The Formation of Edge Waves Under Monochromatic and Random Incident Waves

Abstract

Edge waves are coastal waves trapped near the shore by reflection and refraction. Previous studies show the excitation mechanism of edge waves under monochromatic wave conditions via phase locking and nonlinear growth. However, how efficiently the mechanism would work under random incident waves remains unclear. Consequently, this thesis aims: (1) to provide the first laboratory evidence of edge wave excitation under random incident waves and compare the edge wave growth under random incident waves with that under monochromatic incident waves; (2) to test the excitation mechanism proposed by a theory of edge wave excitation under narrow-banded random incident waves with laboratory measurements; and (3) to examine the performance of numerical models to reproduce the resonance between incident and edge waves. The laboratory experiments consist of cases in which edge wave excitation under monochromatic incident waves and cases in which edge waves are present under random incident waves. In the laboratory, edge waves develop when incident waves are monochromatic, and the edge wave amplitude remains unchanged when the waveform stabilises after the growth. By comparison, the presence of edge waves is intermittent when the incident wave energy is distributed over frequencies (i.e., with frequency spread) and directions (i.e., with directional spread). Edge waves modulate during the intermittent growth. Under incident waves with different levels of spread in frequencies and directions, modulating edge waves differ in amplitudes and durations. The observed intermittent edge wave growth agrees with predictions from the theoretical model. In the theoretical model, when narrow-banded, random incident waves are used, the predictions show that edge wave amplitudes keep modulating over time. Further comparisons based on decomposed incident waves and edge waves from the runup measured in the laboratory show the phase locking/unlocking between incident and edge waves consistent with the observed intermittent presence of edge waves. Both the theory and the measurements suggest that the coupling (uncoupling) phases drive the growth (decrease) of edge wave amplitudes under monochromatic and random incident waves. Two numerical models, SWASH and GPUSPH, are used to reproduce the resonance between edge waves and incident waves. The simulation of edge wave excitation under monochromatic incident waves agrees with the observations during experiments. Meanwhile, certain drawbacks of the models are revealed from the case study. The computation of SWASH is not stable when edge waves are simulated with reflective side boundaries and when two peaks of edge waves merge into one. On the other hand, GPUSPH produces a slowly increasing mean water level in the simulation. All the results - laboratory, theoretical and numerical - contribute to a clear example of how random incident waves affect the hydrodynamics of the nearshore differently from monochromatic waves, and the results recommend random wave conditions to be used in hydrodynamic and morphological models of the nearshore. Future work should explore how morphological changes affect the excitation mechanism of edge waves. Also, the resonance between incident and edge waves should be used as a case study to test more types of wave models in the future.