Britt Raubenheimer

Observations and predictions of run-up

For a significant range of offshore wave conditions and foreshore slopes, run-up observations are compared to semiempirical formulations and predictions of an existing numerical model based on the depth-averaged one-dimensional nonlinear shallow water equations with bore-like breaking wave dissipation and quadratic bottom friction. The numerical model is initialized with time series of sea surface elevation and cross-shore velocity observed in 80 cm mean water depth (approximately 50 m offshore of the mean shoreline) on a gently sloping beach and in 175 cm water depth (100 m offshore of the shoreline) on a steep concave beach. Run-up was measured with a stack of resistance wires at elevations 5, 10, 15, 20, and 25 cm above and parallel to the beach face. At sea swell frequencies (nominally 0.05 < f ≤ 0.18 Hz), run-up energy is limited by surf zone dissipation of shoreward propagating waves so that increasing the offshore wave height above a threshold value does not substantially increase the predicted or observed sea swell run-up excursions (e.g., run-up is “saturated”). Existing semiempirical saturation formulations are most consistent with the observations and numerical model predictions of run-up excursions nearest the bed. In contrast, at infragravity frequencies (0.004 < f ≤ 0.05 Hz) where surf zone dissipation is relatively weak and reflection from the beach face is strong (e.g., saturation formulas are not applicable), the run-up excursions increase approximately linearly with increasing offshore wave height. The numerical model also accurately predicts that the tongue-like shape of the run-up results in sensitivity of run-up measurements to wire elevation. For instance, run-up excursions and mean vertical superelevation (above the offshore still water level) increase with decreasing wire elevation, and continuous thinning of the run-up tongue during the wave uprush can result in large phase differences between run-up excursions measured at different wire elevations. Numerical model simulations suggest that run-up measured more than a few centimeters above the bed cannot be used to infer even the sign of the fluid velocities in the run-up tongue.

Swash on a gently sloping beach

Waves observed in the inner surf and swash zones of a fine grained, gently sloping beach are modeled accurately with the nonlinear shallow water equations. The model is initialized with observations from pressure and current sensors collocated about 50 m from the mean shoreline in about i m depth, and model predictions are compared to pressure fluctuations measured at five shoreward locations and to run-up. Run-up was measured with a vertical stack of five wires supported parallel to and above the beach face at elevations of 5, 10, 15, 20, and 25 cm. Each 60-m-long run-up wire yields time series of the most shoreward location where the water depth exceeds the wire elevation. As noted previously, run-up measurements are sensitive to the wire elevation owing to thin run-up tongues not measured by the more elevated wires. As the wire elevation increases, the measured mean run-up location moves seaward, low-frequency (infragravity) energy decreases, and higher-frequency sea swell energy increases. These trends, as well as the variation of wave spectra and shapes (e.g., wave skewhess) across the inner surf zone, are well predicted by the numerical model.

Spectral evolution of shoaling and breaking waves on a barred beach

Field observations and numerical model predictions are used to investigate the effects of nonlinear interactions, reflection, and dissipation on the evolution of surface gravity waves propagating across a barred beach. Nonlinear interactions resulted in a doubling of the number of wave crests when moderately energetic (about 0.8-m significant wave height), narrowband swell propagated without breaking across an 80-m-wide, nearly flat (2-m depth) section of beach between a small offshore sand bar and a steep (slope = 0.1) beach face, where the waves finally broke. These nonlinear energy transfers are accurately predicted by a model based on the nondissipative, unidirectional (i.e., reflection is neglected) Boussinesq equations. For a lower-energy (wave height about 0.4 m) bimodal wave field, high-frequency seas dissipated in the surf zone, but lower-frequency swell partially reflected from the steep beach face, resulting in significant cross-shore modulation of swell energy. The combined effects of reflection from the beach face and dissipation across the sand bar and near the shoreline are described well by a bore propagation model based on the nondispersive nonlinear shallow water equations. Boussinesq model predictions on the flat section (where dissipation is weak) are improved by decomposing the wave field into seaward and shoreward propagating components. In more energetic (wave heights greater than 1 m) conditions, reflection is negligible, and the region of significant dissipation can extend well seaward of the sand bar. Differences between observed decreases in spectral levels and Boussinesq model predictions of nonlinear energy transfers are used to infer the spectrum of breaking wave induced dissipation between adjacent measurement locations. The inferred dissipation rates typically increase with increasing frequency and are comparable in magnitude to the nonlinear energy transfer rates.

Field observations of wave‐driven setdown and setup

Wave-driven setdown and setup observed for 3 months on a cross-shore transect between the shoreline and 5 m water depth on a barred beach are compared with a theoretical balance between cross-shore gradients of the mean water level and the wave radiation stress. The observed setdown, the depression of the mean water level seaward of the surf zone, is predicted well when radiation stress gradients are estimated from the observations using linear theory at each location along the transect. The observed setdown also agrees with analytical predictions based on offshore wave observations and the assumption of linear, dissipationless, normally incident waves shoaling on alongshore homogeneous bathymetry. The observed setup, the superelevation of the mean water level owing to wave breaking, is predicted accurately in the outer and middle surf zone, but is increasingly underpredicted as the shoreline is approached. Similar to previous field studies, setup at a fixed cross-shore location increases with increasing offshore wave height and is sensitive to tidal fluctuations in the local water depth and to bathymetric changes. Numerical simulations and the observations suggest that setup near the shoreline depends on the bathymetry of the entire surf zone and increases with decreasing surf zone beach slope, defined as the ratio of the surf zone-averaged water depth to the surf zone width. A new empirical formula for shoreline setup on nonplanar beaches incorporates this dependence.

