Wave breaking induced drift

Abstract

Accurately predicting the surface transport in the ocean is crucial for estimating the course of marine pollution, which is considered one of the most pressing environmental issues of the 21st century. In the ocean, floating marine pollution is transported by several mechanisms, including waves. Current models predicting the surface transport set the wave-induced transport component to be equal to the Stokes drift, which is defined as the net drift that a fluid parcel experiences in the direction of a propagating wave. However, Deike et al. (2017) and Pizzo et al. (2019) indicated that the transport induced by the Stokes drift is enhanced by breaking waves. Despite extensive study of the wave breaking phenomenon, it is still not possible to accurately predict the surface transport for breaking waves in deep water irregular seas. Thus, in this thesis, the contribution of the transport from breaking waves to the total wave-induced transport at the surface of a deep-water unidirectional irregular sea is estimated. To do this. a theoretical model is developed. The model computes the transport of individual breaking wave groups from surface elevation measurements of a deep-water unidirectional irregular sea. Thereafter, the contribution of the wave-induced transport from breaking to the total wave-induced transport is defined by an enhancement factor. This enhancement factor shows how much the total surface transport in a wave field without breaking waves is enhanced by the transport of breaking wave groups.

The model that is developed is an extension of the relationship from research by Sinnis et al. (2021). In their research, they defined a transport relationship for isolated breaking wave groups based on the spectral bandwidth and the linear slope of the wave groups. In the model, the transport relation from Sinnis et al. is applied to the breaking wave groups from surface elevation measurements of deep water irregular seas. In order to do this, the surface elevation spectrum was approximated by multiple Gaussian wave groups. From the Gaussian wave groups, the spectral bandwidth and the linear slope could be determined. The breaking waves were identified based on a steepness threshold for the wave groups. The wave-breaking-induced transport was calculated for all individual breaking wave groups.

Additionally, experiments were carried out to validate the theoretical model. The experiments were performed in the Atlantic Basin of Deltares. In this facility, unidirectional irregular waves were generated in deep water. During the experiments, an overhead camera filmed the behavior of quasi-Lagrangian particles floating on top of the waves. The particles were tracked using OpenCV and their trajectories were obtained. Because the particles in breaking waves travel faster than in non-breaking waves, a velocity threshold was used to identify the breaking waves in the trajectories. From the identified breaking waves the wave-breaking-induced transport was quantified.

Furthermore, the theoretical model was validated by comparing the number of breaking waves, the strength of the breaking events, and the enhancement factor with the experimental results. The results showed that all values were in the same order of magnitude and that the wave-breaking-induced transport enhanced the surface transport for non-breaking waves by a factor up to 1.5. Besides, a sensitivity analysis on the relevant parameters showed that the error margin remains within 10% from the mean. In conclusion, the theoretical model gave reasonable predictions of the contribution of the wave-breaking-induced transport in a unidirectional irregular sea. Hence, this framework can be fruitful grounds for further extension of the breaking induced drift in the ocean.