Observations of nonlinear runup patterns on plane and rhythmic beach morphology

Abstract

[1] 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.

The effects of tides on swash statistics on an intermediate beach

“…We investigated the low‐tide increase in infragravity energy using higher‐order spectral (bispectral) analysis. Bispectral analysis has been successfully employed to study nonlinear transfer of energy between frequencies in both the surf [ Elgar and Guza , 1985; Sénéchal et al , 2002] and the swash zone [ Bryan and Coco , 2010]. The technique examines the phase locking between the oscillations at triplets ( f 1 , f 2 , f 3 ), where f 1 and f 2 are two basic frequencies and f 3 = f 1 + f 2 .…”

“…If the modes are independent of each other, as is the case of a field of waves with random phases, no significant bicoherence between them is expected to be observed in the bispectrum. However, considering that swash cycles are somewhat parabolic, and the parabolic shape is composed of the sum of phase‐coupled harmonics with frequencies f , 2 f , 3 f and so on, and zero phase, the bispectral signature of the swash might be expected to show significant bicoherence at ( f , f ), ( f , 2 f ), (2 f , f ) and so forth [e.g., Bryan and Coco , 2010, Figure 2].…”

“…It is possible that these peaks are associated with swash interactions. Bryan and Coco [2010] showed bispectra generated from synthetic swash series in which each swash cycle was made dependant on the previous one. This interaction created an infragravity pattern in the time series caused by sequences of swash cycles (e.g., high‐low‐high‐low crests).…”

Observations of large infragravity wave runup at Banneg Island, France

“…For example, the IGW regime can change locally the position of the water table and alter erosion and accretion processes in the swash zone, and might be related to periodic beach morphology [e.g., Coco et al , ; Huisman et al , , and others]. The relation between IGW runup and offshore wave conditions [ Senechal et al , ; Guza and Feddersen , ], and the dynamics of the saturated runup spectrum [e.g., Bryan and Coco , ] are still not well understood.…”

Spectral signatures for swash on reflective, intermediate and dissipative beaches

“…Furthermore, Baldock et al (1998) and Bryan and Coco (2010) describe low frequency swash energy unrelated to incident waves in the corresponding frequency band.…”