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John Trowbridge
and
Steve Elgar

Abstract

Measurements from a horizontal array of velocity sensors indicate that the alongshore scales of turbulence contributing to the near-bottom Reynolds stress just seaward of the surf zone on an ocean beach range from 0 to approximately 4 times the height of the measurements above the seafloor, with shorter scales during stable stratification than during neutral or unstable stratification. The dependence of alongshore turbulence scales on the stratification, Reynolds stress, and height above the bottom is consistent with semiempirical results from the atmospheric surface layer, implying similar dynamics of near-boundary turbulence in the atmosphere and the shallow coastal ocean.

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John Trowbridge
and
Steve Elgar

Abstract

Velocity measurements within 1 m of the bottom in approximately 4.5-m water depth on a sand beach provide estimates of turbulent Reynolds shear stress, using a dual-sensor technique that removes contamination by surface waves, and inertial-range estimates of dissipation. When combined with wave measurements along a cross-shore transect and nearby wind measurements, the dataset provides direct estimates of the terms in simplified equations for alongshore momentum and turbulence energetics and permits examination of semiempirical relationships between bottom stress and near-bottom velocity. The records are dominated by three events when the measurement site was in the outer part of the surf zone. Near-bottom turbulent shear stress is well correlated with (squared correlation coefficient r 2 = 0.63), but smaller than (regression coefficient b = 0.51 ± 0.03 at 95% confidence), wind stress minus cross-shore gradient of wave-induced radiation stress, indicating that estimates of one or more of these terms are inaccurate or that an additional effect was important in the alongshore momentum balance. Shear production of turbulent kinetic energy is well correlated (r 2 = 0.81) and consistent in magnitude (b = 1.1 ± 0.1) with dissipation, and both are two orders of magnitude smaller than the depth-averaged rate at which the shoaling wave field lost energy to breaking, indicating that breaking-induced turbulence did not penetrate to the measurement depth. Log-profile estimates of stress are well correlated with (r 2 = 0.75), but larger than (b = 2.3 ± 0.1), covariance estimates of stress, indicating a departure from the Prandtl–von Kármán velocity profile. The bottom drag coefficient was (1.9 ± 0.2) × 10−3 during unbroken waves and approximately half as large during breaking waves.

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Steve Elgar
and
Britt Raubenheimer

Abstract

Low-frequency currents and eddies transport sediment, pathogens, larvae, and heat along the coast and between the shoreline and deeper water. Here, low-frequency currents (between 0.1 and 4.0 mHz) observed in shallow surfzone waters for 120 days during a wide range of wave conditions are compared with theories for generation by instabilities of alongshore currents, by ocean-wave-induced sea surface modulations, and by a nonlinear transfer of energy from breaking waves to low-frequency motions via a two-dimensional inverse energy cascade. For these data, the low-frequency currents are not strongly correlated with shear of the alongshore current, with the strength of the alongshore current, or with wave-group statistics. In contrast, on many occasions, the low-frequency currents are consistent with an inverse energy cascade from breaking waves. The energy of the low-frequency surfzone currents increases with the directional spread of the wave field, consistent with vorticity injection by short-crested breaking waves, and structure functions increase with spatial lags, consistent with a cascade of energy from few-meter-scale vortices to larger-scale motions. These results include the first field evidence for the inverse energy cascade in the surfzone and suggest that breaking waves and nonlinear energy transfers should be considered when estimating nearshore transport processes across and along the coast.

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Melissa Moulton
,
Gregory Dusek
,
Steve Elgar
, and
Britt Raubenheimer

Abstract

Although rip currents are a major hazard for beachgoers, the relationship between the danger to swimmers and the physical properties of rip current circulation is not well understood. Here, the relationship between statistical model estimates of hazardous rip current likelihood and in situ velocity observations is assessed. The statistical model is part of a forecasting system that is being made operational by the National Weather Service to predict rip current hazard likelihood as a function of wave conditions and water level. The temporal variability of rip current speeds (offshore-directed currents) observed on an energetic sandy beach is correlated with the hindcasted hazard likelihood for a wide range of conditions. High likelihoods and rip current speeds occurred for low water levels, nearly shore-normal wave angles, and moderate or larger wave heights. The relationship between modeled hazard likelihood and the frequency with which rip current speeds exceeded a threshold was assessed for a range of threshold speeds. The frequency of occurrence of high (threshold exceeding) rip current speeds is consistent with the modeled probability of hazard, with a maximum Brier skill score of 0.65 for a threshold speed of 0.23 m s−1, and skill scores greater than 0.60 for threshold speeds between 0.15 and 0.30 m s−1. The results suggest that rip current speed may be an effective proxy for hazard level and that speeds greater than ~0.2 m s−1 may be hazardous to swimmers.

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Steve Elgar
,
Britt Raubenheimer
, and
R. T. Guza

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, consistent with a vertical flux of cross-shore momentum associated with wave dissipation in the surf zone.

