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Falk Feddersen

Abstract

The 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 scaling is applicable in the midwater column at certain locations, indicating a vertical diffusion of turbulence and ϵ balance. However, observations at different cross-shore locations do not collapse, which is consistent with a cross-shore lag between wave energy gradients and the surface turbulence flux. With strong alongshore currents, a BBL-scaled ϵ indicates that shear production is a significant turbulence source within the surf zone, particularly in the lower water column. Similarly for large currents at one location, the dissipation to shear production ratio approaches one. Both dissipation scalings depend upon wave energy flux gradients. The ratio of BBL to SBL ϵ has complex dependencies but is larger for a deeper part of the surf zone and more obliquely incident waves.

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Falk Feddersen

Abstract

The 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, k y) spectra and the bulk (frequency and k y 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 generation term. Thus, surfzone eddies (vorticity) generally are not generated through a shear instability, with possible exceptions for very narrow banded in frequency and direction and highly obliquely large incident waves. The alongshore wavenumber spectra of breaking wave vorticity forcing is broad with the majority (>80%) of vorticity forcing occurring at short alongshore scales <20 m. However, the alongshore wavenumber spectra of vorticity is red, which may be due to a 2D turbulence inverse energy cascade bringing energy to longer wavelengths or may result from an amplified vorticity response to direct forcing at smaller k y.

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Falk Feddersen

Abstract

High-quality measurements of the turbulent dissipation rate ε are required to diagnose field surf-zone turbulence budgets. Quality control (QC) methods are presented for estimating surf zone ε with acoustic Doppler velocimeter (ADV) data. Bad ADV velocity data points are diagnosed with both the ADV signal strength (SS) and correlation (CORR). The fraction of bad SS data points (δ SS) depends inversely upon the wave-amplitude-normalized transducer distance below the mean sea surface. The fraction of bad CORR data points δ CORR can be elevated when δ SS is low. The δ CORR depends inversely upon the wave-amplitude-normalized sensing volume distance below the mean sea surface, and also increases with increased wave breaking, consistent with turbulence- and bubble-induced Doppler noise. Velocity spectra derived from both “patched” and “interpolated” time series are used to estimate ε. Two QC tests, based upon the properties of a turbulent inertial subrange, are used to reject bad ε data runs. The first test checks that the vertical velocity spectrum’s power-law exponent is near . The second test checks that a ratio R of horizontal and vertical velocity spectra is near 1. Over all δ CORR, 70% of the patched and interpolated data runs pass these tests. However, for larger δ CORR > 0.1 (locations higher in the water column), 50% more patched than interpolated data runs pass the QC tests. Previous QC methods designed for wave studies are not appropriate for ε QC. The results suggest that ε can be consistently estimated over the lower 60% of the water column and >0.1 m above the bed within a saturated surf zone.

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Matthew Spydell and Falk Feddersen

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 a 2D turbulent flow field. The model dispersion is due to the rotational components of the modeled velocity field, indicating the importance of vorticity in driving surf zone dispersion. Modeled irrotational velocities have little dispersive capacity. Surf zone vorticity is generated by finite crest-length wave breaking that results, on the alongshore uniform bathymetry, from a directionally spread wave field. The generated vorticity then cascades to other length scales as in 2D turbulence. Increasing the wave directional spread results in increased surf zone vorticity variability and surf zone dispersion. Eulerian and Lagrangian analysis of the flow indicate that the surf zone is 2D turbulent-like with an enstrophy cascade for length scales between approximately 5 and 10 m and an inverse-energy cascade for scales of 20 to 100 m. The vorticity injection length scale (the transition between enstrophy and inverse-energy cascade) is a function of the wave directional spread.

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Nirnimesh Kumar and Falk Feddersen

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This is part one of a two-part study focused on Stokes drift and transient rip current (TRC) effects on the unstratified (this paper) and stratified (see Part II) inner shelf. A TRC-generating, wave-resolving model funwaveC is coupled to the 3D, wave-averaged wave and circulation model Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST). Two simulations (R1 and R2) are performed on an unstratified inner shelf and surfzone with typical bathymetry and wave conditions. R1 is a COAWST-only simulation (no TRCs), while R2 has funwaveC–COAWST coupling (with TRCs). R2 and funwaveC vertical vorticity (eddy) statistics are similar, indicating that the model coupling accurately generates TRCs, with TRC-induced eddies out to four surfzone widths offshore. R1 has a two-layered, inner-shelf-to-surfzone-connected, mean Lagrangian circulation, while R2 has separate inner shelf and surfzone circulation cells. The R2, TRC-induced, cross-shore and vertical eddy velocities are stronger than the R1 or R2 mean Lagrangian velocity out to four surfzone widths offshore. The R2, inner-shelf, mean, vertical eddy diffusivity is an order of magnitude larger than R1 out to four surfzone widths offshore. Both R1 and R2 are in a Stokes–Coriolis balance at six surfzone widths offshore, as is R1 at three surfzone widths offshore. For R2, TRC-induced horizontal advection and vertical mixing dominate the cross-shore momentum dynamics at three surfzone widths offshore. The R2 surfzone and inner-shelf cross-shore exchange velocity is 2–10 times larger for R1 because of the TRC-induced stirring. Accurate, unstratified, inner-shelf simulations of pollution, larval, or sediment transport must include transient rip currents. In Part II, the effects of Stokes drift and TRCs on the stratified inner shelf are examined.

