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- Author or Editor: R. T. Guza x
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Abstract
The nonlinear dispersion of random, directionally spread surface gravity waves in shallow water is examined with Boussinesq theory and field observations. A theoretical dispersion relationship giving a directionally averaged wavenumber magnitude as a function of frequency, the local water depth, and the local wave spectrum and bispectrum is derived for waves propagating over a gently sloping beach with straight and parallel depth contours. The linear, nondispersive shallow water relation is recovered as the first-order solution, with weak frequency and amplitude dispersion appearing as second-order corrections. Wavenumbers were estimated using four arrays of pressure sensors deployed in 2–6-m depth on a gently sloping sandy beach. When wave energy is low, the observed wavenumbers agree with the linear, finite-depth dispersion relation over a wide frequency range. In high energy conditions, the observed wavenumbers deviate from the linear dispersion relation by as much as 20%–30% in the frequency range from two to three times the frequency of the primary spectral peak, but agree well with the nonlinear Boussinesq dispersion relation, confirming that the deviations from linear theory are finite amplitude effects. In high energy conditions, the predicted frequency and amplitude dispersion tend to cancel, yielding a nearly nondispersive wave field in which waves of all frequencies travel with approximately the linear shallow water wave speed, consistent with the observations. The nonlinear Boussinesq theory wavenumber predictions (based on the assumption of irrotational wave motion) are accurate even within the surf zone, suggesting that wave breaking on gently sloping beaches has little effect on the dispersion relation.
Abstract
The nonlinear dispersion of random, directionally spread surface gravity waves in shallow water is examined with Boussinesq theory and field observations. A theoretical dispersion relationship giving a directionally averaged wavenumber magnitude as a function of frequency, the local water depth, and the local wave spectrum and bispectrum is derived for waves propagating over a gently sloping beach with straight and parallel depth contours. The linear, nondispersive shallow water relation is recovered as the first-order solution, with weak frequency and amplitude dispersion appearing as second-order corrections. Wavenumbers were estimated using four arrays of pressure sensors deployed in 2–6-m depth on a gently sloping sandy beach. When wave energy is low, the observed wavenumbers agree with the linear, finite-depth dispersion relation over a wide frequency range. In high energy conditions, the observed wavenumbers deviate from the linear dispersion relation by as much as 20%–30% in the frequency range from two to three times the frequency of the primary spectral peak, but agree well with the nonlinear Boussinesq dispersion relation, confirming that the deviations from linear theory are finite amplitude effects. In high energy conditions, the predicted frequency and amplitude dispersion tend to cancel, yielding a nearly nondispersive wave field in which waves of all frequencies travel with approximately the linear shallow water wave speed, consistent with the observations. The nonlinear Boussinesq theory wavenumber predictions (based on the assumption of irrotational wave motion) are accurate even within the surf zone, suggesting that wave breaking on gently sloping beaches has little effect on the dispersion relation.
Abstract
In Part I, the energy levels of ocean surface waves at infragravity frequencies (nominally 0.005–0.05 Hz) locally forced by swell in 13-m water depth were shown to be predicted accurately by second-order nonlinear wave theory. However, forced infragravity waves were consistently much less energetic than free infragravity waves. Here, in Part II, observations in depths between 8 and 204 m, on Atlantic and Pacific shelves, are used to investigate the sources and variability of free infragravity wave energy. Both free and forced infragravity energy levels generally increase with increasing swell energy and decreasing water depth, but their dependencies are markedly different. Although free waves usually dominate the infragravity frequency band, forced waves contribute a significant fraction of the total infragravity energy with high energy swell and/or in very shallow water. The observed h −1 variation of free infragravity energy with increasing water depth h is stronger than the h −1/2 dependence predicted for leaky surface gravity waves propagating approximately perpendicular to local depth contours, but is consistent with a heuristic, geometrical optics-based (WKB) model of the refractive trapping of a directionally broad wave field generated close to shore. Preliminary analysis shows that free infragravity waves are indeed directionally broad and that the propagation directions of infragravity waves and incident swell are related. 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 and that less energy is trapped on a narrow shelf than on a wide shelf.