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Falk Feddersen
,
R. T. Guza
, and
Steve Elgar

Abstract

Inverse models are developed that use data and dynamics to estimate optimally the breaking-wave-driven setup and alongshore current, as well as the cross-shore forcing, alongshore forcing, and drag coefficient. The inverse models accurately reproduce these quantities in a synthetic barred-beach example. The method is applied to one case example each from the Duck94 and SandyDuck field experiments. Both inverse solutions pass consistency tests developed for the inverse method and have forcing corrections similar to a roller model and significant cross-shore variation of the drag coefficient. The inverse drag coefficient is related to the wave dissipation, a bulk measure of the turbulence source, but not to the bed roughness, consistent with the hypothesis that breaking-wave-generated turbulence increases the drag coefficient. Inverse solutions from a wider range of conditions are required to establish the generality of these results.

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C. A. Norheim
,
T. H. C. Herbers
, and
Steve Elgar

Abstract

The shoaling evolution of wave spectra on a beach with straight and parallel depth contours is investigated with a stochastic Boussinesq model. Existing deterministic Boussinesq models cast in the form of coupled evolution equations for the amplitudes and phases of discrete Fourier modes describe accurately the shoaling process for arbitrary incident wave conditions, but are numerically cumbersome for predicting the evolution of continuous spectra of natural wind-generated waves. The stochastic formulation used here, based on the closure hypothesis that phase coupling between quartets of wave components is weak, predicts the shoaling evolution of the continuous frequency spectrum and bispectrum of the wave field. The general characteristics of the stochastic model and the dependence of wave shoaling on nonlinearity, initial spectral shape, and bottom profile are illustrated with numerical simulations. Predictions of stochastic and deterministic Boussinesq models are compared with data from a natural barred ocean beach. Both models accurately reproduce the observed nonlinear wave transformation for a range of conditions.

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T. H. C. Herbers
,
Steve Elgar
, and
R. T. Guza

Abstract

This is Part 1 of a two-part study of infragravity-frequency (nominally 0.005–0.05 Hz) motions on the continental shelf. Data from a large aperture (250 m × 250 m) array of 24 bottom-mounted pressure transducers deployed in 13 m depth is used to investigate the local forcing of infragravity motions by nonlinear difference-frequency interactions of surface gravity waves. Second-order nonlinear theory (Hasselmann) and observed swell-sea frequency-directional spectra are used to predict the energy levels of forced infragravity waves. For a wide range of wave conditions, the predicted forced wave levels are lower than the observed energy levels, suggesting that the infragravity band contains a mix of free and forced waves. Bispectral analysis is used to estimate the relative amounts of free and forced infragravity energy. Good agreement between bispectrum-based estimates and theoretical predictions of forced wave energy confirms that second-order nonlinear theory accurately predicts locally forced infragravity motions. The contribution of forced waves to the total infragravity energy, ranging from less than 0.1% to about 30%, is largest when the infragravity energy is maximum, consistent with previously noted trends in similar water depths. The bispectral technique developed here to estimate the energy of forced and free infragravity waves is used in Part 2 to investigate, with data from single-point pressure gauges, the shelfwide variability of free infragravity energy.

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Steve Elgar
,
T. H. C. Herbers
, and
R. T. Guza

Abstract

The energy of seaward and shoreward propagating ocean surface gravity waves on a natural beach was estimated with data from an army of 24 bottom-mounted pressure sensors in 13-m water depth, 2 km from the North Carolina coast. Consistent with a parameterization of surface wave reflection from a plane sloping beach by Miche, the ratio of seaward to shoreward propagating energy in the swell-sea frequency band (0.044–0.20 Hz) decreased with increasing wave frequency and increasing wave height, and increased with increasing beach-face slope. Although most incident swell-sea energy dissipated in the surf zone, reflection was sometimes significant (up to 18% of the incident swell-sea energy) when the beach face was steep (at high tide) and the wave field was dominated by low-energy, low-frequency swell. Frequency-directional spectra show that reflection of swell and sea was approximately specular. The ratio of seaward to shoreward propagating energy in the infragravity frequency band (0.010–0.044 Hz) varied between about 0.5 and 3 and increased with increasing swell energy. This trend suggests that infragravity waves generated in very shallow water, and refractively trapped on the sloping seabed, are significantly dissipated over a 50-km wide shelf during storms.

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T. H. C. Herbers
,
N. R. Russnogle
, and
Steve Elgar

Abstract

The spectral energy balance of ocean surface waves breaking on a natural beach is examined with field observations from a cross-shore array of pressure sensors deployed between the shoreline and the outer edge of the surf zone near Duck, North Carolina. Cross-shore gradients in wave energy flux were estimated from spectral changes observed between closely spaced sensors. Direct, empirical estimates of nonlinear energy exchanges between different frequency components of the wave spectrum were obtained from observed bispectra using Boussinesq theory for near-resonant triad wave–wave interactions. The large decrease in energy flux observed across the surf zone in the energetic part of the wave spectrum is balanced closely by the estimated nonlinear energy transfers from the spectral peak to higher frequencies. In the high-frequency tail of the spectrum, observed energy flux gradients are small and do not balance the nonlinear energy transfers. This analysis indicates that the observed decay of wave spectra in the surf zone is primarily the result of nonlinear energy transfers to higher frequencies, and that dissipation occurs in the high-frequency tail of the spectrum where energy levels are relatively low.

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