B.G. Ruessink

Modeling the alongshore current on barred beaches

Mean alongshore currents observed on two barred beaches are compared with predictions based on the one-dimensional, time- and depth-averaged alongshore momentum balance between forcing (by breaking waves, wind, and 10–100 km scale alongshore surface slopes), bottom stress, and lateral mixing. The observations span 500 hours at Egmond, Netherlands, and 1000 hours at Duck, North Carolina, and include a wide range of conditions with maximum mean currents of 1.4 m/s. Including rollers in the wave forcing results in improved predictions of the observed alongshore-current structure by shifting the predicted velocity maxima shoreward and increasing the velocity in the bar trough compared with model predictions without rollers. For these data, wave forcing balances the bottom stress within the surfzone, with the other terms of secondary importance. The good agreement between observations and predictions implies that the one-dimensional assumption holds for the range of conditions examined, despite the presence of small alongshore bathymetric nonuniformities. With stronger bathymetric variations the model skill deteriorates, particularly in the bar trough, consistent with earlier modeling and laboratory studies.

Calibration and verification of a parametric wave model on barred beaches

Abstract Since its introduction in 1978, the Battjes and Janssen model has proven to be a popular framework for estimating the cross-shore root-mean-square wave height H rms transformation of random breaking waves in shallow water. Previous model tests have shown that wave heights in the bar trough of single bar systems and in the inner troughs of multiple bar systems are overpredicted by up to 60% when standard settings for the free model parameter γ (a wave height-to-depth ratio) are used. In this paper, a new functional form for γ is derived empirically by an inverse modelling of γ from a high-resolution (in the cross-shore) 300-h H rms data set collected at Duck, NC, USA. We find that, in contrast to the standard setting, γ is not cross-shore constant, but depends systematically on the product of the local wavenumber k and water depth h . Model verification with other data at Duck, and data collected at Egmond and Terschelling (Netherlands), spanning a total of about 1600 h, shows that cross-shore H rms profiles modelled with the locally varying γ are indeed in better agreement with measurements than model predictions using the cross-shore constant γ . In particular, model accuracy in inner bar troughs increases by up to 80%. Additional verifications with data collected on planar laboratory beaches show the new functional form of γ to be applicable to non-barred beaches as well. Our optimum γ cannot be compared directly to field and laboratory measurements of height-to-depth ratios and we do not know of a physical mechanism why γ should depend positively on kh .

Modeling cross-shore sandbar behavior on the timescale of weeks

We compare predictions of a coupled, wave-averaged, cross-shore waves-currents-bathymetric evolution model to observations of onshore and offshore nearshore sandbar migration. The observations span a 10- and 44-day period with onshore/offshore bar migration at Duck, North Carolina, and at Hasaki, Kashima Coast, Japan, respectively, a 3.5-month period of onshore bar migration at Duck, and a 22-day period of offshore bar migration at Egmond, Netherlands. With best fit parameter values the modeled temporal evolution of the cross-shore bed profiles agrees well with the observations. Model skill, defined as 1 minus the ratio of prediction to no-change error variances, ranges from 0.50 at Egmond to 0.88 for the prolonged onshore bar migration at Duck. Localized (in time and space) reductions in model skill coincide with alongshore variations in the observed morphology. Consistent with earlier observations, simulated offshore bar migration takes place during storms when large waves break on the bar and is due to the feedback between waves, undertow, suspended sediment transport, and the sandbar. Simulated onshore bar migration is predicted for energetic, weakly to nonbreaking conditions and is due to the feedback between near-bed wave skewness, bedload transport, and the sandbar, with negligible to small effects of bound infragravity waves and near-bed streaming. Under small waves and conditions, when breaking and nonbreaking conditions alternate with the tide, the sandbar is predicted to remain stationary. The intersite differences in the optimum parameter values are, at least partly, induced by insensitivity to parameter variations, parameter interdependence, and errors in the offshore wave forcing.

The behaviour of a multiple bar system in the nearshore zone of Terschelling, the Netherlands: 1965–1993

Abstract The behaviour of a multiple bar system in the nearshore zone of the island of Terschelling, the Netherlands, is investigated on the time scale of years using a data set of soundings. The data set covers the period from 1965 to 1993. The behaviour is analysed in terms of bar crest position and in terms of morphometric parameters, such as bar crest depth, height, width, and volume. Two or three breaker bars are permanently present in the study area. Each individual bar passes through three stages during its existence: (1) generation close to the shore, (2) seaward migration and (3) degeneration at the outer margin of the nearshore bar zone. The key factor controlling the behaviour of the inner bars is the crest depth of the outer bar. Three different couplings between the behaviour of the individual bars have been observed: (1) bar stage changes due to the degeneration of the outer bar, (2) prevention of the transition of an inner bar from the first to the second stage, caused by the appearance from alongshore of a new outer bar having a small crest depth and (3) difference in mean annual seaward migration rate caused by the possible presence of a more seaward positioned bar. It is hypothesized that the crest depth of the outer bar governs the relative importance of processes inducing shoreward and seaward migration in the inner nearshore bar zone and therefore controls the behaviour of the nearshore bar zone on the time scale of years.

