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[1] In this paper the energy budget of wave group-induced subharmonic gravity waves in the nearshore region is examined on the basis of the energy equation for long waves in conjunction with analyses of a high-resolution laboratory data set of one-dimensional random wave propagation over a barred beach. The emphasis is on the growth of forced subharmonics and the deshoaling of the reflected free waves in the shoaling zone. The incident lower-frequency subharmonics are nearly fully reflected at the shoreline, but the higher-frequency components appear to be subject to a significant dissipation in a narrow inshore zone including the swash zone. The previously reported phase lag of the incident forced waves behind the short-wave groups is confirmed, and its key role in the transfer of energy between the grouped short waves and the shoaling bound waves is highlighted. The cross-shore variation of the local mean rate of this energy transfer is determined. Using this as a source function in the wave energy balance allows a very accurate prediction of the enhancement of the forced waves in the shoaling zone, where dissipation is insignificant. The phase lag appears to increase with increasing frequency, which is reflected in a frequency-dependent growth rate, varying very nearly from the free-wave variation $ h À1/4 (Green's law) for the lower frequencies to the shallow-water equilibrium limit for forced subharmonics $h À5/2 for the higher frequencies. This observed frequency dependence is tentatively generalized to a dependence on a normalized bed slope, controlling whether a so-called mild-slope regime or a steep-slope regime prevails, in which enhanced incident forced waves dominate over breakpointgenerated waves or vice versa.

A numerical model, XBeach, calibrated and validated on field data collected at Roi‐Namur Island on Kwajalein Atoll in the Republic of Marshall Islands, was used to examine the effects of different coral reef characteristics on potential coastal hazards caused by wave‐driven flooding and how these effects may be altered by projected climate change. The results presented herein suggest that coasts fronted by relatively narrow reefs with steep fore reef slopes (~1:10 and steeper) and deeper, smoother reef flats are expected to experience the highest wave runup. Wave runup increases for higher water levels (sea level rise), higher waves, and lower bed roughness (coral degradation), which are all expected effects of climate change. Rising sea levels and climate change will therefore have a significant negative impact on the ability of coral reefs to mitigate the effects of coastal hazards in the future.

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[1] The growth rate, shoreline reflection, and dissipation of low-frequency waves are investigated using data obtained from physical experiments in the Delft University of Technology research flume and by parameter variation using the numerical model Delft3D-SurfBeat. The growth rate of the shoaling incoming long wave varies with depth with an exponent between 0.25 and 2.5. The exponent depends on a dimensionless normalized bed slope parameter b, which distinguishes between a mild-slope regime and a steep-slope regime. This dependency on b alone is valid if the forcing short waves are not in shallow water; that is, the forcing is off-resonant. The b parameter also controls the reflection coefficient at the shoreline because for small values of b, long waves are shown to break. In this mild-slope regime the dissipation due to breaking of the long waves in the vicinity of the shoreline is much higher than the dissipation due to bottom friction, confirming the findings of Thomson et al. (2006) and Henderson et al. (2006). The energy transfer from low frequencies to higher frequencies is partly due to triad interactions between low-and high-frequency waves but with decreasing depth is increasingly dominated by long-wave self-self interactions, which cause the long-wave front to steepen up and eventually break. The role of the breaking process in the near-shore evolution of the long waves is experimentally confirmed by observations of monochromatic free long waves propagating on a plane sloping beach, which shows strikingly similar characteristics, including the steepening and breaking.

[1] A 3 week field study was conducted to investigate the dynamics of low-frequency (infragravity) wave motions over a fringing reef at Ningaloo Reef, Western Australia. Short-period wave motions (0.04-0.2 Hz) were observed to dissipate on the reef crest beyond which infragravity wave motions (0.004-0.04 Hz) gradually dominated toward the lagoon. However, both the short waves and the infragravity waves were relatively small (both <0.3 m) on the reef flat owing to the shallow water depth (<2 m). The results revealed that the surf zone generation of free infragravity wave motions on the steep ($1:20) fore-reef slope was dominated by breakpoint forcing (as opposed to shoaling bound waves), which was also supported by detailed numerical simulations of the generation process. This is consistent with theory suggesting the efficiency of the breakpoint forcing mechanism should be high in this steep-slope regime. Shoreward propagating infragravity waves traveled across the reef but were damped by bottom friction dissipation; however, this was at a rate much smaller than experienced by the residual short waves. With these rates of frictional dissipation also strongly dependent on the water depth over the reef, the infragravity wave heights increased at higher water levels and hence were strongly modulated by the tide. Due to the strong dissipation of infragravity waves over this wide and shallow reef that is hydraulically rough, any seaward propagating infragravity waves that reflected at the shoreline were small, leading to the dominance of progressive (shoreward propagating) infragravity wave motions throughout the reef and lagoon.

Sea-level rise and wave-driven flooding will damage freshwater resources of most atolls and soon render them uninhabitable.

[1] The cross-shore propagation of group-bound long waves is investigated. A detailed laboratory data set from Boers [1996] is analyzed using primarily the cross-correlation function for a sequence of closely spaced cross-shore locations, thus visualizing the propagation of the short-wave envelope and attendant low-frequency motion in detail. The results confirm the previously observed lag of the forced subharmonics behind the short-wave envelope that increases with decreasing water depth. The forced subharmonics are found to be released and reflected at the shoreline and to propagate in offshore direction as free waves. A theoretical, linear model for the forced wave evolution accurate to first order in the relative bottom slope is presented; it predicts a bottom-slope induced, spatially varying phase shift between the short-wave envelope and forced waves which is in good agreement with the observations. The phase shift has dynamical consequences since it allows energy transfer between the short-wave groups and the forced low-frequency response.