Abstract
In Part I, the energy levels of ocean surface waves at infragravity frequencies (nominally 0.005–0.05 Hz) locally forced by swell in 13-m water depth were shown to be predicted accurately by second-order nonlinear wave theory. However, forced infragravity waves were consistently much less energetic than free infragravity waves. Here, in Part II, observations in depths between 8 and 204 m, on Atlantic and Pacific shelves, are used to investigate the sources and variability of free infragravity wave energy. Both free and forced infragravity energy levels generally increase with increasing swell energy and decreasing water depth, but their dependencies are markedly different. Although free waves usually dominate the infragravity frequency band, forced waves contribute a significant fraction of the total infragravity energy with high energy swell and/or in very shallow water. The observed h −1 variation of free infragravity energy with increasing water depth h is stronger than the h −1/2 dependence predicted for leaky surface gravity waves propagating approximately perpendicular to local depth contours, but is consistent with a heuristic, geometrical optics-based (WKB) model of the refractive trapping of a directionally broad wave field generated close to shore. Preliminary analysis shows that free infragravity waves are indeed directionally broad and that the propagation directions of infragravity waves and incident swell are related. 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 and that less energy is trapped on a narrow shelf than on a wide shelf.
Abstract
Previous field observations indicate that the directional spread of swell-frequency (nominally 0.1 Hz) surface gravity waves increases during shoreward propagation across the surf zone. This directional broadening contrasts with the narrowing observed seaward of the surf zone and predicted by Snell’s law for bathymetric refraction. Field-observed broadening was predicted by a new model for refraction of swell by lower-frequency (nominally 0.01 Hz) current and elevation fluctuations. The observations and the model suggest that refraction by the cross-shore currents of energetic shear waves contributed substantially to the observed broadening.
Abstract
Previous field observations indicate that the directional spread of swell-frequency (nominally 0.1 Hz) surface gravity waves increases during shoreward propagation across the surf zone. This directional broadening contrasts with the narrowing observed seaward of the surf zone and predicted by Snell’s law for bathymetric refraction. Field-observed broadening was predicted by a new model for refraction of swell by lower-frequency (nominally 0.01 Hz) current and elevation fluctuations. The observations and the model suggest that refraction by the cross-shore currents of energetic shear waves contributed substantially to the observed broadening.
Regional Swell Transformation by Backward Ray Tracing and SWANAbstract
Beach erosion and wave-induced flooding models are often initialized in O(10)-m depth, seaward of the surfzone, with wave conditions estimated from regional nonlinear spectral wave models [e.g., Simulating Waves Nearshore (SWAN)]. These models are computationally expensive for high-resolution, long-term regional O(100)-km hindcasts, and they limit examination of the effect of different climate scenarios on nearshore processes. Alternatively, computationally fast models with reduced linear wave physics enable long-term hindcasts at high spatial (<100 m) resolution. Linear models, that efficiently transform complete spectral details from deep water through complex offshore bathymetry, are appropriate for low-frequency swell wave energy propagation. Here, two numerically different linear methods are compared: backward ray-tracing and stationary linear SWAN simulations. The methods yield similar transformations from deep water (seaward of offshore islands in Southern California) to the nearshore, O(10)-m depth. However, SWAN is sensitive to model spatial resolution, especially in highly sheltered regions, where with typical (1–2 km) resolution SWAN estimates of nearshore energy vary by over a factor of 2 relative to ray tracing. Alongshore radiation stress estimates from SWAN and ray tracing also differ, and in some cases the climatological means have opposite signs. Increasing the SWAN resolution to 90 m, higher than usually applied to regional models, yields the nearshore transforms most similar to ray tracing. Both accurate rays and high-resolution SWAN require significant computation time; however, ray tracing is more efficient if transforms are needed at relatively few locations (compared with every grid point), or if computer memory is limited. Though presently less user friendly than SWAN, ray tracing is not affected by numerical diffusion or limited by model domain size or spatial resolution.
