Impact of Free Long Waves on Dune Erosion Predictions in Numerical Modelling

Abstract

This report presents the methodology and findings of a study on the impacts of free long waves on dune erosion predictions in XBeach. In this paper a distinction is made between two types of infragravity waves: bound infragravity waves and free infragravity waves. Bound infragravity waves are generated by short-wave group forcings and are bound to the propagation of the wave groups. Conversely, free waves are infragravity waves that are released from the wave-group in the surfzone, reflect at the shoreline, and propagate back out of the surf zone. In a semi-enclosed basin with mild bathymetric changes such as the North Sea, free long waves that reflect off one coast can propagate large distances and impact other coastlines.

Modelling the response of a coastline during a storm event requires an offshore boundary condition that represents the incident short and long waves. The boundary condition for the incident infragravity waves is often derived by assuming a local equilibrium between the directionally spread sea-swell waves and bound infragravity waves following the K. Hasselmann (1962) method. This approach has proven to be problematic for two main reasons. First, the method tends to overestimate the incident infragravity wave height by assuming a local equilibrium is achieved at the model boundary; however, observations have shown that the transfer of energy from the short-wave groups to the underlying bound wave is gradual on a sloping bed. Second, by applying the equilibrium K. Hasselmann (1962) method it is implied that only bound infragravity waves are present at the boundary underestimating the total incident infragravity wave energy.

An analysis of XBeach in surfbeat mode revealed that the model can confidently predict infragravity wave behaviour on a natural beach slope with two well-developed bars during a storm event by calibrating the roller breaker slope coefficient and wave breaker coefficient. Infragravity wave heights were reasonably accurately predicted in the surfzone, but the model generally overpredicted the most energetic infragravity waves.

Further, the study investigated the impact of free infragravity waves on dune erosion predictions by simulating the behaviour of two 1D planar beach slopes to the inclusion of free long waves at the boundary. The study revealed that on a beach with a 1:35 slope the relative increase in dune erosion volume was 44.1% when the bound infragravity energy is equal to the free infragravity energy relative to the case excluding free waves. For the same conditions, a 20.6% increase was observed in the maximum runup. For a milder 1:70 slope a 36.4% and 6.1% increase in dune erosion and maximum runup was observed.

The results demonstrate that the dune response of a coastline is sensitive to the inclusion of incident free infragravity waves at the boundary. Moreover, neglecting the presence of free infragravity waves at the boundary may underpredict the dune response during a storm event.