The role of offshore boundary conditions in the uncertainty of numerical prediction of wave overtopping using non-linear shallow water equations

Abstract

The paper examines the variability of wave overtopping parameters predicted by numerical models based on non-linear shallow water equations, due to the boundary conditions obtained from wave energy density spectra. Free surface elevation time series at the boundary are generated using the principle of linear superposition of the spectral components. The components' phases are assumed to be random, making it possible to generate an infinite number of offshore boundary conditions from only one spectrum.A reference case was provided by carrying out overtopping tests on a simple concrete structure in a wave flume. Numerical tests using the measured free surface elevation at the toe of the structure were carried out. Three parameters were analysed throughout the paper: the overtopping discharge, the probability of overtopping and the maximum overtopping volume. These showed very good agreement between the numerical solver prediction and the overtopping measurements. Subsequently, the measured spectra at the toe were used to generate a population of reconstructed offshore boundary time series for each test, following a Monte Carlo approach. A sensitivity analysis determined that 500 tests were suitable to perform a statistical analysis on the predicted overtopping parameters. Results of these tests show that the variability in the predicted parameters is higher for the smaller number of overtopping waves in the modelled range and decreases significantly as overtopping becomes more frequent. The characteristics of the distributions of the predictions have been studied. The average value of the three parameters has been compared with the measurements. Although the accuracy is lower than that achieved by the model when the measured time series are used at the boundary, the prediction is still fairly accurate above all for the highest overtopping discharges. The distribution of the modelled probability of overtopping was found to follow a normal distribution, while the maximum value follows a GEV one. The overtopping discharge shows a more complex behaviour, values in the middle of the tested range follow a Weibull distribution, while a normal distribution describes the top end of the range better.Results indicate that when the probability of overtopping is smaller than 5%, a sensitivity analysis on the seeding of the offshore boundary conditions is recommended.