Modelling refraction of waves over tidal channels

Abstract

For the design of coastal structures, the hydraulic loads that act on the coast should be known. These are often based on extrapolation of measurements. However, if the physical relation is unknown, large errors could be made. Therefore, a numerical model can be set up to take the most important processes into account.Yet, uncertainties are present in these numerical models as well. Taking for example the spectral wave model SWAN, it is hypothesised that the wave bottom refraction is not always properly modelled. Previous studies concluded that SWAN overestimates this refraction process near tidal channels, leading to an underestimation of waves entering the channel.This study uses the model SWAN in which different sensitivities are tested to assess the effect on refraction. The focus will be on the spatial and directional resolution as well as the wave propagation scheme that SWAN uses to discretise the propagation terms, which are the default SORDUP scheme and the optional BSBT scheme. From previous studies it is known that also physical processes could impact the bottom refraction, however these are only addressed shortly in this study. The aim of this study is to analyse the current performance of SWAN with respect to refraction and to assess how this performance can be improved.First, an analysis of a simple schematic channel case is made in SWAN, where waves propagate from shallow to deeper water. Physical source terms and wind wave-growth were deactivated in this part. It is found that a coarser spatial resolution can lead to a weaker wave refraction. This is caused by the way SWAN determines the turning rate, which is underestimated by SWAN compared to the theory of Snellius. On the other hand, an overestimation of wave refraction was observed for cases were waves should enter the channel. This is partly caused by the increased diffusion. These findings were taken into practice in a study of the Eastern Wadden Sea, specifically along the Ems channel, where waves propagated from deeper to shallower water. A coarser spatial resolution and the BSBT scheme showed less wave penetration from offshore into the Ems channel. The storm of January 2017 was simulated in SWAN after which a comparison was made to measurements. It was found that SWAN underestimated the wave energy for frequencies<0.15Hz. However, this did not improve by refining the resolution in both spatial and directional domain or by applying a different propagation scheme. SWAN thus overestimates the wave refraction due to bottom gradients if waves propagate to shallower water. In case waves travel to deeper water, refraction can be underestimated. If all physical source terms are deactivated, the effects of resolution on refraction are clearly visible. Including the source terms diminishes this effect. Along the channel edges, effects of increased spatial resolution are notable giving a significant wave height of 12-14cm (6-9%) closer to the measured condition. However, the effects at the coast near Uithuizerwad are negligible.