Abstract

Direct numerical simulation (DNS), based on solution of the Navier Stokes equations, is used to study the characteristics of the transformation of monochromatic waves over a simplified fringing reef, including wave shoaling, and wave breaking that occurs under certain circumstances. The reef geometry involves a sloped plane beach extended with a simple submerged horizontal reef flat. The characteristics are studied for several case studies involving a selection of submergence depths on the reef flat and for a range of incident wave conditions, corresponding to nonbreaking, a spilling breaker and a plunging breaker, are considered. The results are compared with those of laboratory experiments (Kouvaras and Dhanak, 2018). Consistent with other studies, generation of harmonics of the fundamental wave frequency is found to accompany the wave transformation over the reef and the process of transfer of energy through wave breaking. The energy flux decreases dramatically in the onshore direction when the waves break. The more severe the wave breaking process, the greater the decrease in energy flux, particularly in the wave shoaling process. Most of the wave energy is carried by the first harmonic throughout its passage over the fringing reef. In nonbreaking waves, the energy gradually transfers from the first harmonic to the second harmonic due to bottom effects in terms of flat wave troughs and secondary waves. The further the distance away from the fore edge of the reef, the larger the percentage of the transmission, resulting in a single dominant harmonic frequency at the end of the wave surfing zone. For breaking waves, the energy carried by the first harmonic gradually decreases in the onshore direction. Energy transmission between harmonics is not as efficient as nonbreaking waves, while wave dissipation is significant in the wave breaking process.

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