Long waves approaching a cliff over a variable bathymetry are investigated. The waves experience extreme runup amplifications at the cliff, and wave breaking may occur. Kinematic, steepness, and wave height to depth metrics are applied locally to the crests. The generally accepted maximum value of wave height to depth is observed to sometimes be exceeded during wave interactions with the cliff. This is both spatially and temporally local and coincides with large amplifications of steep waves.


Long incident waves result in large runup amplifications at coastal cliffs. Runup amplification over a flat bathymetry is significantly larger than that given by linear theory (factor of 5-6 as opposed to 2) due to a combination of reflection, constructive interference, dispersion and nonlinear effects (Akrish et al., 2016a; Carbone et al., 2013; Viotti et al., 2014). Furthermore, strong variations in depth enhance the amplification of waves (Viotti and Dias, 2014). Runup over a variable bathymetry results in even greater runup amplifications (up to factor of 12), but introduces breaking waves (Herterich and Dias, Submitted). The impact of steep near-breaking waves on a cliff may result in a fast jet-like runup (Cooker and Peregrine, 1995), and can cause major coastal damage (Wolters and Muller, 2004).

In numerical simulations over a flat bathymetry, small-amplitude long waves do not exhibit breaking during runup at a cliff. However, once a variable bathymetry is introduced, steep wave fronts develop. Physically, the breaking of water surface waves is the overturning of the wave crest. The onset of wave breaking is typically characterised by a steep asymmetric wave and the formation of whitewater (due to entrained air from turbulence) at the crest tip that falls down the face of the wave. The physics of a breaking wave leads to several different criteria for determining the onset of wave breaking over a deep-to-intermediate flat bathymetry: geometric (Wu and Nepf, 2002), kinematic (Stansell and MacFarlane, 2002; Wu and Nepf, 2002), energetic (Barthelemy et al., 2015; Seiffert and Ducrozet, 2016). These criteria are evaluated locally, as the extremal conditions for wave breaking may not be seen in global wave-parameter values. The above criteria for wave breaking were considered for a simplified variable bathymetry representative of the Aran Islands, Ireland (Herterich and Dias, Submitted). Here, both bathymetry and cliff interaction influence the wave behaviour: phase velocities slow down and fluid velocities speed up. With initial amplitudes close to the breaking/non-breaking transition value, results are consistent with a deep-to-intermediate flat bathymetry. However, there are inconsistencies when the initial amplitude is close to the breaking/non-breaking transition value.

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