Modelling the dynamics of large scale shoreline sand waves

Resumen

Shoreline sand waves are shoreline undulations with a length scale of several kilometres and a time scale of years to decades. They occur on many coasts, migrating in the direction of the dominant littoral drift and they introduce a variability into the shoreline position that can be greater than the long term coastal trend. The objective of this thesis is to provide more insight into the formation and dynamics of shoreline sand waves and, in particular, to explore the role of the so called high angle wave instability. Previous studies showed that the shoreline can be unstable under very oblique wave incidence. This high angle wave instability develops due to the feedback of shoreline changes and the associated changes in the bathymetry into the wave field. Wave propagation over this perturbed bathymetry leads to specific gradients in the alongshore transport that can cause the growth and migration of shoreline sand waves. In this thesis a quasi 2D non-linear morphodynamical model is improved and used to explore high angle wave instability and predict the formation and evolution of shoreline sand waves. The model assumes that the large scale and long term shoreline dynamics is controlled by the wave driven alongshore transport so that the details of the surfzone morphodynamics are not resolved. It overcomes some of the limitations of previous modelling studies on high angle wave instability. The wave field is computed with a simple wave module over the evolving bathymetry and an empirical formula is used to compute the alongshore transport. Cross-shore dynamics is described in a parameterized way and the model is capable of describing shoreline perturbations with a finite and dynamic cross-shore extent. The conditions under which shoreline instability can lead to the formation of shoreline sand waves are refined. Generic simulations with constant wave conditions and random initial perturbations show that the shoreline becomes unstable when the wave incidence angle at the depth of closure (i.e., the most offshore extent of the shoreline perturbations) is larger than a critical angle of about 42 degrees and shoreline sand waves develop in unison. The cross-shore dynamics plays an essential role because it determines the offshore extent of the shoreline perturbations. Using default model parameters, wave conditions and cross-shore profile, the sand waves develop with wavelengths between 2 and 5 km, the time scale for their formation is between 5 and 10 years and they migrate downdrift at about 0.5 km/yr. Simulations with a localized large scale perturbation trigger the formation of a downdrift sand wave train. Larger wave obliquity, higher waves and shorter wave periods strengthen the shoreline instability. A more realistic wave climate, with alternating high and low angle wave incidence reduces the potential for shoreline instability. A percentage of about 80% of high angle waves is required for sand wave formation. It is demonstrated that the range of low wave angles that can occur on a coast is larger than the range of high wave angles, and that the stabilizing effect produced by low angle waves (causing diffusion) is bigger than the destabilizing effect produced by high angle waves (causing growth and migration). Even if high angle waves are not dominant, the instability mechanism might still play a role in the persistence and downdrift migration of large scale shoreline perturbations. The model results are in qualitative agreement with observations of shoreline sand waves. The quasi 2D approach provides new insight into the physical mechanisms behind high angle wave instability and the occurrence of a minimal and optimal length scale for sand wave formation. Essential physical processes are wave energy dispersion due to wave refraction, wave energy focusing near the crest of a sand wave and the monotonic decrease of the gradients in alongshore transport for increasing length scales.