Modelling of wave penetration in complex areas : WTI - hydraulische belastingen

For the Dutch Legal Flood Safety Assessment (WTI) calculations of the Hydraulic Boundary Conditions, which are to be finalized by the end of 2015 and established by the Minister in 2017, wave statistics obtained at deeper water buoys needs to be transformed to the toe of the dike using the wave action model SWAN. This transformation is particularly challenging in complex tidal inlet systems such as the Wadden Sea and the Western Scheldt in the Netherlands. Although significant model improvements – particularly in the propagation and bottom friction dissipation - have been made, one of the unresolved issues is that the penetration of North Sea waves (0.03 – 0.20 Hz) into the tidal inlets is still underestimated by SWAN. \r\n\r\nThe hypothesis is that nonlinear interactions, especially ones that include a combination of super-and sub-harmonic triad interactions, play a major role in the transmission of energy from flats into the channel, and that this process can explain SWAN’s under-prediction of wave energy penetration. The goal of the study is to verify the hypothesis. Since SWAN lacks the relevant physics to study this problem, the Boussinesq-type TRITON model is used instead to verify the hypothesis.\r\n\r\nFrom the idealized cases with monochromatic and bi-chromatic waves propagating up and down a slope we conclude that the TRITON model results confirm the conceptual idea of 2D nonlinear interactions raised by Toledo (2013). Both sub-harmonic wave interactions (to lower frequencies) and super-harmonic wave interactions (to higher frequencies) prove to be important. Sub-harmonic wave interactions between second harmonic and basic component clearly show the generation of a wave component of the same frequency as the primary component but at a wider angle of approach. As a consequence, the energy density spectra become directionally broader.\r\nThe consequences can be transferred to the situation with waves propagating on a tidal flat towards a channel. Whereas the basic components approach the channel under a sharp angle, such that they will not be able to enter the channel due to refraction, the subharmonic components could approach the channel under a less sharp angle and enter the channel.\r\n\r\nIn the second part of the study TRITON and SWAN computations have been carried out with long- and short-crested waves propagating over a flat and approaching a channel under various angles. We conclude that the reduction of wave energy in the channel at the primary peak of the spectrum increases when the attack angle with respect to the channel orientation decreases. This reduction is an outcome of refraction at the flat-channel interface. Due to 2D nonlinear triad interactions the directional variance density spectrum broadens and more wave components are able to propagate across the interface into the channel. A clear difference between the TRITON and SWAN energy density spectra in the channel is observed. The 2D nonlinear interactions cannot be modelled with the co-linear 1D approach in SWAN. \r\n\r\nThe hypothesis that nonlinear interactions play a major role in the transmission of energy from flats into the channel is confirmed, at least for the cases considered in this study. Additional investigations are still required in order to get a clearer view of the general picture. It is strongly recommended to examine under which conditions SWAN underestimates the wave energy when propagating into complex tidal inlet systems. In addition, it is recommended to extend the presently implemented three-wave interaction formulation in SWAN to account for directional super- and sub-harmonic interactions.