The average shape of large waves in the coastal zone

Abstract The ability of the NewWave focused wave group (the scaled auto-correlation function) to represent the average shape in time of large waves in a random sea state makes it a useful tool for the design of offshore structures. However, the profile has only been validated against field data for waves on deep and intermediate water depths. A similar validation is advisable when applying NewWave to shallow water problems, where waves are less dispersive and more nonlinear. For this purpose, data recorded by two Channel Coastal Observatory (CCO) wave buoys during two large storms in January 2014 are analysed to assess the ability of NewWave to replicate the average shape of large waves in shallow water. A linear NewWave profile is shown to successfully capture the average shape of the largest waves from the Perranporth and Porthleven wave buoys during these large storm events. The differences between the measurements obtained by a surface-following buoy and a fixed sensor become important when considering the ability of a second-order corrected NewWave profile to capture weakly nonlinear features of the measured data. A general expression for this effect is presented for weakly nonlinear waves on intermediate water depths, leading to Lagrangian second-order sum corrections to the linear NewWave profile. A second-order corrected NewWave profile performs reasonably well in capturing the average features of large waves recorded during the January storms. These findings demonstrate that the NewWave profile is valid in relatively shallow water ( k p D values less than 0.5), and so may have potential for use as a design wave in coastal engineering applications.