Abstract
Beach erosion and wave-induced flooding models are often initialized in O(10)-m depth, seaward of the surfzone, with wave conditions estimated from regional nonlinear spectral wave models [e.g., Simulating Waves Nearshore (SWAN)]. These models are computationally expensive for high-resolution, long-term regional O(100)-km hindcasts, and they limit examination of the effect of different climate scenarios on nearshore processes. Alternatively, computationally fast models with reduced linear wave physics enable long-term hindcasts at high spatial (<100 m) resolution. Linear models, that efficiently transform complete spectral details from deep water through complex offshore bathymetry, are appropriate for low-frequency swell wave energy propagation. Here, two numerically different linear methods are compared: backward ray-tracing and stationary linear SWAN simulations. The methods yield similar transformations from deep water (seaward of offshore islands in Southern California) to the nearshore, O(10)-m depth. However, SWAN is sensitive to model spatial resolution, especially in highly sheltered regions, where with typical (1–2 km) resolution SWAN estimates of nearshore energy vary by over a factor of 2 relative to ray tracing. Alongshore radiation stress estimates from SWAN and ray tracing also differ, and in some cases the climatological means have opposite signs. Increasing the SWAN resolution to 90 m, higher than usually applied to regional models, yields the nearshore transforms most similar to ray tracing. Both accurate rays and high-resolution SWAN require significant computation time; however, ray tracing is more efficient if transforms are needed at relatively few locations (compared with every grid point), or if computer memory is limited. Though presently less user friendly than SWAN, ray tracing is not affected by numerical diffusion or limited by model domain size or spatial resolution.
Abstract
Aerial images are used to quantify the concentration of fluorescent Rhodamine water tracing (WT) dye in turbid and optically deep water. Tracer releases near the shoreline of an ocean beach and near a tidal inlet were observed with a two-band multispectral camera and a pushbroom hyperspectral imager, respectively. The aerial observations are compared with near-surface in situ measurements. The ratio of upwelling radiance near the Rhodamine WT excitation and emission peaks varies linearly with the in situ dye concentrations for concentrations <20 ppb (r 2 = 0.70 and r 2 = 0.85–0.88 at the beach and inlet, respectively). The linear relationship allows for relative tracer concentration estimates without in situ calibration. The O(1 m) image pixels resolve complex flow structures on the inner shelf that transport and mix tracer.
Abstract
Aerial images are used to quantify the concentration of fluorescent Rhodamine water tracing (WT) dye in turbid and optically deep water. Tracer releases near the shoreline of an ocean beach and near a tidal inlet were observed with a two-band multispectral camera and a pushbroom hyperspectral imager, respectively. The aerial observations are compared with near-surface in situ measurements. The ratio of upwelling radiance near the Rhodamine WT excitation and emission peaks varies linearly with the in situ dye concentrations for concentrations <20 ppb (r 2 = 0.70 and r 2 = 0.85–0.88 at the beach and inlet, respectively). The linear relationship allows for relative tracer concentration estimates without in situ calibration. The O(1 m) image pixels resolve complex flow structures on the inner shelf that transport and mix tracer.
Abstract
A drifter designed to measure surf zone circulation has been developed and field tested. Drifter positions accurate to within a few meters are estimated in real time at 0.1 Hz using the global positioning system (GPS) and a shore-to-drifter radio link. More accurate positions are estimated at 1 Hz from postprocessed, internally logged data. Mean alongshore currents estimated from trajectories of the 0.5-m-draft drifters in 1–2-m water depth agree well with measurements obtained with nearby, bottom-mounted, acoustic current meters. Drifters deployed near the base of a well-developed rip current often followed eddylike paths within the surf zone before being transported seaward.
Abstract
A drifter designed to measure surf zone circulation has been developed and field tested. Drifter positions accurate to within a few meters are estimated in real time at 0.1 Hz using the global positioning system (GPS) and a shore-to-drifter radio link. More accurate positions are estimated at 1 Hz from postprocessed, internally logged data. Mean alongshore currents estimated from trajectories of the 0.5-m-draft drifters in 1–2-m water depth agree well with measurements obtained with nearby, bottom-mounted, acoustic current meters. Drifters deployed near the base of a well-developed rip current often followed eddylike paths within the surf zone before being transported seaward.
