AbstractsPhysics

It has been found by many researchers that low frequency (LF) waves dominate the wave energy spectrum in very shallow water. Given that many longshore and cross-shore morphological processes are located within this zone, LF waves play an important role in determining morphological change, especially dune erosion and overwash during storm events. The numerical model, XBeach [Roelvink et al. (2008)], has been developed to simulate such morphological processes which are influenced by LF waves. For hydrodynamics, it utilizes the wave forcing determined from a second generation wave module to drive linearized shallow water equations within a flow module. The objective of this thesis focuses on validating the hydrodynamics of XBeach with particular attention paid to the estimated LF waves. This is particularly important to correctly estimate morphological changes, as it is highly dependent on the accurate representation of waves and currents. In the validation study, XBeach is used to replicate the flume experiment of van Noorloos [2003] in which bichromatic and irregular wave conditions are imposed on a plane sloping beach. The advantage of using this experiment is that measurements have a high spatial resolution, allowing for decomposition into incoming and outgoing wave components. Group-varying time-averaged short wave parameters are used to investigate the accuracy of the short wave module in XBeach, while at the same time the relationship between the short waves and LF waves are determined by looking at the energy transfer to and from the LF components. The results confirm many previous findings, such as the plus 180 degree phase difference between the short wave envelope and the bound LF wave, the dominance of LF wave energy in shallow water and the ability of LF waves to extend their reach to the uppermost parts on a beach. Given the limitations of the assumptions based on linear wave theory, the short wave results from XBeach are quite good, especially when using a newly modified breaker parameterization of Battjes and Janssen [1978] by Roelvink [Pers. Com. 2009]. The main shortfall of the model is that it tends to overestimate the bound LF wave heights in shallow water for irregular waves. This is believed to be partly due to the overestimation of the energy and radiation stresses contained in the short waves in this region. In reality, as waves approach breaking, the non-linearities present in the waves increase, which, during breaking, effectively redistributes energy within the wave spectrum. Since frequency dependent shoaling of short waves is not currently enabled in XBeach, the energy within the HF band may tend to encourage continued shoaling of the LF waves in the surf zone. As such, it is recommended that the current wave action conservation scheme be improved to allow for either reduction or redistribution of the short wave energy during shoaling. Wave run-up as modelled with the linearized shallow water equations is shown to over-steepen the front of the LF wave in the swash zone. This effect is a…