Field observations of the influence of infragravity waves on wave overtopping at a dike on a shallow foreshore

Infragravity (IG) waves are low-frequency waves (0.0033 Hz < f < 0.05 Hz) that exist: (i) being bound to the wave groups of high-frequency sea-swell (SS) waves (0.05 Hz < f < 1 Hz), (ii) generated by the moving breakpoint due to the groupiness of the SS waves (Bertin et al., 2018), and (iii) as free IG waves released from the SS wave groups and reflected from neighbouring coasts (Rijnsdorp et al., 2021). Offshore in deeper water (h/Hm0,o > 4, with h the water depth and Hm0,o the offshore significant wave height), IG waves become most apparent during storm conditions, but are still rather limited in wave height (order of a couple of cm). However, at the toe of coastal structures with a shallow foreshore depth (1 < ht/Hm0,o < 4, with ht the water depth at the toe), the energy of IG waves becomes more significant relative to the SS wave frequency band of the wave spectrum (Hofland et al., 2017), becomes equally important for very shallow foreshores (0.3 < ht/Hm0,o < 1), and even dominates SS wave energy for extremely shallow foreshore depths (ht/Hm0,o < 0.3). IG wave growth on mildly sloped shallow foreshores is a result of IG wave shoaling and SS wave energy transfer to IG waves via nonlinear wave-wave interactions (Bertin et al., 2018), and the relative growth of IG to SS wave energy is further aided by SS wave breaking. Coastal urban areas along the Belgian coast (and in other low-lying countries worldwide) rely on a hybrid beach-dike coastal defense system for protection against flooding. During design storm conditions, the nourished beach erodes to a very to extremely shallow foreshore in front of a low-crested impermeable sea dike. Wave overtopping at this type of structure has been shown to be affected by IG waves, based on physical (Altomare et al., 2016) and numerical modelling (Lashley et al., 2021) for shallow to extremely shallow foreshores. However, field observations of the influence of IG waves on wave overtopping have been scarce (van Gent and Giarusso, 2003) and the influence of free IG waves has not been investigated yet. Indeed, the amount of IG wave energy that is expected to arrive at the coastline, not only depends on IG waves naturally bound to the SS wave groups, but also on free IG waves generated offshore or locally reflected from the coast (edge waves). The Belgian continental shelf is characterized by the prevalence of offshore sandbanks (see Figure 1a), which might be an additional source of free IG waves, due to ss wave breaking