Numerical Modeling of Shoreline Undulations

The present thesis considers undulations on sandy shorelines. The aim of the study is to determine the physical mechanisms which govern the morphologic evolution of shoreline undulations, and thereby to be able to predict their shape, dimensions and evolution in time. In order to do so a numerical model has been developed which describes the longshore sediment transport along arbitrarily shaped shorelines. The numerical model is based on a spectral wave model, a depth integrated flow model, a wave-phase resolving sediment transport description and a one-line shoreline model. First the theoretical length of the shoreline undulations is determined in the linear regime using a shoreline stability analysis based on the numerical model. The analysis shows that the length of the undulations in the linear regime depends on the incoming wave conditions and on the coastal profile. For larger waves and flatter profiles the length of the undulations increases. Secondly the evolution of the shoreline undulations from the linear regime to the fully non-linear regime is described using the numerical shoreline evolution model. In the fully non-linear regime down drift spits and migrating shoreline undulations are described by the model. The shoreline evolution is considered for both constant and varying wave forcing and both periodic model domains with a single undulation as well as periodic model domains with multiple undulation are considered. Three different shoreline shapes are found depending on the wave conditions and the coastal profile: undulations with no spits, undulations with flying spits and undulations with reconnecting spits. It is further shown that the evolution of the shoreline undulations is governed mainly by the angle between the shoreline and the incoming waves and the curvature of the shoreline. Thirdly the shoreline evolution model is tuned to two naturally occurring shorelines. On one of the shorelines, the west coast of Namibia, the shoreline model is able to describe the observed shoreline features in both a qualitative and quantitative way. The model over-predicts the scale of the feature and under predicts the migration speeds of the features. On the second shoreline, the shoreline model predicts undulations lengths which are longer than the observed undulations. Lastly the thesis considers field measurements of undulations of the bottom bathymetry along an otherwise straight coast at the DanishWest Coast. Two bathymetric datasets and two time series of wave measurements are used in order to determine the following properties: The offshore extent of shoreline undulations, the amount of sediment transported alongshore in the shoreline undulations, the relationship between the shoreline undulations and longshore bars and the relationship between the morphology and the hydrodynamics. In one of the data sets the shoreline undulations are well correlated with undulations on the depth contours between -5 m and +2 m relative to mean sea level. An analysis of the wave climate shows that this shoreline is right at the limit between a stable and an unstable shoreline.