Parametric depth-induced-breaking dissipation models have shown great skill at predicting time averaged wave heights across the surf zone. First proposed by Battjes & Janssen (1978), these models balance the incoming wave energy flux with a roller dissipation term. This roller dissipation term is estimated by calculating the dissipation for one characteristic broken wave and then multiplying this quantity by the fraction of broken waves. To describe the fraction of broken waves, a typical assumption asserts that wave heights are nearly Rayleigh distributed [Thornton & Guza (1983)] allowing a sea state to be described by only a few parameters. While many experiments have validated the cross shore wave height profiles, few field experiments have been performed to analyze the probability distribution of breaking wave heights over a barred beach profile. The goal of the present research is to determine the distribution of broken and unbroken wave heights across a natural barred beach profile. Field data collected during the Surf Zone Optics experiment (a Multi-disciplinary University Research Initiative) in Duck, North Carolina, consisted of an array of in-situ pressure sensors and optical remote sensing cameras. Sea surface elevation time series from the in-situ pressure sensors are used here to resolve wave height distributions at multiple locations across the surf zone. Breaking wave height distributions are resolved based upon a combination of the pressure sensor and optically based breaker detection algorithm. Since breaking is easily able to be tracked by video imaging, breaking waves are flagged in the sea surface elevation series and binned into a broken wave height distribution. Results of this analysis are compared with model predictions based upon the Battjes & Janssen (1978), Thornton & Guza (1983) and Janssen & Battjes (2007) models to assess the validity of each wave height distribution model.
Keen, A. S.; Holman, R. A.
Mean cross-shore currents observed across a barred surf zone are compared to model predictions. The model is based on a simplified momentum balance with a turbulent boundary layer at the bed. Turbulent exchange is parameterized by an eddy viscosity formulation, with the eddy viscosity A? independent of time and the vertical coordinate. Mean currents result from gradients due to wave breaking and shoaling, and the presence of a mean setup of the free surface. Descriptions of the wave field are provided by the wave transformation model of Thornton and Guza . The wave transformation model adequately reproduces the observed wave heights across the surf zone. The mean current model successfully reproduces the observed cross-shore flows. Both observations and predictions show predominantly offshore flow with onshore flow restricted to a relatively thin surface layer. Successful application of the mean flow model requires an eddy viscosity which varies horizontally across the surf zone. Attempts are made to parameterize this variation with some success. The data does not discriminate between alternative parameterizations proposed. The overall variability in eddy viscosity suggested by the model fitting should be resolvable by field measurements of the turbulent stresses. Consistent shortcomings of the parameterizations, and the overall modeling effort, suggest avenues for further development and data collection.
Haines, John W.; Sallenger, Asbury H., Jr.
Incorporation of wave dissipation due to breaking in both time-domain and frequency domain models have long been a subject of study. Until recently, the formulation of wave breaking in frequency domain models have been based on lumped-parameter dissipation models based on a Rayleigh distribution function for the wave heights in the surf zone (Battjes and Janssen, 1978; Thornton and Guza, 1983). Modifications to improve the dissipation model include allowing for nonlinear energy transfer (Mase and Kirby, 1992), which leads to improvements in predictions of the skewness and asymmetry. Bredmose (2004) show how time- domain wave breaking models can be included in a frequency domain version of the Boussinesq model using a time-domain inversion of the roller model. However, frequency domain versions of the Boussinesq model tend to perform poorly until the waves are close to breaking. In this study, we will show how time-domain wave breaking models can be included in frequency domain models that are based on the mild-slope formulation. We will then compare the results of using such a breaking model to the empirical bulk-dissipation formulation. Comparisons will include wave height distributions, skewness, and asymmetry. We will also discuss implications of using different breaking models on sediment transport.
Veeramony, J.; Kaihatu, J. M.
Recent studies have shown that the spectral wind wave model SWAN (Simulating Waves Nearshore) underestimates wave heights and periods in situations of finite depth wave growth. In this study, this inaccuracy is addressed through a rescaling of the Battjes and Janssen (1978) bore-based model for depth-induced breaking, considering both sloping bed surf zone situations and finite depth wave growth conditions. It is found that the variation of the model error with the breaker index ?BJ in this formulation differs significantly between the two types of conditions. For surf zones, clear optimal values are found for the breaker index. By contrast, under finite depth wave growth conditions, model errors asymptotically decrease with increasing values of the breaker index (weaker dissipation). Under both the surf zone and finite depth wave growth conditions, optimal calibration settings of ?BJ were found to correlate with the dimensionless depth kpd (where kp is the spectral peak wave number and d is the water depth) and the local mean wave steepness. Subsequently, a new breaker index, based on the local shallow water nonlinearity, expressed in terms of the biphase of the self-interactions of the spectral peak, is proposed. Implemented in the bore-based breaker model of Thornton and Guza (1983), this breaker index accurately predicts the large difference in dissipation magnitudes found between surf zone conditions and finite depth growth situations. Hence, the proposed expression yields a significant improvement in model accuracy over the default Battjes and Janssen (1978) model for finite depth growth situations, while retaining good performance for sloping bed surf zones.
van der Westhuysen, André J.
