W. C. O'Reilly

A comparison of two spectral wave models in the Southern California Bight

Abstract Two models, a spectral refraction model (Longuet-Higgins) and a parabolic equation method (PEM) refraction-diffraction model (Kirby), are used to simulate the propagation of surface gravity waves across the Southern California Bight. The Bight contains numerous offshore islands and shoals and is significantly larger (≈ 300 km by 300 km) than regions typically studied with these models. The effects of complex bathymetry on the transformation of incident wave directional spectra, S0(f,θ0), which are very narrow in both frequency and direction are difficult to model accurately. As S0(f,θ0) becomes broader in both dimensions, agreement between the models improves and the spectra predicted at coastal sites become less sensitive to errors in the bathymetry grid, to tidal changes in the mean water depth, and to uncertainty in S0(f,θ0) itself. The smoothing associated with even relatively narrow (0.01 Hz-5° bandwidth) S0(f,θ0) is usually sufficient to bring the model predictions of shallow water energy into at least qualitative agreement. However, neither model is accurate at highly sheltered sites. The importance of diffraction degrades the predictions of the refraction model, and a positive bias [O (10%) of the deep ocean energy] in the refraction-diffraction model estimates, believed to stem from numerical “noise” (Kirby), may be comparable to the low wave energy. The best agreement between the predicted spectra generally occurs at moderately exposed locations in deeper waters within the Bight, away from shallow water diffractive effects and in the far-field of the islands. In these cases, the differences between the models are small, comparable to the errors caused by tidal fluctuations in water depth as waves propagate across the Bight. The accuracy of predicted energies at these sites is likely to be limited by the uncertainty in specifying S0(f,θ0).

Swell Transformation across the Continental Shelf. Part I: Attenuation and Directional Broadening

Abstract Extensive wave measurements were collected on the North Carolina–Virginia continental shelf in the autumn of 1999. Comparisons of observations and spectral refraction computations reveal strong cross-shelf decay of energetic remotely generated swell with, for one particular event, a maximum reduction in wave energy of 93% near the Virginia coastline, where the shelf is widest. These dramatic energy losses were observed in light-wind conditions when dissipation in the surface boundary layer caused by wave breaking (whitecaps) was weak and wave propagation directions were onshore with little directional spreading. These observations suggest that strong dissipation of wave energy takes place in the bottom boundary layer. The inferred dissipation is weaker for smaller-amplitude swells. For the three swell events described here, observations are reproduced well by numerical model hindcasts using a parameterization of wave friction over a movable sandy bed. Directional spectra that are narrow off the s...

Swell Transformation across the Continental Shelf. Part II: Validation of a Spectral Energy Balance Equation

Abstract State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated using extensive field observations of swell evolution across the North Carolina continental shelf and hindcasts performed with the spectral wave prediction model CREST. The spectral energy balance equation, including bottom friction and wave–bottom scattering source terms, was integrated numerically for selected time periods with swell-dominated conditions. Incident wave spectra at the model boundary were estimated from buoy measurements near the shelf break, assuming weak spatial variations in the offshore wave field. The observed strong and variable decay of the significant wave height across the shelf is predicted accurately with an overall scatter index of 0.15. Predicted wave directional properties at the peak frequency also agree well with observations, with a 5° root-mean-square error on the mean direction at the peak frequency and a 0.22 scatter index for the directional spread. Slight modifi...

A Hybrid Eulerian–Lagrangian Model for Spectral Wave Evolution with Application to Bottom Friction on the Continental Shelf

Abstract A hybrid Eulerian–Lagrangian wave model is presented that solves the spectral energy balance equation for surface gravity waves in varying depth. The energy of each spectral component is advected along (Lagrangian) ray trajectories. The source terms in the energy balance equation (e.g., interactions between wave components and nonconservative processes) are computed on a fixed Eulerian grid and interpolated onto the ray trajectories. The source terms are integrated in time along the rays. This integration is performed in parallel over the entire model domain. The main advantage of this new model, named CREST (Coupled Rays with Eulerian Source Terms), is that refraction of waves by subgrid-scale depth variations is evaluated accurately using precomputed rays, and thus the model can be applied with relatively coarse source term grids to large coastal areas. Hindcasts of swell evolution across the North Carolina continental shelf are presented for a source term restricted to energy dissipation in th...

A Comparison of Directional Buoy and Fixed Platform Measurements Of Pacific Swell

Abstract The performance of the Datawell Directional Waverider and the National Data Buoy Center (NDBC) 3-m discus buoy, widely used to measure the directional properties of surface gravity waves, are evaluated through comparisons to an array of six pressure transducers mounted 14 m below the sea surface on a platform in 200-m depth. Each buoy was deployed for several months within a few kilometers of the platform. The accuracy of the platform ground-truth array was verified by close agreement of wavenumber estimates with the theoretical linear dispersion relation for surface gravity waves. Buoy and array estimates of wave energy and directional parameters, based on integration of the directional moments across the frequency band of energetic swell (0.06–0.14 Hz), are compared for a wide range of wave conditions. Wave energy and mean propagation direction estimates from both buoys agree well with the platform results. However, the Datawell buoy provides significantly better estimates of directional spread...

Propagation of swell across a wide continental shelf

The transformation of ocean swell across a wide, shallow (nominal depths 25–50 m) continental shelf is examined with data from a 100 km long transect of bottom pressure recorders extending from the shelf break to the beach at Duck, North Carolina. The analysis is restricted to periods with light winds when surface boundary layer processes (e.g., wave generation by wind and wave breaking in the form of whitecaps) are expected to be relatively unimportant. The majority of the observations with low-energy incident swell conditions (significant wave heights <1 m) shows weak variations in swell energy across the shelf, in qualitative agreement with predictions of a spectral refraction model. Although the predicted ray trajectories of waves propagating over the irregular shelf bathymetry are quite sensitive to the deep water incident wave directions, the predicted spatial energy variations for broadbanded wave fields are small and relatively insensitive to incident wave conditions, consistent with the observations. Whereas swell dissipation on the shelf appears to be insignificant in low-energy conditions, strong attenuation of swell energy levels (a factor 4 between the shelf break and nearshore sites) was observed in high-energy conditions (significant wave height 2.5 m). This decay, not predicted by the energy-conserving refraction model, indicates that dissipative bottom boundary layer processes can play an important role in the transformation of swell across wide continental shelves.

Australia-Bermuda Sound Transmission Experiment (1960) Revisited

Abstract Detonations at the depth of the sound channel axis off Perth, Australia were recorded on Bermuda hydrophones at a 178°.2 range (180° is antipodal). The analysis by Shockley et al. of this 1960 transmission experiment allows for the geographic variation in the sound speed profile along the great circle path. The agreement between measured and computed travel times is within 10 s. We have modified the Shockley et al. analysis by allowing for Earth flattening and lateral refraction. The appropriate path on an ellipsoidal Earth is the geodesic, and this differs significantly from the put circle for nearly antipodal ranges. The southernmost point of the geodesic is at 52°1 S as compared to 47°.3 S for the great circle, and the geodesic travel time lags the great circle travel time by an unacceptable 34 s on account of the cold, slow waters at high southern latitudes. The effect of lateral refraction is in the opposite sense: the appropriate refracted ray path is northward of the great circle; in fact ...