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B2) Wave propagation over foreshores

Start: 09/2017
End: 09/2021
Status: Active

Contact details

Christopher H. Lashley

Delft University of Technology

Download here the PhD thesis related to this project.


This project developed new empirical methods to estimate the relative magnitude or significance of infragravity waves and the mean overtopping discharge at coastal defences with shallow foreshores. For wave overtopping, two methods were proposed: the first augments the traditional approach where phase-averaged numerical modelling is first used to estimate wave parameters at the toe, followed by an empirical estimate of the wave overtopping. The second approach is fully empirical and uses deep-water wave parameters as input and directly account for infragravity waves. These approaches were then assembled into a probabilistic framework capable of quantifying the impact of infragravity waves on safety along the Dutch Wadden Sea coast.

Figure 1 - Top: Dike-foreshore system in the Wadden Sea, near Eemshaven in the North of The Netherlands (Photo by Jaap van Duin - TUDelft). Bottom: Recent field campaign to measure waves and currents during the yearly winter storms in the same location (Photo by Pieter van der Gaag - TU Delft).

Motivation and practical challenge

To incorporate nature-based solutions, such as the effect of salt marshes and mudflats, in the design and assessment of sea dikes, we must fully understand their impact on waves and the likelihood of flooding during extreme storms. While the influence of such shallow environments on short-period wind waves (periods less than 25 seconds) is well understood and accounted for, what happens to longer-period infragravity waves (periods of minutes) is still not fully understood. During extreme storms, these waves typically propagate, reaching up to coastal dikes. Despite their importance for flood safety and coastal dynamics, the current approaches neglect or only indirectly consider the IG waves in the analysis. In the Netherlands, this challenge presents itself in the Wadden Sea, which is quite shallow for kilometres and experiences waves generated locally and in the North Sea. The improved understanding of these waves propagating over the foreshores is also useful for building with nature in other coastal areas such as the Caribbean Islands where I am from.

Research challenge

The research seeks to answer: under what conditions are these infragavity waves significant at the structure toe, and given that they are significant, what is their impact on flood safety?

Figure 2. Components of the research to estimate the influence of nearshore waves according to the offshore and dike characteristics for more accurate dike designs and flood risk assessments. Source of the physical model tests photo: Corrado Altomare and Tomohiro Suzuki (Flanders Hydraulics Research, Belgium).

Innovative components

The following methods were applied and validated as much as possible with field measurement campaigns to answer the above questions:

  • Numerical modelling: while field measurements and physical model tests are often difficult and expensive to implement, numerical models may be used to understand better the interaction between waves and the foreshore in a timely and cost-effective manner. This research applied state-of-the-art numerical modelling tools such as SWAN, SWASH, XBeach and OpenFOAM to estimate the nearshore wave heights and the volumes of waves overtopping the dike.
  • Empirical modelling: Using existing physical model tests and new numerical data, the relationship between the foreshore, nearshore waves and the volume of water that may overtop the dike were captured in simple empirical relations. These relations may then guide coastal advisors towards more accurate dike designs and flood risk assessments. Thereby, they can estimate the influence of infragravity waves that are often enhanced due to shallow waters according to: (1) the magnitude of the offshore waves; (2) the foreshore characteristics such as the slope and vegetation coverage; and (3) the slope of the dike.

Relevant for whom and where?

The improved understanding of wave propagation over shallow foreshores is useful for coastal engineers, researchers, ecologists and flood risk advisors.

The research components are applied into a case study located in the North of The Netherlands.

Progress and practical application

Findings indicate that infragavity waves become significant at locations exposed to high offshore swell with shallow, mildly sloping foreshores and reduced vegetated cover. Additionally, the numerical model comparison highlighted that more computationally-demanding models do not guarantee improved accuracy in predicting nearshore wave parameters or overtopping discharge.

The influence of infragravity waves in the nearshore is further significant for shallower water depths, milder foreshore slopes, reduced vegetated cover, and milder dike slopes. Moreover, with empirical adjustments, phase-averaged models like SWAN —which on their own do not model infragravity waves— can be used to estimate infragravity waves. For further details about each finding, see the related outputs.

