Influence of directional spreading on wave overtopping of sea dikes with gentle and shallow foreshores
Introduction
Coastal areas worldwide are at risk because of anthropogenic and natural hazards, which are expected to increase due to changing climate (Weisse et al., 2012). Effects of the climate change, such as the sea level rise and the occurrence of more severe and frequent storms represent major threats to coastal defences. The mean sea level has been increasing during the last century on average of 1–2 mm/year, tendency that is worsening during the last few decades (Jevrejeva et al., 2006). Besides, the 20th century has seen already a number of severe storms causing damage and flooding worldwide. Examples of these storms are: the North Sea flood of 1953, considered to be the worst natural disaster of the 20th century both in the Netherlands, Belgium and the United Kingdom, claiming 2,551 lives and leading to damages for more than 0.6 bn USD; Xynthia in 2010 (63 casualties and damages for more than 1.4 bn USD); Xaver in 2013 (15 casualties, ≥ 1.3 bn USD). Worldwide, the Hurricane Katrina caused over 125 bn USD damages and 1,800 casualties only in USA in 2005, probably the most destructive hurricane in the latest 20 years in USA, followed by Harvey (2017, 68 fatalities and 125 bn USD damages) and Sandy (2012, 233 fatalities 68.7 bn USD). In the same geographical area, in 2017 the Hurricane Maria struck and devastated Dominica, the U.S. Virgin Islands, and Puerto Rico, with over 3,000 fatalities and 91.61 bn USD damages. All the aforementioned events are just a few examples of a long list of severe weather conditions that are likely to occur again, enhanced by the climate change. In particular, low-lying countries are ones of the most exposed areas to wave overtopping and sea flood. These countries are characterised by densely populated and low-elevation coastal areas that, despite the increasing risk for flooding, are experiencing a continuous population growth. In many low-elevation coastal areas, very shallow, long and gentle foreshores lie in front of the coastal protections. Only a few studies are available in literature on wave overtopping prediction for such a beach layout and specifically in combination with sea dikes (van Gent et al., 2007; Altomare et al., 2016; Suzuki et al., 2017). These studies analysed the case of long-crested wave conditions, being based on wave flume experimental campaigns or 2DV numerical modelling. However, it is of high importance to understand the influence of gentle and shallow foreshores for real three-dimensional sea states (short-crested waves) on wave transformation and wave overtopping. Guza and Feddersen (2012) demonstrated influence of directional spreading for wave run-up and Suzuki et al. (2014) showed one for wave overtopping by phase resolving wave models. However, those were limited to the numerical modelling. While numerical solvers can help to characterise wave transformation and overtopping for short-crested waves (Zijlema et al., 2011; Roelvink et al., 2009), not many data are available for a proper model validation are available for the aforementioned conditions with shallow and gentle foreshores under realistic sea states, i.e. short-crested waves. Physical model tests have been usually carried out for structures lying on horizontal bottom and deep or intermediate water conditions ate the toe, not taking into account the influence of gentle and shallow foreshores (e.g. Nørgaard et al., 2014; van Gent and Van der Werf, 2019). Besides, the behaviour of free and bound infragravity waves over a sloping bottom (Janssen et al., 2003; Battjes et al., 2004; van Dongeren et al., 2007) under realistic sea states will be of interest. It would be important to take into account the characteristics of free and bound long waves, which dominate the hydrodynamics in the shallow foreshore, in order to understand overtopping phenomena in shallow foreshore condition better.
Physical model tests have been carried out in the shallow-water wave basin at Flanders Hydraulics Research (FHR) in Antwerp, Belgium, to analyse the influence of directional spreading on wave overtopping and post-overtopping processes on sloping sea dikes with 1:35 foreshore slope in case of very and extremely shallow water conditions (Hofland et al., 2017). The experimental campaign is part of the CREST (Climate REsilience coast) project (http://www.crestproject.be/en), a Belgian-funded project and the goal of which is to increase the knowledge of coastal processes nearshore and landward.
In the present work, the influence of wave short-crestedness on mean overtopping discharge is discussed. The results are compared with existing semi-empirical formulae from literature. This work aims at representing a first step towards a more comprehensive understanding of wave overtopping of sea dikes for cases with very and extremely shallow foreshores due to real three-dimensional sea states.
Section snippets
Shallow water criteria
The foreshore can be defined as the part of the seabed bathymetry in front of the dike toe, that causes processes like wave breaking and refraction. The most recent criterion to define the shallowness of the foreshores has been published by Hofland et al. (2017). The authors characterise the shallowness of the foreshore by means of the ratio of the still water depth near the structure, ht, by the offshore wave height, Hm0,o, in deep waters (Fig. 1). Table 1 shows the ranges of foreshore
Average wave overtopping assessment in existing literature
Wave overtopping occurs when sea waves run up coastal defences which are not high enough to prevent flows over their crest. Wave overtopping is a very complex phenomenon because it varies in time and space during the same storm event. It is common practice to assess the mean or average overtopping discharge that can be defined as the ratio between the total volume of water that overtops a coastal defence by the duration of the storm event. Hence, mean wave overtopping is widely used worldwide
Experimental campaign
Physical model experiments have been carried out in the wave basin equipped with multi-directional wave generation system at FHR. Within the framework of the CREST project, the wave basin was employed primarily to study the effects of wave overtopping and post-overtopping processes (e.g. overtopping wave layer characteristics and force) of the short-crestedness of the waves in very and extremely shallow water conditions with the presence of a gentle foreshore.
Average overtopping discharge
The results in terms of average wave overtopping discharge are summarised and discussed in the present section. First a general overview of all results, including long-crested and short-crested waves is given. Later on, a more detailed analysis of the influence of short-crestedness is carried out. Finally, the results are compared versus the prediction of Eq. (9) and Eq. (4). The measured average discharge (expressed in l/s/m) is plotted against the incident wave height at the toe in Fig. 4.
Conclusions
The influence of directional spreading on overtopping of sea dike with gentle foreshore in very and extremely shallow water conditions is analysed in the present work. Physical model tests were carried out in the multi-directional wave basin of Flanders Hydraulics Research. Main focus was to characterise the wave transformation and wave overtopping on sea dikes and compare long- and short-crested wave cases. The results show a clear influence of the directional spreading (i.e. wave
Disclaimer
The presented results reflect only the authors view and the Research Executive Agency (REA) is not responsible for any use that may be made of the information it contains.
CRediT authorship contribution statement
Corrado Altomare: Conceptualization, Investigation, Methodology, Writing - original draft, Formal analysis. Tomohiro Suzuki: Investigation, Formal analysis, Validation, Writing - review & editing. Toon Verwaest: Supervision, Writing - review & editing, Project administration.
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