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Falk Feddersen and Fabrice Veron

Abstract

Near the shore, cross-shore winds strongly affect the location of the break point and the breaking-wave height. From casual observation from the beach, wind direction (onshore or offshore) and speed also appear to affect wave shape (i.e., skewness and asymmetry), although as of yet this effect has not been quantified near the shore. The effect of wind on shoaling wave shape is investigated with laboratory experiments using monochromatic waves and onshore-directed wind. Wind increases the shoaling wave energy at discrete multiples of the primary frequency and has a significant effect on the wave shape at both a deeper and shallower shoaling locations. At the shallower location, the ratio of wave energy at 2 times the primary frequency to the primary frequency is also a function of wind speed, indicating interaction between the wind and the nonlinear wave shoaling process. Nearshore wave models do not account for these wind effects. Incorrect predictions of third-order velocity moments (wave shape), believed to control wave-driven sediment transport, would result in incorrect beach morphological evolution predictions.

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Nirnimesh Kumar and Falk Feddersen

Abstract

This is Part II of a two-part study focused on Stokes drift and transient rip current (TRC) effects on the unstratified (Part I) and stratified (this paper) inner shelf. Part I focuses on funwaveC–Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) coupling and TRC effects on mixing and exchange on an unstratified inner shelf. Here, two simulations (R3 and R4) are performed on a stratified inner shelf and surfzone with typical bathymetry, stratification, and wave conditions. R3 is a COAWST-only simulation (no TRCs), while R4 has funwaveC–COAWST coupling (with TRCs). In R4, TRCs lead to patchy, near-surface cooling, vertical isotherm displacement, and increased water column mixing. For both R3 and R4, the mean Lagrangian circulation has two nearly isolated surfzones and inner-shelf overturning circulation cells, with a stronger, R4, inner-shelf circulation cell. The R4, inner-shelf, vertical velocity variability is 2–3 times stronger than a simulation with TRCs and no stratification. Relative to R3, R4 eddy diffusivity is strongly elevated out to three surfzone widths offshore due to TRCs and TRC-induced density overturns. The R4 inner-shelf stratification is reduced nearshore, and mean isotherms slope more strongly than R3 because of the TRC-enhanced irreversible mixing. At six surfzone widths offshore, both R3 and R4 are in geostrophic balance, explaining the stratified (summertime) observed deviation from Stokes–Coriolis balance. In this region, baroclinic pressure gradients induced by sloping isotherms induce an alongshore geostrophic jet offshore, strongest in R4. In R4, TRCs result in an enhanced (2–10 times) cross-shore exchange velocity across the entire inner shelf, relative to R3. Accurate, stratified, inner-shelf simulations of pollution, larval, or sediment transport must include transient rip currents.

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Falk Feddersen and J. H. Trowbridge

Abstract

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 (kε) 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.

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

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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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Matthew S. Spydell, Falk Feddersen, and Jamie Macmahan

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Oceanographic relative dispersion Dr2 (based on drifter separations r) has been extensively studied, mostly finding either Richardson–Obukhov (Dr2~t3) or enstrophy cascade [Dr2~exp(t)] scaling. Relative perturbation dispersion Dr2 (based on perturbation separation rr 0, where r 0 is the initial separation) has a Batchelor scaling (Dr2~t2) for times less than the r 0-dependent Batchelor time. Batchelor scaling has received little oceanographic attention. GPS-equipped surface drifters were repeatedly deployed on the Inner Shelf off of Pt. Sal, California, in water depths ≤ 40 m. From 12 releases of ≈18 drifters per release, perturbation and regular relative dispersion over ≈4 h are calculated for 250 ≤ r 0 ≤ 1500 m for each release and the entire experiment. The perturbation dispersion Dr2 is consistent with Batchelor scaling for the first 1000–3000 s with larger r 0 yielding stronger dispersion and larger Batchelor times. At longer times, Dr2 and scale-dependent diffusivities begin to suggest Richardson–Obukhov scaling. This applies to both experiment averaged and individual releases. For individual releases, nonlinear internal waves can modulate dispersion. Batchelor scaling is not evident in Dr2 as the correlations between initial and later separations are significant at short time scaling as ~t. Thus, previous studies investigating Dr2(t) are potentially aliased by initial separation effects not present in the perturbation dispersion Dr2(t). As the underlying turbulent velocity wavenumber spectra is inferred from the dispersion power law time dependence, analysis of both Dr2 and Dr2 is critical.

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