The transformation of random wave heights during shoaling, including waves breaking in the surf zone, was measured with an extensive array of instruments in the field. The initially Rayleigh height distributions in 10‐m depth were observed to be modified by shoaling and breaking into new distributions which are again nearly Rayleigh but with some energy loss. Using locally measured Hrms, the Rayleigh distribution describes the measured central moments of H1/3 and H1/10 with average errors of −0.2% and −1.8%, respectively. The Rayleigh distribution is used to describe the random nature of wave heights in a single‐parameter transformation model based on energy flux balance. The energy losses associated with wave breaking are parameterized using observed breaking wave distributions coupled with a periodic bore dissipation model. Using incident waves measured in 10‐m depth as input conditions, the model predicts Hrms at shoreward locations within a rms error of ±9%. The single free parameter of the model, a constant B representing the fraction of foam on the face of a wave, was chosen to best fit the data. The resulting large value of B implies that the simple periodic bore dissipation function substantially underestimates the actual dissipation.

[1] Shoreline location and incident wave energy, observed for almost 5 years at Torrey Pines beach, show seasonal fluctuations characteristic of southern California beaches. The shoreline location, defined as the cross-shore position of the mean sea level contour, retreats by almost 40 m in response to energetic winter waves and gradually recovers during low-energy summer waves. Hourly estimates of incident wave energy and weekly to monthly surveys of the shoreline location are used to develop and calibrate an equilibrium-type shoreline change model. By hypothesis, the shoreline change rate depends on both the wave energy and the wave energy disequilibrium with the shoreline location. Using calibrated values of four model free parameters, observed and modeled shoreline location are well correlated at Torrey Pines and two additional survey sites. Model free parameters can be estimated with as little as 2 years of monthly observations or with about 5 years of ideally timed, biannual observations. Wave energy time series used to calibrate and test the model must resolve individual storms, and model performance is substantially degraded by using weekly to monthly averaged wave energy. Variations of free parameter values between sites may be associated with variations in sand grain size, sediment availability, and other factors. The model successfully reproduces shoreline location for time periods not used in tuning and can be used to predict beach response to past or hypothetical future wave climates. However, the model will fail when neglected geologic factors are important (e.g., underlying bedrock limits erosion or sand availability limits accretion).

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Aspects of the nonlinear dynamics of waves shoaling between 9 and 1 m water depths are elucidated via the bispectrum. Bispectral-signal levels are generally high, indicating significant nonlinear coupling. In 9 m depth, the biphases of interactions involving frequencies at, and higher than, the peak of the energy spectra are suggestive of Stokes-like nonlinearities (Hasselman, Munk & MacDonald 1963). Further shoaling gradually modifies these biphases to values consistent with a wave profile that is pitched shoreward, relative to a vertical axis. Bicoherence and biphase observations with a double-peaked (swell and wind-wave) power spectrum provide evidence for excitation of modes at intermediate frequencies via difference interactions, as well as the sum interactions responsible for harmonic growth. Shoreward-propagating low-frequency (surf-beat) energy is shown to have statistically significant coupling to higher-frequency modes within the power-spectral peak. In 18 m depth, the biphase of these interactions is close to 180°, a value consistent with the classical concept of bound long waves. In shallower water, however, substantial biphase evolution occurs, and there is no longer a unique phase relationship between surf beat and the envelope of high-frequency waves. The contributions to sea-surface-elevation skewness and asymmetry (with respect to a vertical axis) from interactions among various wave triads are given by the real and imaginary parts of the bispectrum, respectively. In very shallow water, coupling between surf beat and higher-frequency waves results in a skewness with sign opposite to, and about 40% of the magnitude of, the skewness resulting from interactions between the power-spectral-peak frequency and higher frequencies.

Run-up (swash) oscillations were measured on a gently sloping beach face for a variety of incident wave conditions. Run-up energy spectra at wind wave frequencies show anf -3 dependence and energy levels that are independent of incident wave height. This suggests saturation. In contrast, run-up energy at surf beat periods increase approximately linearly with increasing incident wave energy. Thus, in the inner surf zone, where wave breaking limits the energy at wind wave frequencies, the principal manifestation of large incident wind waves is energetic surf beat.

