Falk Feddersen

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.

Momentum balances on the North Carolina inner shelf

Four months of moored current, pressure, temperature, conductivity, wave, and wind observations on the North Carolina shelf indicate three dynamically distinct regions: the surf zone, the inner shelf between the surf zone and the 13-m isobath, and the midshelf. In the surf zone the along-shelf momentum balance is between the cross-shelf gradient of the wave radiation stress and the bottom stress. The linear drag coefficient in the surf zone is about 10 times larger than seaward of the surf zone. On the inner shelf the along-shelf momentum balance is also frictional; the along-shelf wind stress and pressure gradient are balanced by bottom stress. In the cross-shelf momentum balance the pressure gradient is the superposition of roughly equal contributions from the Coriolis force (geostrophy) and wave setdown from shoaling, unbroken surface gravity waves. At midshelf the along-shelf momentum balance is less frictional and hence flow accelerations are important. The cross-shelf momentum balance is predominantly geostrophic because the greater depth and smaller bottom slope at midshelf reduce the importance of wave setdown. The cross-shelf density gradient is in thermal wind balance with the vertical shear in the along-shelf flow in depths as shallow as 10 m. The dominant along-shelf momentum balances provide a simple estimate of the depth-averaged, along-shelf current in terms of the measured forcing (i.e., wind stress, wave radiation stress divergence, and along-shelf pressure gradient) that reproduces accurately the observed cross-shelf variation of the depth-averaged, along-shelf current between the surf zone and midshelf.

Alongshore momentum balances in the nearshore

The one-dimensional, time-averaged (over many wave periods) along- shore momentum balance between forcing by wind and breaking waves and the bottom stress is examined with field observations spanning a wide range of con- ditions on a barred beach. Near-bottom horizontal currents were measured for 2 months at 15 locations along a cross-shore transect extending 750 m from the shoreline to 8-m water depth. The hourly averaged bottom stress was estimated from observed currents using a quadratic drag law. The wave radiation stress was estimated in 8-m depth from an array of pressure sensors, and the wind stress was estimated from an anemometer at the seaward end of a nearby pier. The combined wind and wave forcing integrated over the entire cross-shore transect is balanced by the integrated bottom stress. The wind stress contributes about one third of the forcing over the transect. Analysis of the momentum balances in different cross-shore regions shows that in the surf zone, wave forcing is much larger than wind forcing and that the bottom drag coefficient is larger in the surf zone than farther seaward, consistent with earlier studies.

Observing Surf-Zone Dispersion with Drifters

Abstract Surf-zone dispersion is studied using drifter observations collected within about 200 m of the shoreline (at depths of less than about 5 m) on a beach with approximately alongshore uniform bathymetry and waves. There were about 70 individual drifter releases, each 10–20 min in duration, on two consecutive days. On the first day, the sea-swell significant wave height Hs was equal to 0.5 m and mean alongshore currents |υ| were moderate (<0.1 m s−1). On the second day, the obliquely incident waves were larger, with Hs equal to 1.4 m, and at some surf-zone locations |υ| was greater than 0.5 m s−1. The one-particle diffusivity was larger, with larger waves and stronger currents. On both days, the one-particle diffusivity tensor is nonisotropic and time-dependent. The major axis is initially parallel to the cross-shore direction, but after a few wave periods it is aligned with the alongshore direction. In both the along- and cross-shore directions, the asymptotic diffusivity is reached sooner within, r...

Velocity moments in alongshore bottom stress parameterizations

The time-averaged alongshore bottom stress is an important component of nearshore circulation models. In a widely accepted formulation the bottom stress is proportional to , the time average of the product of the instantaneous velocity magnitude |u→| and the instantaneous alongshore velocity component υ. Both mean and fluctuating (owing to random, directionally spread waves) velocities contribute to . Direct estimation of requires a more detailed specification of the velocity field than is usually available, so the term is parameterized. Here direct estimates of based on time series of near-bottom currents observed between the shoreline and 8-m water depth are used to test the accuracy of parameterizations. Common parameterizations that are linear in the mean alongshore current significantly underestimate for moderately strong alongshore currents, resulting in overestimation of a drag coefficient determined by fitting modeled (with a linearized bottom stress) to observed alongshore currents. A parameterization based on a joint-Gaussian velocity field with the observed velocity statistics gives excellent overall agreement with the directly estimated and allows analytic investigation of the statistical properties of the velocity field that govern . Except for the weakest flows, depends strongly on the mean alongshore current and the total velocity variance but depends only weakly on the mean wave angle, wave directional spread, and mean cross-shore current. Several other nonlinear parameterizations of are shown to be more accurate than the linear parameterizations and are adequate for many modeling purposes.

