Surface Wave Processes on the Continental Shelf and Beach


Thomas H. C. Herber


There is a growing need for surface wave information on the continental shelf and beach to estimate sea state, and to provide input for models of currents, sediment transport, radar backscatter and aerosol generation. While surface wave spectra in the open ocean evolve slowly over distances of O(100-1000 km), wave properties on the continental shelf and beach are highly variable (typical length scales of 0.1-10 km) owing to a variety of topographic effects (e.g., shoaling, refraction, scattering) and strongly enhanced nonlinear interactions and dissipation. The long-term goal of this research is to develop a better understanding of the physical processes that affect the generation, propagation and dissipation of surface waves in shallow coastal waters, and improve the accuracy of models that predict the transformation of wave properties across the shelf and beach. The principal collaborators in this research are Steve Elgar, R. T. Guza, and W. C. O'Reilly.

Specific objectives are:


A combination of theory, analytical and numerical models, and field experiments is used to investigate the physical processes that affect surface wave properties on the continental shelf and beach. In intermediate continental shelf depths, nonresonant nonlinear interactions force a broad spectrum of phase-coupled motions. Predictions of forced secondary and tertiary waves excited in triad and quartet interactions are obtained with Hasselmann's (1962) dispersive, weakly nonlinear finite depth theory. The transformation of swell spectra across the shelf is predicted with models based on a spectral energy balance that include the effects of refraction (Longuet-Higgins, 1957) and resonant quartet interactions (Hasselmann, 1962).

On beaches near-resonant triad interactions cause strong evolution of wave spectra over distances of only a few wavelengths. A new stochastic shoaling model is under development, based on the Boussinesq equations for weakly nonlinear, weakly dispersive waves (Peregrine, 1967), that can be applied to random, directionally spread wind waves propagating over a gently sloping beach with approximately straight and parallel depth contours. While the wind waves and associated high-frequency harmonics are mostly dissipated in the surf zone, the nonlinearly excited infragravity waves reflect from the beach and radiate seward across the shelf as free waves (Longuet-Higgins and Stewart, 1962). A spectral WKB approximation is used to describe the refraction and topographic trapping of infragravity waves radiated from shore.

Extensive field data are used to verify predictions of topographic and nonlinear effects, and to estimate the energy losses owing to bottom friction and wave breaking. The data sets include coherent arrays of pressure sensors and current meters deployed near Duck, NC, Cape Canaveral, FL, Norfolk, VA, and Point Conception, CA, and single point wave measurements (pressure sensors and directional buoys) from numerous field sites. As part of this project a dense transect of pressure sensors was deployed across the North Carolina shelf to obtain detailed measurements of the shelf-wide variability of swell and infragravity waves. Analysis techniques applied to the measurements include various inverse methods to extract directional and wavenumber properties from array cross-spectra, bispectral and trispectral analysis to detect nonlinear coupling, as well as standard statistical methods to determine empirical relationships between observed variables.


During DUCK94 a cross-shelf transect of 11 bottom-mounted and 9 surface-moored pressure transducers was deployed on the seafloor of the North Carolina shelf, extending from the shoreline to the shelf break (87 m depth, 100 km from shore). High-quality data was collected throughout the four-month-long deployment spanning a wide range of conditions (including Hurricane Gordon with a maximum significant wave height of approximately 8 m).

Analysis of observations from a large number of field sites (Fig. 1) shows that infragravity-frequency (nominally 0.005-0.05 Hz) motions on the continental shelf are a mixture of forced waves locally excited by nonlinear wave interactions and free waves predominantly radiated from nearby shores. Bispectral analysis was used to estimate the relative contributions of forced (phase-coupled to local wave groups) and free (not coupled) waves to the infragravity band. Estimates of forced and free infragravity energy at several sites are shown in Figs. 2-4. Both free and forced infragravity energy levels generally increase with increasing swell energy and decreasing water depth (Fig. 2), but their dependencies are markedly different. While forced infragravity wave energy is approximately proportional to the swell energy squared (Fig. 2a) consistent with quadratic coupling, a weaker (roughly linear) dependence is observed for free infragravity waves (Fig. 2b). Forced wave energy levels decrease sharply with increasing water depth owing to a weakening of the nonlinearity (Fig. 2a). Free wave levels decrease gradually with increasing depth owing to unshoaling and refractive trapping (Fig. 2b). Although free waves usually dominate the infragravity band, forced waves contribute a significant fraction of the total infragravity energy with high energy swell and/or in very shallow water.

While forced infragravity energy levels are a function only of the local water depth and wave field (Figs. 2a, 3a, 4a), free infragravity energy levels also depend on the general geographic surroundings. Comparisons of observations from the same depth and with similar swell conditions, but on different shelves, suggest that more free infragravity wave energy is radiated from wide, sandy beaches than from rocky, cliffed coasts (Fig. 3b), and that less energy is refractively trapped on a narrow shelf than on a wide shelf (Fig. 4b).

Infragravity waves are important to harbor oscillations, sediment transport, and other nearshore processes. This study, using theoretical models and field data, has yielded new and significant insights into the complex processes controlling the generation and propagation of infragravity waves.


Hasselmann, K., 1962: On the non-linear energy transfer in a gravity-wave spectrum, Part 1. General theory. J. Fluid Mech., 12, 481-500.

Longuet-Higgins, M. S., and R. W. Stewart, 1962: Radiation stress and mass transport in surface gravity waves with application to 'surf beats.' J. Fluid Mech., 13, 481-504.

Peregrine, D. H., 1967: Long waves on a beach. J. Fluid Mech. 27, 815-827.

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