A two-dimensional parametrization of a surf zone with a time-dependent breakpoint due to groupiness in the incident wave field is developed. The breakpoint is defined in terms of a mean position X plus a modulation Aa. Free wave solutions are obtained on a plane beach at the group frequency and its harmonics. Shoreward of the breakpoint, standing waves are found, while seaward an outgoing progressive wave exists. The amplitude of the standing wave is relatively insensitive to the incident wave field. The amplitude of the outgoing wave depends on X, the group frequency o, and the beach slope tan •. For certain values of X --(o2X?g tan •) the amplitude of the outgoing wave goes to zero. It appears that any 'resonant' response of the standing wave shoreward of the breakpoint is suppressed by seaward radiation of energy by the outgoing wave.in the onshore-offshore direction.

[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.

Long-term (1 month) observations of waves and currents over a natural reef are presented which show a strong correlation between offshore rms incident wave height and cross-reef currents at subtidal frequencies. The energy spectrum of the cross-reef currents shows a significant peak at twice the semidiurnal tidal frequency, while the spectrum of sea surface elevation over the reef flat shows no corresponding peak. Furthermore, experimental results reported by Goutlay (1993) show setup over the reef occurs in the absence of a beach, and the cross-reef transport decreases with an increase in the sea surface slope across the reef fiat due to a n' increase in setup at the top of the reef face. Analytic solutions for flow forced by wave breaking over an idealized reef explain the above features of cross-reef flows in the absence of a beach. Through the surf zone on the reef face the cross-reef gradient in the radiation stress due to wave breaking is partitioned between balancing an offshore pres. sure gradient associated with setup over the reef and forcing a mean flow across the reef. Over the reef fiat, where the depth is constant, there is no forcing due to wave breaking and the flow is driven by a pressure gradient which results from the setup through the surf zone. The magnitude of the setup through the surf zone is such that the transport across the reef flat matches the transport through the surf zone which is forced by the gradient in the radiation stress. Solutions are presented for general reef geometry, defined by the reef width and slope of the seaward reef face, and incident wave forcing, defined by the depth at the breakpoint and the depth of water over the reef. As the depth over the reef goes to zero, the solutions converge to the plane beach solutions described by Longuet-Higgins and Stewart (1964), wave setup is maximized, and the cross-reef transport is zero. In other cases the relative magnitudes of the setup and the cross-reef transport depend on the geometry of the reef and the incident wave forcing.

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