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

• Focused wave group run-up on a beach and overtopping a seawall are studied
• Comparison between using linear and second-order wave generation is made
• Second-order error waves, arising from linear wave generation, are identified
• Error waves contaminate the wave field and erroneously enlarge run-up and overtopping
• Linear wave generation is found to be inadequate for coastal wave group studies

BackgroundFocused wave groups offer a means for coastal engineers to determine extreme run-up and overtopping events.Research purposeThis 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.MethodsThe 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 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.ResultsFocused 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.ConclusionsThus, the use of second-order wave-maker theory for wave group run-up and overtopping experiments is instead recommended.