Abstract. Mean alongshore currents observed on two barred beaches are compared with predictions based on the one-dimensional, time-and depth-averaged alongshore momentum balance between forcing (by breaking waves, wind, and 10-100 km scale alongshore surface slopes), bottom stress, and lateral mixing. The observations span 500 hours at Egmond, Netherlands, and 1000 hours at Duck, North Carolina, and include a wide range of conditions with maximum mean currents of 1.4 m/s. Including rollers in the wave forcing results in improved predictions of the observed alongshore-current structure by shifting the predicted velocity maxima shoreward and increasing the velocity in the bar trough compared with model predictions without rollers. For these data, wave forcing balances the bottom stress within the surfzone, with the other terms of secondary importance. The good agreement between observations and predictions implies that the one-dimensional assumption holds for the range of conditions examined, despite the presence of small alongshore bathymetric nonuniformities. With stronger bathymetric variations the model skill deteriorates, particularly in the bar trough, consistent with earlier modeling and laboratory studies.

Genetically, beach cusps are of at least two types: those linked with incident waves which are surging and mostly reflected (reflective systems) and those generated on beaches where wave breaking and nearshore circulation cells are important (dissipative systems). The spacings of some cusps formed under reflective wave conditions both in the laboratory and in certain selected natural situations are shown to be consistent with models hypothesizing formation by either (1) subharmonic edge waves (period twice that of the incident waves) of zero mode number or (2) synchronous (period equal to that of incident waves) edge waves of low mode. Experiments show that visible subharmonic edge wave generation occurs on nonerodable plane laboratory beaches only when the incident waves are strongly reflected at the beach, and this observation is quantified. Edge wave resonance theory and experiments suggest that synchronous potential edge wave generation can also occur on reflective beaches and is a higher‐order, weaker resonance than the subharmonic type. In dissipative systems, modes of longshore periodic motion other than potential edge waves may be important in controlling the longshore scale of circulation cells and beach morphologies. On reflective plane laboratory beaches, initially large subharmonic edge waves rear‐rage sand tracers into shapes which resemble natural beach cusps, but the edge wave amplitudes decrease as the cusps grow. Cusp growth is thus limited by negative feedback from the cusps to the edge wave excitation process. Small edge waves can form longshore periodic morphologies by providing destabilizing perturbations on a berm properly located in the swash zone. In this case the retreating incident wave surge is channelized into breeches in the berm caused by the edge waves, and there is an initially positive feedback from the topography to longshore periodic perturbations.

The generation and propagation of infragravity waves (frequencies nominally 0.004–0.04 Hz) are investigated with data from a 24‐element, coherent array of pressure sensors deployed for 9 months in 13‐m depth, 2 km from shore. The high correlation between observed ratios of upcoast to downcoast energy fluxes in the infragravity (FupIG/FdownIG) and swell (Fupswell/Fdownswell) frequency bands indicates that the directional properties of infragravity waves are strongly dependent on incident swell propagation directions. However, FupIG/FdownIG is usually much closer to 1 (i.e., comparable upcoast and downcoast fluxes) than is Fupswell/Fdownswell, suggesting that upcoast propagating swell drives both upcoast and downcoast propagating infragravity waves. These observations agree well with predictions of a spectral WKB model based on the long‐standing hypothesis that infragravity waves, forced by nonlinear interactions of nonbreaking, shoreward propagating swell, are released as free waves in the surf zone and subsequently reflect from the beach. The radiated free infragravity waves are predicted to be directionally broad and predominantly refractively trapped on a gently sloping shelf. The observed ratios FseaIG/FshoreIG of the seaward and shoreward infragravity energy fluxes are indeed scattered about the theoretical value 1 for trapped waves when the swell energy is moderate, but the ratios deviate significantly from 1 with both low‐ and high‐energy swell. Directionally narrow, shoreward propagating infragravity waves, observed with low‐energy swell, likely have a remote (possibly trans‐oceanic) energy source. High values (up to 5) of FseaIG/FshoreIG, observed with high‐energy swell, suggest that high‐mode edge waves generated near the shore can be suppressed by nonlinear dissipation processes (e.g., bottom friction) on the shelf.