Observations of nonlinear runup patterns on plane and rhythmic beach morphology

Abstract

Application of nonlinear forecasting and bispectral analysis to video observations of runup over cuspate topography shows that these alongshore patterns in the morphology are accompanied by changes to the fundamental behavior of the runup time series. Nonlinear forecasting indicates that at beach cusp horns, the behavior of swash flow is more predictable and global (meaning that characteristics of individual swash events are well represented by the behavior of the time series as a whole). Conversely, at beach cusp bays, the behavior of swash flow is less predictable and more local (meaning that the characteristics of individual swash events are best represented by the behavior of a small fraction of the time series). Bispectral analysis indicates that there is a nonlinear transfer of energy from the incident wave frequency f to the infragravity frequency ∼f/2 which only occurs in the bay, suggesting that the local behavior is caused by interactions between successive swash cycles which are magnified by channeling caused by the beach cusp geometry. The local behavior and the bispectral signatures are not present in offshore measurements, and they are not present in runup time series collected when the beach was planar. These results provide evidence that interactions between successive runups are a fundamental characteristic of beach cusp bays. Ultimately, these interactions could lead to the growth of an infragravity wave with an alongshore wavelength forced by the presence of beach cusps.