Abstract
Coastal safety assessments with wave-resolving storm impact models require a proper offshore description for the incoming infragravity (IG) waves. This boundary condition is generally obtained by assuming a local equilibrium between the directionally-spread incident sea-swell wave forcing and the bound IG waves. The contribution of the free incident IG waves is thus ignored. Here, in-situ observations of IG waves with wave periods between 100 s and 200 s at three measurement stations in the North Sea in water depths of O(30) m are analyzed to explore the potential contribution of the free and bound IG waves to the total IG wave height for the period from 2010 to 2018. The bound IG wave height is computed with the equilibrium theory of Hasselmann using the measured frequency-directional sea-swell spectra as input. The largest IG waves are observed in the open sea with a maximum significant IG wave height of O(0.3) m at 32 m water depth during storm Xaver (December 2013) with a concurrent significant sea-swell wave height in excess of 9 m. Along the northern part of the Dutch coast, this maximum has reduced to O(0.2) m at a water depth of 28 m with a significant sea-swell wave height of 7 m and to O(0.1) m at the most southern location at a water depth of 34 m with a significant sea-swell wave height of 5 m. These appreciable IG wave heights in O(30) m water depth represent a lower bound for the expected maximum IG wave heights given the fact that in the present analysis only a fraction of the full IG frequency range is considered. Comparisons with the predicted bound IG waves show that these can contribute substantially to the observed total IG wave height during storm conditions. The ratio between the predicted bound- and observed total IG variance ranges from 10% to 100% depending on the location of the observations and the timing during the storm. The ratio is typically high at the peak of the storm and is lower at both the onset and waning of the storm. There is significant spatial variability in this ratio between the stations. It is shown that differences in the directional spreading can play a significant role in this. Furthermore, the observed variability along the Dutch coast, with a substantially decreased contribution of the bound IG waves in the south compared to the northern part of the Dutch coast, are shown to be partly related to changes in the mean sea-swell wave period. For the southern part of the Dutch coast this corresponds to an increased difference with the typically assumed equilibrium boundary condition although it is not clear how much of the free IG-energy is onshore directed barring more sophisticated observations and/or modeling.
Highlights
The interference of sea-swell waves is controlled by the frequency-directional spectrum of the incident waves resulting in wave groups with periods between approximately 25 s to 200 s
Modeling the impact of incident IG waves on beaches and dikes requires an offshore boundary condition that represents the incident IG waves, i.e., directed toward the coast [7]. This boundary condition is generally obtained by assuming a local equilibrium between the directionally-spread incident sea-swell wave forcing and the bound IG waves [1,8]
Along the northern part of the Dutch coast, this maximum has reduced to O(0.2) m at a water depth of 28 m with a sea-swell wave height of 7 m and to O(0.1) m at the most southern location at a water depth of 34 m with a significant sea-swell wave height of 5 m
Summary
The interference of sea-swell waves is controlled by the frequency-directional spectrum of the incident waves resulting in wave groups with periods between approximately 25 s to 200 s. Modeling the impact of incident IG waves on beaches and dikes requires an offshore boundary condition that represents the incident IG waves, i.e., directed toward the coast [7] This boundary condition is generally obtained by assuming a local equilibrium between the directionally-spread incident sea-swell wave forcing and the bound IG waves [1,8]. Ardhuin et al [11] and Rawat et al [12] have shown that IG waves generated at one coast can reflect and propagate across regional and even oceanic scales where they arrive as free incident IG waves at another coast This implies that the local equilibrium approximation may underestimate the incident IG energy. Depending on the coastal configuration, the local equilibrium approximation may result in an overestimation or underestimation of the incident IG waves
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