A GPS-Tracked Surf Zone Drifter*

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.

Tidal water table fluctuations in a sandy ocean beach

Tidal water table fluctuations observed for 27 days in a gently sloped ocean beach are predicted well by numerical models based on the Boussinesq equation driven with the observed 10 min-averaged shoreline (ocean-beach intersection) motion. Diurnal and semidiurnal water table fluctuations are almost completely damped 100 m landward of the mean shoreline location on this fine-grained sand beach, but fluctuations at spring-neap periods (≈14 days) are attenuated less. Comparison of the observations with the predictions suggests that the asymmetries in the water table level time series measured in this study result from nonlinearity owing to the large (relative to the wavelength) horizontal shoreline excursions, rather than from nonlinearity owing to finite-amplitude water table fluctuations. Cross-shore variations of the aquifer depth are predicted to have a small effect on the landward decay rate of the water table fluctuations. The seepage face width is predicted accurately and depends on the nonplanar beach profile. In general, the development of a seepage face is predicted to have little effect on the water table level landward of the intertidal region.

Quality control of acoustic Doppler velocimeter data in the surfzone

Acoustic Doppler velocimeter measurements in the surfzone can be corrupted by bubbles and suspended sediment, lack of submergence during the passage of wave troughs, biofouling, blockage (e.g., from kelp on instrument mounting frames) of the flow field near the current meter or of the path between the sampled fluid volume and the acoustic transducers, and by insufficient distance between an accreting seafloor and the sample volume. Individual bad acoustic Doppler velocity values can be detected (and subsequently replaced) from low along-beam signal-to-noise ratios and from low coherence between successive acoustic returns used to estimate velocity. In addition, corrupted data runs can be identified from ratios of pressure to velocity variance that deviate from linear theory, and from low coherence between time series of collocated pressure and wave-orbital velocities. Unmeasured vertical tilts of a current meter can be estimated from horizontal and vertical velocities, and corrected for numerically.

Effects of wave rollers and bottom stress on wave setup

[1] Setup, the increase in the mean water level associated with breaking waves, observed between the shoreline and about 6-m water depth on an ocean beach is predicted well by a model that includes the effects of wave rollers and the bottom stress owing to the mean flow. Over the 90-day observational period, the measured and modeled setups are correlated (squared correlation above 0.59) and agree within about 30%. Although rollers may affect setup significantly on beaches with large-amplitude (several meters high) sandbars and may be important in predicting the details of the cross-shore profile of setup, for the data discussed here, rollers have only a small effect on the amount of setup. Conversely, bottom stress (calculated using eddy viscosity and undertow formulations based on the surface dissipation, and assuming that the eddy viscosity is uniform throughout the water column) significantly affects setup predictions. Neglecting bottom stress results in underprediction of the observed setup in all water depths, with maximum underprediction near the shoreline where the observed setup is largest.

Current Meter Performance in the Surf Zone

Abstract Statistics of the nearshore velocity field in the wind–wave frequency band estimated from acoustic Doppler, acoustic travel time, and electromagnetic current meters are similar. Specifically, current meters deployed 25–100 cm above the seafloor in 75–275-cm water depth in conditions that ranged from small-amplitude unbroken waves to bores in the inner surf zone produced similar estimates of cross-shore velocity spectra, total horizontal and vertical velocity variance, mean currents, mean wave direction, directional spread, and cross-shore velocity skewness and asymmetry. Estimates of seafloor location made with the acoustic Doppler sensors and collocated sonar altimeters differed by less than 5 cm. Deviations from linear theory in the observed relationship between pressure and velocity fluctuations increased with increasing ratio of wave height to water depth. The observed covariance between horizontal and vertical orbital velocities also increased with increasing height to depth ratio, consisten...

Field observations of wave setup

Wave setup is assumed to be a balance between the cross-shore convergence of the onshore flux of momentum (wave radiation stress Sxx) in the surfzone and a cross-shore pressure gradient. Oceanic observations between the 2- and 8-m isobaths near Duck, North Carolina, provide a test of the wave setup balance without assuming that wave height in the surfzone is proportional to water depth. Analysis of data from a cross-shore array of 11 pressure gauges and 10 sonar altimeters deployed during the fall of 1994 indicates the wave setup balance holds to at least the accuracy of the pressure measurements (a few centimeters). The correlation between the two terms in the setup balance is 0.93, and the linear regression slope is 1.05±0.19. Accurate estimates of the cross-shore pressure gradient require density measurements to adjust pressure measurements taken at different depths to the same level. The assumption that pressure and bathymetry are linear between the 2- and 8-m isobaths (or the more common assumption that the height of normally incident, shallow water waves is proportional to the water depth) introduces errors of up to 6 cm for the conditions considered here. Given this assumption, 3.5 years of data from pressure gauges in 2 and 8 m of water indicate that the wave setup balance is valid for a wide range of conditions (correlation 0.71 and regression slope 0.98±0.08).