Recommendations for practice

  • Even when the infragravity wave height at the structure is minor, their influence on the wave period—and, by relation, wave overtopping—can be significant.
  • The influence of infragravity waves is highly dependent on local bathymetric and forcing conditions. It is recommended that a quick check for the expected magnitude of the infragravity waves always be carried out using the tools developed here.
  • It is important to assess not only wave attenuation but also the evolution of the mean wave period over the foreshore.

Last modified: 30/12/2021

Contributing researchers

Christopher H. Lashley

Delft University of Technology

Supervisory team

Prof. Jentsje van der Meer

IHE-Delft Bas Jonkman

Delft University of Technology

Dr. Jeremy Bricker

Delft University of Technology

Contributing partners

Project outputs

Comparison of Implicit and Explicit Vegetation Representations in SWAN Hindcasting Wave Dissipation by Coastal Wetlands in Chesapeake Bay

Assessing the accuracy of nearshore numerical models—such as SWAN—is important to ensure their effectiveness in representing physical processes and predicting flood hazards. Results show that treating vegetation simply as enhanced bottom roughness (implicitly) underestimates wave energy dissipation. The explicit vegetation representation, however, shows good agreement with field data.

24/12/2018 by Christopher H. Lashley et al.

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Bevat: Publication open access journal

Contribution of Infragravity Waves to Run-up and Overwash in the Pertuis Breton Embayment (France)

The analysis shows that gravity waves rapidly decrease across the embayment while infragravity (IG) waves are enhanced. These findings show that the contribution of IG waves to dune overwash along the bay is significant and highlight the need for any method or model to consider IG waves when applied to similar environments.


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Benchmarking of numerical models for wave overtopping at dikes with shallow mildly sloping foreshores

Overtopping is an order of magnitude lower when infragravity waves are neglected. Using more computationally-demanding models does not guarantee improved accuracy. Despite well-modelled infragravity waves, XBeach Surfbeat underestimates overtopping. With empirical corrections, phase-averaged models like SWAN can account for infragravity waves.

01/08/2020 by Christopher H. Lashley et al.

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Bevat: Publication upon journal access

Relative Magnitude of Infragravity Waves at Coastal Dikes with Shallow Foreshores: A Prediction Tool

Here, we combine physical and numerical modeling to: (1) assess the influence of various offshore, foreshore, and dike slope conditions on the dominance of infragravity waves (IG) waves over those at sea and swell (SS) frequencies; and (2) develop a predictive model that allows practitioners to quickly estimate the relative magnitude of IG.

11/06/2020 by Christopher H. Lashley et al.

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Bevat: Publication open access journal

Formulating Wave Overtopping at Vertical and Sloping Structures with Shallow Foreshores Using Deep-Water Wave Characteristics

Accurate estimates of wave height and period at the structure toe often proves difficult and requires the use of either physical modeling or high-resolution numerical wave models. Here, we follow Goda's method to establish an accurate prediction by directly incorporating the foreshore slope and the relative water depth at the structure toe.

31/08/2021 by Christopher H. Lashley et al.

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Bevat: Publication open access journal

The Influence of Infragravity Waves on the Safety of Coastal Defences: A Case Study of the Dutch Wadden Sea

A newly developed framework not to overestimate safety along the many coastlines around the world that have shallow foreshores (e.g. saltmarshes and mudflats). Considering the influence of very long waves, which are often neglected in flood risk assessments is important when calculating the likelihood of waves overtopping the dikes.

01/11/2021 by Christopher H. Lashley et al.

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Bevat: Publication upon journal access



Reflection: Foreshores - useful for manageable flood safety or just beautiful nature?

In the 19th and early 20th centuries, salt marshes were mainly created for agriculture in the North of the Netherlands. More recently, we have reconsidered the value of these vegetated foreshores for flood safety.

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PhD Defence - Wave propagation over foreshores

03/11/2021 by Christopher H. Lashley

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