[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.

[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] 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.

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, non-linear interactions in deep water; 4, white-capping dissipation; 5, non-linear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. Keywords

Surface-following buoys are widely used to collect routine ocean wave measurements. While accelerometer and tilt sensors have been used for decades to measure the wave-induced buoy displacements, alternative global positioning system (GPS) sensor packages have been introduced recently that are generally smaller, less expensive, and do not require calibration. In this study, the capabilities of several GPS sensors are evaluated with field observations in wind-sea and swell conditions off the California coast. The GPS buoys used in this study include Datawell Directional Waverider and Mini Directional Waverider buoys equipped with a specialized GPS Doppler shift sensor, and a low-cost experimental drifter equipped with an ''off the shelf'' GPS receiver for absolute position tracking. Various GPS position receivers were attached to the Waverider buoys to evaluate their potential use in low-cost wave-resolving drifters. Intercomparisons between the Datawell GPS-based buoys, the experimental GPS drifter, and a conventional Datawell buoy with an accelerometer-tilt-compass sensor package, show good agreement in estimates of wave frequency and direction spectra. Despite the limited (several meters) absolute accuracy of the GPS position receivers, the horizontal wave orbital displacements are accurately resolved, even in benign (significant wave height less than 1 m) swell conditions. Vertical sea surface displacements were not well resolved by the GPS position receivers with built-in or small patch antennas, but accurately measured when an external precision antenna was attached to the drifter. Overall, the field tests show excellent agreement between Datawell buoys using GPS and motion-sensor packages, and demonstrate the feasibility of observing ocean surface waves with lowcost GPS-tracked drifters.

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In this paper, the combined effects of refraction and nonlinearity on the evolution of ocean surface wave statistics are considered and possible implications for the likelihood of extreme waves, also known as freak or rogue waves, are examined. A frequency-angular spectrum model is derived that accounts for cubic nonlinear dynamics and weak lateral homogeneity of the medium. Through Monte Carlo simulations, the evolution of wave statistics in freely developing waves, waves over an opposing shearing current, and waves refracted over an isolated topographical feature is modeled. The simulations show that freely developing, directionally spread wave fields generally maintain near-Gaussian statistics, which was also found in earlier model studies. However, the enhanced nonlinearity caused by the refractive focusing of narrowband wave fields can result locally in strongly non-Gaussian statistics and an associated increased likelihood of extreme wave events.