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 New Wave-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 non-linear 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 andovertopping 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 overtoppingvolumes.Conclusions: Thus, the use of second-order wave-maker theory for wave group run-up and overtopping experiments is instead recommended.