Non-hydrostatic wave modelling of coral reefs with the addition of a porous in-canopy model

Abstract

One sixth of the world's coastline consist of coral reefs and provide natural flood defence for the people who live in the coastal region behind the reef. However, a rising sea level, changing wave conditions and degradation of corals threaten the coastal safety of these reefs.Numerical models can be applied to study the reef-hydrodynamics and the effects of coral degradation on the reef-hydrodynamics. When non-linear processes are important or the individual waves need to be determined, a phase resolving model is preferred. Within this thesis two issues regarding the application of non-hydrostatic models to coral reefs were studied.

Due to the large bottom gradient in front of a reef, the offshore boundary has to be located in deep water, which means that frequency dispersion becomes important. The accuracy of frequency dispersion within non-hydrostatic models depends on the number of vertical layers. However, the addition of a vertical layer increases the computational time extremely. Therefore, a reduced two layer non-hydrostatic model (XBeach-nh+) was developed with the assumption of a constant non-hydrostatic pressure in the lower layer. In theory, XBeach-nh+ is capable of modelling the wave transformation from deep to shallow water, but the applied boundary conditions cannot force deep water waves. On top of that XBeach-nh+ has never been properly validated for reef environments.

Furthermore, the corals (growing on the reef flat) have a large effect on the reef-hydrodynamics by dissipating a large part of the wave energy. There exist different formulations to include vegetation into a non-hydrostatic wave model, but these formulations are mainly applicable for cylinder shaped geometries, whereas corals are more complex in shape. Apart from the shape, the in-canopy velocity can be significantly different from the free stream velocity. Therefore, a porous in-canopy model was implemented to model the in-canopy velocity, which was used to determine the canopy-induced force on the depth-averaged flow computation.

Firstly, the inclusion of the second reduced layer improves the dispersion relation up to a relative depth ($kh$) of 5 for linear waves. A simulation of biochromatic waves over a plane beach showed that XBeach-nh+ is capable of modelling the energy transfer between the major wave components. Both steeping and reflection of the sub-harmonic were modelled according to the measurements. Furthermore, the validation of random waves over a fringing reef showed the capability of XBeach-nh+ to model the reef-hydrodynamics for different wave conditions (rel. bias of -0.003 for total wave height, -0.081 for LF-waves and -0.103 for the setup). Moreover, the addition of the second reduced layer gives a more robust prediction for all modelled wave conditions, whereas the one-layer model contains more scatter.

Secondly, the in-canopy model captures the canopy-induced force when the canopy parameters were known. Both the in-canopy flow of unidirectional and oscillating flow fields was accurately modelled when the results were compared to the measured velocity though cylinders and corals. Although, the canopy parameters were not always known, it was shown that an un-calibrated in-canopy model, based on porosity and canopy height, gives a competitive result compared to a fully calibrated shear stress formulation. The applicability of XBeach-nh+ in 2-dimensional domain with a coral covered reef flat was shown by modelling a 5 day Swell event at Ningaloo Reef. Reasonably accurate results were achieved when using the in-canopy model, based on the canopy properties.