The nonlinear dynamics of finite amplitude shear instabilities of alongshore currents in the nearshore surf zone over barred beach topography are studied using numerical experiments. These experiments extend the recent study of Allen et al. , which utilized plane beach (constant slope) topography by including shore-parallel sandbars. The model involves finite-difference solutions to the nonlinear shallow water equations for forced, dissipative, initial-value problems and employs periodic boundary conditions in the alongshore direction. Effects of dissipation are modeled by linear bottom friction. Forcing for the alongshore currents is specified using a model formulated by Thornton and Guza  (T-G). Distinct classes of flows develop depending on the dimensionless parameter Q, the ratio of an advective to a frictional timescale. For Q greater than a critical value Qc the flows are linearly stable. For ?Q=Qc-Q >0 the flow is unstable. For small values of ?Q, equilibrated shear waves develop that propagate alongshore at phase speeds and wavelengths that are in agreement with predictions from linear theory for the most unstable mode. At intermediate values of ?Q, unsteady vortices form and exhibit nonlinear interactions as they propagate alongshore, occasionally merging, pairing, or being shed seaward of the sandbar. At the largest values of ?Q examined, the resulting flow field resembles a turbulent shear flow. A net effect of the instabilities at large AQ is to distribute the time-averaged alongshore momentum from local maxima of the T-G forcing, located over the sandbar and near the shore, into the region of the trough. The across-shore structure of the time-averaged alongshore current is in substantially better qualitative agreement with observations than that given by a steady frictional balance with T-G forcing. The results point to the possible existence in the nearshore surf zone of an energetic eddy field associated with instabilities of the alongshore current.
Slinn, Donald N.; Allen, J. S.; Newberger, P. A.; Holman, R. A.
The nonlinear dynamics of unstable alongshore currents in the nearshore surf zone over variable barred beach topography are studied using numerical experiments. These experiments extend the recent studies of Allen et al.  and Slinn et al. , which utilized alongshore uniform beach topographies by including sinusoidal alongshore variation to shore parallel sandbars. The model involves finite difference solutions to the nonlinear shallow water equations for forced, dissipative, initial value problems and employs periodic boundary conditions in the alongshore direction. Effects of dissipation are modeled by linear bottom friction. Forcing for the alongshore currents is provided by gradients in the radiation stress, which are specified using linear theory and the dissipation function for breaking waves formulated by Thornton and Guza . Distinct flows develop depending on the amplitude ? and wavelength ? of the topographic variability and the dimensionless parameter Q, the ratio of an advective to a frictional timescale. For Q greater than a critical value QC the flows are linearly stable. For ?Q = QC - Q>0 the flow can be unstable. For small values of ?Q the effect of increasing ?; is to stabilize or regularize the flows and to cause the mean flow to approximately follow contours of constant depth. Equilibrated shear waves develop that propagate along the mean current path at phase speeds and wavelengths that are close to predictions for the most unstable mode from linear theory applied to alongshore-averaged conditions. At intermediate values of ?Q, unsteady vortices form and exhibit nonlinear interactions as they propagate along the mean current path, occasionally merging, pairing, or being shed seaward of the sandbar. Eddies preferentially form in the mean current when approaching alongshore troughs of the sandbar and break free from the mean current when approaching alongshore crests of the sandbar. At the largest values of ?Q examined the resulting flow fields resemble a turbulent shear flow and are less strongly influenced by the alongshore variability in topography. As the amplitude of the alongshore topographic variability increases, alongshore wavenumber-frequency spectra of the across-shore velocity show a corresponding increase in energy at both higher alongshore wavenumbers and over a broader frequency range with significant energy at wavenumbers of topographic variability and harmonics. Across-shore fluxes of mass and momentum generally increase with increasing topographic amplitude and increasing ?Q. Time- and space-lagged correlations of the across-shore velocity show that correlation length scales decrease as topographic perturbation amplitudes increase. Terms from the vorticity equation show that the alongshore variation of the radiation stresses and the value of ?Q are of importance to the flow behavior. Hybrid experiments separating effects of spatially variable forcing and the dynamic influence of topography on time-averaged currents show that the effects are generally comparable with the relative importance of each effect a function of ?Q. The results show that topographic variability has a significant influence on nearshore circulation.
Slinn, Donald N.; Allen, J. S.; Holman, R. A.