Vertical Structure of Dissipation in the Nearshore

Abstract The vertical structure of the dissipation of turbulence kinetic energy was observed in the nearshore region (3.2-m mean water depth) with a tripod of three acoustic Doppler current meters off a sandy ocean beach. Surface and bottom boundary layer dissipation scaling concepts overlap in this region. No depth-limited wave breaking occurred at the tripod, but wind-induced whitecapping wave breaking did occur. Dissipation is maximum near the surface and minimum at middepth, with a secondary maximum near the bed. The observed dissipation does not follow a surfzone scaling, nor does it follow a “log layer” surface or bottom boundary layer scaling. At the upper two current meters, dissipation follows a modified deep-water breaking-wave scaling. Vertical shear in the mean currents is negligible and shear production magnitude is much less than dissipation, implying that the vertical diffusion of turbulence is important. The increased near-bed secondary dissipation maximum results from a decrease in the tu...

Lagrangian Drifter Dispersion in the Surf Zone: Directionally Spread, Normally Incident Waves

Abstract Lagrangian drifter statistics in a surf zone wave and circulation model are examined and compared to single- and two-particle dispersion statistics observed on an alongshore uniform natural beach with small, normally incident, directionally spread waves. Drifter trajectories are modeled with a time-dependent Boussinesq wave model that resolves individual waves and parameterizes wave breaking. The model reproduces the cross-shore variation in wave statistics observed at three cross-shore locations. In addition, observed and modeled Eulerian binned (means and standard deviations) drifter velocities agree. Modeled surf zone Lagrangian statistics are similar to those observed. The single-particle (absolute) dispersion statistics are well predicted, including nondimensionalized displacement probability density functions (PDFs) and the growth of displacement variance with time. The modeled relative dispersion and scale-dependent diffusivity is consistent with the observed and indicates the presence of ...

The Effect of Wave Breaking on Surf-Zone Turbulence and Alongshore Currents: A Modeling Study*

The effect of breaking-wave-generated turbulence on the mean circulation, turbulence, and bottom stress in the surf zone is poorly understood. A one-dimensional vertical coupled turbulence (k–) and mean-flow model is developed that incorporates the effect of wave breaking with a time-dependent surface turbulence flux and uses existing (published) model closures. No model parameters are tuned to optimize model–data agreement. The model qualitatively reproduces the mean dissipation and production during the most energetic breaking-wave conditions in 4.5-m water depth off of a sandy beach and slightly underpredicts the mean alongshore current. By modeling a cross-shore transect case example from the Duck94 field experiment, the observed surf-zone dissipation depth scaling and the observed mean alongshore current (although slightly underpredicted) are generally reproduced. Wave breaking significantly reduces the modeled vertical shear, suggesting that surf-zone bottom stress cannot be estimated by fitting a logarithmic current profile to alongshore current observations. Model-inferred drag coefficients follow parameterizations (Manning– Strickler) that depend on the bed roughness and inversely on the water depth, although the inverse depth dependence is likely a proxy for some other effect such as wave breaking. Variations in the bed roughness and the percentage of breaking-wave energy entering the water column have a comparable effect on the mean alongshore current and drag coefficient. However, covarying the wave height, forcing, and dissipation and bed roughness separately results in an alongshore current (drag coefficient) only weakly (strongly) dependent on the bed roughness because of the competing effects of increased turbulence, wave forcing, and orbital wave velocities.

The Generation of Surfzone Eddies in a Strong Alongshore Current

AbstractThe surfzone contains energetic two-dimensional horizontal eddies with length scale larger than the water depth. Yet, the dominant eddy generation mechanism is not understood. The wave-resolving model funwaveC is used to simulate surfzone eddies in four case examples, from the SandyDuck field experiment, that had alongshore uniform bathymetry. The funwaveC model is initialized with the observed bathymetry and the incident wave field in 8-m depth and reproduces the observed cross-shore structure of significant wave height and mean alongshore current. Within the surfzone, the wave-resolving funwaveC-modeled E(f, ky) spectra and the bulk (frequency and ky integrated) rotational velocities are consistent with the observations below the sea–swell band (<0.05 Hz), demonstrating that the model can be used to diagnose surfzone eddy generation mechanisms. In the mean-squared perturbation vorticity budget, the breaking wave vorticity forcing term is orders of magnitude larger than the shear instability gene...

Observations of the Surf-Zone Turbulent Dissipation Rate

AbstractThe contributions of surface (breaking wave) boundary layer (SBL) and bottom (velocity shear) boundary layer (BBL) processes to surf-zone turbulence is studied here. The turbulent dissipation rate ϵ, estimated on a 160-m-long cross-shore instrumented array, was an order of magnitude larger within the surf zone relative to seaward of the surf zone. The observed ϵ covaried across the array with changing incident wave height, tide level, and alongshore current. The cross-shore-integrated depth times ϵ was correlated with, but was only 1% of, the incident wave energy flux, indicating that surf-zone water-column turbulence is driven directly (turbulence injected by wave breaking) or indirectly (by forcing alongshore currents) by waves and that the bulk of ϵ occurs in the upper water column. This small fraction is consistent with laboratory studies. The surf-zone-scaled (or Froude-scaled) ϵ is similar to previous field observations, albeit somewhat smaller than laboratory observations. A breaking-wave ϵ...