Wave Attenuation and Wave Set-Up on a Coastal Reef

Abstract

This study deals with the breaking of waves on coastal reefs, with special emphasis on energy dissipation (wave height attenuation), wave spectrum modification and the characteristics of wave set-up. It has an engineering perspective; its main objective is to provide the practicing engineer with much needed information on the design conditions for coastal structures. Although the problem is three-dimensional in nature considerations here are limited to two-dimensional conditions. The study consists of a review of existing literature, further development of theoretical concepts, a field study and a hydraulic model study. Chapter 1 is an introduction. It gives a short description of the hydrodynamic processes associated with waves breaking on a reef and it describes the goals and scope of investigations. Chapter 2 contains a discussion of some relevant aspects of nonlinear waves. The distinction followed by Whitham(1974), who distinguishes two main classes of waves as hyperbolic waves and dispersive waves, is followed. Of particular relevance is the concept of group velocity in nonlinear waves as an element for the computation of energy flux in both field and model experiments. Chapter 3 is devoted to the significant part bottom friction plays in wave dissipation over a shallow reef. The starting point of discussion is the bottom friction in linear waves. The bottom friction coefficient appears to be a function of both the wave Reynolds number and the relative roughness of the bottom. The effect of nonlinearity on bottom friction is evaluated by considering bottom friction losses for a solitary wave and by evaluating the effects of shoaling, breaking, and currents on the bottom friction coefficient. The various aspects of energy dissipation in breaking waves are discussed in Chapter 4. After a general discussion of the behavior of waves before and after breaking, the similarity between energy dissipation in a breaking wave and in a bore is considered in more detail. This similarity is used to define a breaking loss parameter, the value of which has been evaluated in this study from both field and model data. It appears that the proposed parameter is a useful concept in the evaluation of energy losses from wave breaking. Chapters 5 and 6 deal with aspects of wave set-up. In Chapter 5 the problem is treated as a stationary one. In the evaluation of radiation stresses required for the determination of the wave set-up, nonlinear aspects are also considered. Chapter 6 deals with the effects of a modulation wave train on the wave set-up on the reef. Aspects of the wave spectrum and the characteristics of the spectrum for various water depths are discussed in Chapter 7. Also discussed are the various possible ways to determine the energy density spectrum from the time series and the limitations of this spectrum to describe the characteristic features of waves in shallow water. Field experiments and their principal results are discussed in Chapter 8 and the results of the laboratory experiments in Chapter 9. In addition, the limitations of the experimental set-up to deal with wave attenuation and wave set-up in very shallow water in a scale model are evaluated. In Chapter 10 the computational aspects of wave attenuation and wave set-up are discussed both in respect to the analyses of field and model data and for prediction purposes. A summary, conclusion and recommendations are presented in Chapter 11 the acknowledgements in Chapter 12, and the bibliography in Chapter 13.