Beach elevation change observations from the United States west and east coasts are used to identify statistically the dominant cross-shore patterns in sand level fluctuations, and these changes are related to equilibrium beach profile concepts. Three to seven years of observations at four beaches in Southern California include monthly surveys of the subaerial (near MSL) beach, and quarterly surveys from the backbeach to about 8m depth. At Duck, North Carolina, observations include 31 years of monthly surveys from the dunes to about 8m depth. On the Southern California beaches, the dominant seasonal pattern is subaerial erosion in winter and accretion in summer. Seasonal fluctuations of 3m in shoreline vertical sand levels, and 50m in subaerial beach width, are not uncommon. The sand eroded from the shoreline in winter is stored in an offshore sand bar and returns to the beach face in summer. Wave conditions in Southern California also vary seasonally, with energetic waves arriving from the north in winter, and lower energy, longer period southerly swell arriving in summer. A spectral refraction model, initialized with a regional network of directional wave buoys, is used to estimate hourly wave conditions, in 10m water depth. Using an equilibrium hypothesis, that the shoreline (defined as the cross-shore location of the MSL contour) change rate depends on the wave energy and the wave energy disequilibrium, Yates (2009) modeled the time-varying shoreline location at several Southern California beaches with significant skill. The four free model parameters were calibrated to fit observations. Following Yates (2009), we extend the equilibrium shoreline model to include the horizontal displacement of other elevation contours. At the Southern California sites, the modeled contour translation depends on the incident wave energy, the present contour configuration, and observation-based estimates of the contour behavior (based on EOF spatial amplitudes). At Duck, seasonal variations of the wave field (measured immediately offshore) are large, but shoreline changes (usually <30cm) are smaller than in Southern California. Maximum vertical variations occur just seaward of the shoreline and the nearshore bathymetry is often barred. Plant (1999) show that bar crest position at Duck has equilibrium-like behavior. We will present the results of equilibrium shoreline and profile modeling at Duck. At both sites, we diagnose sources (e.g. grain size and incident waves) of the sometimes strong observed alongshore variations in sand level change patterns. Funding was provided by the US Army Corps of Engineers and the California Department of Boating and Waterways. REFERENCES Plant, N. G., R. A. Holman, M. H. Freilich, and W. A. Birkemeier (1999), A simple model for interannual sandbar behavior, J. Geophys. Res., 104(C7), 15,755-15,776. Yates, M. L., R. T. Guza, and W. C. O'Reilly (2009), Equilibrium shoreline response: Observations and modeling, J. Geophys. Res., 114, C09014.
Ludka, B. C.; Guza, R. T.; McNinch, J. E.; O'Reilly, W.
Long waves may cause significant disturbances for port operations. This paper is concerned with the long wave problems at Ferrol, a port in NW Spain. Long wave periods range between a few tens of seconds to several hours. In shallow water their wavelengths are on the order of hundreds of meters to kilometres. As a result, these waves can match the natural periods of oscillation of semi-enclosed bodies of water like gulfs, bays, fiords, or harbours, resulting in resonant oscillations. During resonance, the vertical displacement of the free surface increases until the energy input is balanced by losses due to friction, flow separation, boundary absorption, and radiation from the mouth (Okihiro et al., 1993). The induced horizontal displacements of the water mass are responsible for the large movements on ships. The non-linear interaction of long and wind waves and the direct atmospheric forcing are the main sources of long waves in the ocean. In the first case, the long waves are also known as infragravity waves and tend to have relatively small periods. In the second case, the atmospheric forced long waves, different mechanisms have been used to explain their generation. Atmospheric disturbances passing over the continental shelf (Sepic et al., 2008) or wind convection cells (de Jong and Battjes, 2004) are two of the causes for these 'meteorological' waves. Whatever their cause, they tend to have relatively large periods and, therefore, a significant potential to excite the first modes of oscillation of harbours. In addition, other different forcing mechanisms can generate long waves, including submerged landslides (Cecioni and Bellotti, 2010) and seisms (Candella et al., 2008). Disturbances to load and unload operations have been reported from 2005 at the Exterior Port of Ferrol (NW Spain). On-site measurements of sea-level oscillations revealed energy peaks possibly related to resonant processes (López et al., 2012; López and Iglesias, 2013). This work is focused on the long waves at the Port of Ferrol and their implications for the operations at the port. References Candella, R.N., Rabinovich, A.B., Thomson, R.E., 2008. The 2004 Sumatra tsunami as recorded on the Atlantic coast of South America. Adv. Geosci. 14, 117-128. Cecioni, C., Bellotti, G., 2010. Modeling tsunamis generated by submerged landslides using depth integrated equations. Appl. Ocean Res. 32(3), 343-350. de Jong, M.P.C., Battjes, J.A., 2004. Low-frequency sea waves generated by atmospheric convection cells. Journal of Geophysical Research-Oceans 109(C1), C01011. López, M., Iglesias, G., 2013. Artificial Intelligence for estimating infragravity energy in a harbour. Ocean Eng. 57(0), 56-63. López, M., Iglesias, G., Kobayashi, N., 2012. Long period oscillations and tidal level in the Port of Ferrol. Appl. Ocean Res. 38(0), 126-134. Okihiro, M., Guza, R.T., Seymour, R.J., 1993. Excitation of Seiche Observed in a Small Harbor. J. Geophys. Res. 98(C10), 18201-18211. Sepic, J., Orlic, M., Vilibic, I., 2008. The Bakar Bay seiches and their relationship with atmospheric processes. Acta Adriat. 49(2).
Lopez, Mario; Iglesias, Gregorio