Observations of swash under highly dissipative conditions

Video measurements of swash were made at the low-sloping beach of the multiple bar system at Terschelling, Netherlands. The majority of the measurements were conducted under highly dissipative conditions with Iribarren numbers ξ0 (the ratio of beach slope to the square root of offshore wave steepness) less than 0.2. Infragravity (0.004–0.05 Hz) waves dominated the swash with an average ratio of infragravity and total swash height Rig/R of 0.85. Using linear regression we investigated the dependence of swash parameters on environmental conditions such as short-wave height, period, and local beach slope. On average, Rig was about 30% of the offshore wave height H0; the slope in the linear H0 dependence of Rig amounted to only 0.18, considerably smaller than that observed on steeper beaches. The data set shows evidence for saturation of the higher infragravity frequencies for ξ0 less than, roughly, 0.27. In our opinion, this saturation caused the constant of proportionality in the linear relationship between Rig/H0 and ξ0 to be significantly larger than that observed under higher Iribarren number regimes. The saturated tails of the swash spectra had an approximate f−3 roll-off (where f is frequency), whereas, in general, the nonsaturated parts were white. This lack of significant peaks casts doubt on the causality between infragravity waves and nearshore bars.

Video observations of nearshore bar behaviour. Part 2: alongshore non-uniform variability

Abstract Changes in nearshore sandbar morphology comprise of an alongshore uniform and non-uniform component. The former reflects the overall on/offshore migration, while the latter expresses changes in quasi-rhythmic non-uniformities, such as crescentic plan shapes. Here we focus on the alongshore-uniform component, quantified from a 3.4-year data set of daily time-exposure video images of the double barred nearshore at Noordwijk, Netherlands. The high temporal resolution and the long duration of the data set allowed us to quantify the cross-shore bar migration at weekly, seasonal and inter-annual time scales and, accordingly, to compare the contribution of all three components to the total variability in cross-shore bar position. The maximum observed offshore-directed weekly, seasonal and inter-annual bar migration rates were 10, 0.5 and 0.2 m/day . Maximum onshore rates at weekly and seasonal scales were 8 and 0.5 m/day , while onshore migration at the inter-annual scale was not observed. The inter-annual bar migration dominated the bar crest variability over time spans longer than 10–13 months, whereas changes on the weekly scale were the dominant source of variability on time spans shorter than 7–10 months. Seasonal bar migration only dominated the bar crest variability at the outer bar on time spans between 7 and 13 months. In general, Noordwijk appears to be a site with a strong inter-annual signal, with limited seasonal variability, and with fluctuations at weekly scales that are long compared to the characteristic time scale of individual events, suggesting a response to sequences of events rather than to individual events.

Observations of velocities, sand concentrations, and fluxes under velocity‐asymmetric oscillatory flows

[1] U‐tube measurements of instantaneous velocities, concentrations, and fluxes for a well‐sorted, medium‐sized sand in oscillatory sheet flow are analyzed. The experiments involved two velocity‐asymmetric flows, the same two flows with an opposing current of 0.4 m/s, and a mixed skewed‐asymmetric flow, all with a velocity amplitude of 1.2 m/s and flow period of 7 s. We find that the net positive transport rate beneath velocity‐ asymmetric oscillatory flow results from large, but opposing sand fluxes during the positive and negative flow phase. With an increase in velocity asymmetry and, in particular, velocity skewness, the difference in the magnitude of the fluxes in the two half cycles increases, leading to larger net transport rates. This trend is consistent with the observed increase in skewness of the oscillatory bed shear stress. Phase‐lag effects, whereby sand stirred during the negative flow phase has not settled by the time of the negative‐to‐positive flow reversal and is subsequently transported during the positive flow phase, are notable but of minor importance to the net transport rate compared to earlier experiments with finer sands. In the vertical, the oscillatory flux is positive above the no‐ flow bed. Within the sheet flow pick‐up layer, the oscillatory flux is negative and similar in magnitude to the positive flux induced by the residual flow. The 0.4 m/s opposing current causes more sand to be picked up during the negative than during the positive flow phase. Above the no‐flow bed the resulting negative oscillatory flux is comparable in magnitude to the current‐related flux.

