predictions and laboratory measurements of free surface elevation, run-up distances and overtopping volumes for the test cases driven by linear paddle signals. Errors in run-up distance and overtopping volume, arising from linear wave generation, are then assessed numerically by repeating the test cases using second-order accurate paddle signals. Results: Focused wave groups generated using first-order wave-maker theory are found to be substantially contaminated by a preceding long error wave, resulting in erroneously enhanced run-up distances and overtopping volumes. Conclusions: Thus, the use of second-order wave-maker theory for wave group run-up and overtopping experiments is instead recommended.