Wave-to-wave variability of skewness and asymmetry in the cross-shore: A combined laboratory and modelling study

Abstract

Reducing depths drive wave shapes to deform from nearly sinusoidal to non-linear, in the form of skewness and asymmetry. This non-linearity is reflected in the induced orbital velocity, which has strong implications for wave driven sediment transport. Commonly, non-linearity is calculated over a total time series comprising numerous waves or modelled using parameterisations (such as the ones founded on the Ursell-number) which are based on local short wave height and period, as well as water depth. These approaches neglect the potentially large wave-to-wave variability in skewness and asymmetry related to the grouped structure of the incident waves and the resulting presence of infragravity waves. The aim of this study is to analyse the wave-to-wave variability in the development of skewness and asymmetry in the cross-shore direction, on a steep and gentle slope, with an emphasis on the role of infragravity waves, by means of a data model approach. A total of three experimental settings from the GLOBEX dataset (Ruessink et al., 2013), containing high resolution data on the propagation of bichromatic waves over a gentle sloping bed (1:80), was analysed. The same three boundary wave conditions were modelled over a steep sloping beach (1:10), using numerical model SWASH. Both the laboratory and modelled data were analysed using an individual wave tracking algorithm developed for this study, capable of identifying the development of skewness, asymmetry, wave height, period, local depth and Ursell-number. Wave-to-wave variability was observed to be generally larger on a gentle bed slope, and explicitly in the inner surf zone (Sk i,range & A i,range ≈1.6). On a steep bed slope, the largest wave to wave variability was found in the outer breaking zone (Sk i,range & As i,range ≈0.6), and reduced in the inner surf zone. Through analysis of the relation between the Ursell-number and Sk and As, it is concluded that variability in short wave characteristics (e.g. wave height) determines wave-to-wave variability in the offshore and shoaling zone. At locations where infragravity wave height to depth ratio was large (inner surf zone, on a gentle bed), wave-to-wave variability in non-linearity was found to increase. Though further research into other complex hydrodynamic processes in the inner surf zone is suggested, infragravity waves are thought to impact wave-to-wave variability in skewness and asymmetry.