Effect of hydrodynamics and bathymetry on video estimates of nearshore sandbar position

Remote sensing of wave breaker patterns, clearly visible as high-intensity bands in time exposure video images, has become a powerful tool to obtain large-scale (kilometers) and long-term (years) time series of nearshore sandbar position. However, intensity-based bar crest positions xi differ from directly measured positions xb by a time-varying distance Δx, which is of O(10 m) and depends on the offshore wave height H0, the water level η0, and the bathymetry itself. The effect of these parameters on Δx was investigated from simultaneous video observations and bathymetric surveys, obtained in the double-barred system at Egmond aan Zee, Netherlands, and from wave model predictions, assuming that the roller energy represents image intensity. When the wave field over a bar was predicted to be nonsaturated, xi was observed and predicted to move offshore as either η0 decreased or H0 increased. Under saturated conditions, Δx only responded to changes in η0. Additional model investigations showed that an increase in outer bar crest depth, similar to that observed during interannual bar behavior, significantly reduced the Δx variability at the outer bar and increased the Δx variability at the inner bar. Implications of our observational and model findings for studying sandbar position from video imagery are outlined.

The systematic contribution of transporting mechanisms to the cross-shore sediment transport in water depths of 3 to 9 m

The systematic contributions of short waves, infragravity waves and mean flows to the cross-shore sediment transport were studied with direct measurements of instantaneous near-bed sediment concentrations and velocities as well as with an energetics-based sediment transport model using measured time series of near-bed cross-shore flow as input. The study was conducted at four cross-shore positions in the multiple bar system of Terschelling, Netherlands during three field campaigns, each with a five-week duration. The data were collected in 3- to 9-m water depth during a wide range of conditions, from low-energy non-breaking conditions to almost fully saturated breakers. The height over depth ratio Hs/h was applied at all four measuring stations as a local conditional parameter. All model predictions were grouped into Hs/h classes with a width of 0.02 to highlight the generality of the data. The energetics approach predicted that the suspended load dominated over the bedload at all four stations. Both the sediment flux measurements as well as the model predictions showed that the largest contributors to the gross suspended sediment transport were made by the short waves and the undertow, inducing an onshore and offshore transport, respectively. Their contributions to the gross suspended transport were about 40 to 50% under surf zone conditions. Bound infragravity waves were observed and predicted to result in an offshore directed transport that was of subordinate magnitude compared to the observed and estimated magnitudes by the short waves and the undertow. However, as these transports almost cancelled out because of their about equal magnitude but opposite sign, the suspended transport by bound infragravity waves may not be ignored and may, rather paradoxically, have a relatively large influence on the net suspended sediment transport. Hydrodynamical processes that do not seem to be of importance to the onshore and offshore sediment transport in 3- to 9-m water depth in the long run are mean flows under non-breaking conditions and free infragravity motions. A direct comparison between measured sediment fluxes and the model predictions suggests that simple energetics models are suitable for predicting cross-shore sediment transport in 3- to 9-m water depth.

The behaviour of nearshore bars on the time scale of years: a conceptual model

Abstract Soundings of the sandy Dutch coast have demonstrated the presence of a multiple bar system that exhibits cyclic, offshore-directed migration on the time scale of years (medium-term). A cycle comprises bar generation, interannual offshore migration and decay. In this paper we propose a conceptual model in which we qualitatively outline the relationships between short-term (hourly) process knowledge (waves, currents, sediment transport), based on a 15-week data set of near-bed hydrodynamics obtained in the multiple bar system of Terschelling (the Netherlands), and medium-term bar behaviour. The short-term process knowledge is aggregated to the medium-term by combining probabilistic characterisations of medium-term wave conditions and sediment transports estimated from the short-term field measurements. Essential to the conceptual model is the observed cross-shore change in short-term conditions that dominate medium-term onshore and offshore sediment transport (〈q〉on and 〈q〉off, respectively). In the cross-shore direction, the conditions contributing most to 〈q〉on change from predominantly breaking situations outside the bar zone to mainly non-breaking conditions on the beach. In contrast, 〈q〉off remains restricted to breaking conditions over the entire profile. In the model we qualitatively describe how this cross-shore change in the forcing conditions results in interannual offshore bar migration, bar decay and the onset of the next cycle. As such, our model may serve as a first step towards a more coherent, quantitative model on medium-term periodic bar behaviour.