Modeling storm effects on sand wave dynamics

Abstract

Sand waves are wavy bed patterns that are observed in sandy shallow seas. They have wavelengths of hundreds of meters and heights of up to 10 meters. Sand waves are dynamic, meaning that their height can change and they can migrate up to tens of meters per year. The combination of shallow water, large crest height and their dynamical character implies that a good understanding of sand waves is required for various human activities at seas such as the North Sea. This will help improve surveying and dredging policies required for navigation safety. Other activities that benefit from a better understanding are placement of pipelines and cables and the construction of wind farms. Sand waves are generated by the interaction between the sandy seabed and the tidal current. Undulations in the seabed affect the current such that tidally averaged circulation cells transport sediment towards the crest. On the other hand, gravity tends to favor downslope sediment transport towards the trough. It is the competition between these two processes that determines the formation of sand waves. Next to the forming mechanism there are various other factors affecting sand wave dynamics. Observations show that sand wave height reduces and their migration rate increases during periods of stormy weather compared to calm conditions. The aim of this research is to understand how storms affect sand wave dynamics. Wind waves and wind-driven currents are the storm-related processes investigated in this thesis. Two new process-based idealized sand wave models have been developed that include these storm processes. The first model is based on linear stability analysis to systematically investigate the initial formation stage. To investigate the effect of storm processes on finite-amplitude sand wave dynamics a second model has been developed, which is fully nonlinear. With the linear stability model it is found that wind waves decrease the growth rate and increase the preferred wavelength of sand waves. Although wind waves in this model do not induce migration on their own, they do enhance migration caused by other processes. Wind-driven currents particularly affect sand wave migration. By breaking the { in the model { symmetrical tidal current, sand waves migrate in the direction of the residual current. Wind-driven ow can both increase and decrease the growth of sand waves, depending on wind direction and the Coriolis effect. By combining typical North Sea wave and wind conditions (corresponding to the Euro Platform) with the linear stability model, using a statistical weighted averaging method, it is found that storms mainly affect sand wave migration. Also a seasonality in sand wave migration is found. During winter, when stormy conditions occur more often, migration is larger compared to during summer. Using the nonlinear sand wave model, the evolution towards equilibrium is investigated. Wind waves reduce the equilibrium height and enhance the migration speed caused by wind-driven currents. Wind-driven currents result in asymmetrical sand wave shapes and migration in the direction of their steepest slope. Migration decreases with increasing sand wave height. Simulations of the evolution from randomly distributed small perturbations towards a fully grown sand wave field (for different wave and wind conditions) display larger sand waves overtaking smaller ones. This shows that sand waves interact with each other in complicated ways. Finally, it is found that the intermittent occurrence of storms and fair-weather conditions can lead to a dynamic equilibrium, were sand waves tend to grow towards the equilibrium states corresponding to fair-weather and stormy conditions, but due to limited adaptation time sand waves never reach those equilibrium states. Even short periods of storms can already significantly affect sand wave dynamics. This research provides process-based support for the influence of storms on sand wave dynamics, as found earlier by observational studies. Furthermore, the two newly developed sand wave models can be used for applications such as sand mining, nautical dredging, wind farms and pipelines.