Surfzone Eddies Research Articles

Wave Breaking Eddies And Transient Rip Current Dynamics In Large-Scale Wave Basin Experiments

Rip currents transport contaminants, nutrients, larvae, and, unfortunately, occasionally even swimmers between the surf zone and inner shelf. Transient rip currents are ephemeral ejections associated with surfzone eddies that are ubiquitous even on alongshore-uniform beaches. During directionally spread wave conditions, depth-limited breaking along finite-length regions, known as short-crested breaking, leads to spatial variation in the breaking force and corresponding vertical vorticity input to the water column. An inverse energy cascade from the injected vorticity may result in larger scale horizontal surfzone eddies, consistent with two-dimensional turbulence. These large-scale eddies enhance dispersion within the surf zone and may mutually advect offshore as a transient rip current. While this hypothesis is widely discussed in the literature, we do not have strong observational evidence for the processes connecting the wave field to the formation of large-scale horizontal eddies. To overcome the challenges of isolating and measuring the processes leading to transient rip currents in the field, we examined these processes in large-scale laboratory experiments.

Two-dimensional inverse energy cascade in a laboratory surf zone for varying wave directional spread

Surfzone eddies enhance the dispersion and transport of contaminants, bacteria, and larvae across the nearshore, altering coastal water quality and ecosystem health. During directionally spread wave conditions, vertical vortices (horizontal eddies) are injected near the ends of breaking crests. Energy associated with these eddies may be transferred to larger-scale, low-frequency rotational motions through an inverse energy cascade, consistent with two-dimensional turbulence. However, our understanding of the relationships between the wave conditions and the dynamics and energetics of low-frequency surfzone eddies are largely based on numerical modeling. Here, we test these relationships with remotely sensed and in situ observations from large-scale directional wave basin experiments with varying wave conditions over alongshore-uniform barred bathymetry. Surface velocities derived with particle image velocimetry were employed to assess the spatial scales of low-frequency surfzone eddies and compute structure functions with alongshore velocities. Second-order structure functions for directionally spread waves (σθ≥10°) are consistent with energy flux to larger or smaller length scales, while normally incident, unidirectional waves do not display this behavior. Third-order structure functions suggest that the surfzone flows exhibit a bidirectional energy cascade—a direct cascade to smaller and inverse cascade to larger length scales—during large directional spreads waves (σθ≥18°). However, there is not decisive evidence of an inverse energy cascade for moderate directional spreads (σθ=10°). Energy flux varies by cross-shore location and increases with increasing directional spread and wave height. Eddy decorrelation length scales weakly depend on wave directional spread. These findings advance our understanding of the dynamics linking wave breaking to large-scale rotational motions that enhance mixing and lead to rip currents, important conduits for cross-shore material exchange.

Observations of two-dimensional turbulence in the surfzone

Low-frequency, many-minute-period horizontal surfzone eddies are an important mechanism for the dispersion of material, transporting larvae, pollutants, sediment, and swimmers both across and along the nearshore. Previous numerical, laboratory, and field observations on alongshore uniform bathymetry with no or roughly uniform mean background flows suggest that the low-frequency eddies may be the result of a two-dimensional inverse energy cascade that transfers energy from relatively small spatial-scale vorticity injected by depth limited breaking waves to larger and larger spatial scales. Here, using remotely sensed high-spatial resolution estimates of currents, those results are extended to surfzones with strong complex mean circulation patterns [flows O(1 m/s)] owing to nonuniform bathymetry. Similar to previous results, wavenumber spectra and second-order structure functions calculated from the observations are consistent with a two-dimensional inverse energy cascade. The size of the largest eddies is shown to depend on the surfzone width and the spatial scales of the mean currents. Third-order structure functions also are consistent with an inverse cascade for spatial scales greater than ∼50 m. At smaller scales, the third-order structure functions suggest a mixture of inverse and forward cascades.

Headland Rip Very Low Frequency Fluctuations and Surfzone Eddies During High-Energy Wave Events

Abstract A wave-group-resolving model is used to investigate the driving mechanisms and the spatiotemporal variability of very low frequency (VLF) fluctuations of a headland deflection rip, measured during a 4-m oblique wave event. Surfzone eddies (SZE) occurring in the presence of a strongly sheared longshore current V at a longshore-uniform beach are first modeled. The spectral signature and the variability of SZE are displayed and compared with the literature. The model is then used to explore the dynamics of vorticity in the surf zone and against a headland under energetic oblique wave conditions. The resulting weakly sheared V is found to host large-scale SZE propagating toward the headland at a speed decreasing seaward. Vorticity animations and spectral diagrams indicate that VLF fluctuations of the deflection rip are driven by the deflection of the upstream SZE. In line with measurements, periods from 40 min to 1 h dominate the spectrum hundreds of meters from the headland at low tide. At high tide, vorticity spectra in the rip are much narrower than in the surf zone, suggesting that the headland enforces the merging of SZE. This mechanism is further analyzed using idealized simulations with varying headland lengths, aiming at extending traditional deflection patterns at the VLF scale. Finally, we discuss the existence of a continuum in SZE driving mechanisms, going from fully wave-group-driven to both wave-group- and shear-instability-driven SZE for weakly and strongly sheared V, respectively. This continuum suggests the importance of wave groups to produce SZE under energetic wave conditions.

Modeled Three‐Dimensional Currents and Eddies on an Alongshore‐Variable Barred Beach

AbstractCirculation in the nearshore region, which is critical for material transport along the coast and between the surf zone and the inner shelf, includes strong vortical motions. The horizontal length scales and vertical structure associated with vortical motions are not well documented on alongshore‐variable beaches. Here, a three‐dimensional phase‐resolving numerical model, Simulating WAves till SHore (SWASH), is compared with surfzone waves and flows on a barred beach, and is used to investigate surfzone eddies. Model simulations with measured bathymetry reproduce trends in the mean surfzone circulation patterns, including alongshore currents and rip current circulation cells observed for offshore wave heights from 0.5 to 2.0 m and incident wave directions from 0 to 15° relative to shore normal. The length scales of simulated eddies, quantified using the alongshore wavenumber spectra of vertical vorticity, suggest that increasing wave directional spread intensifies small‐scale eddies ((10) m). Simulations with bathymetric variability ranging from alongshore uniform to highly alongshore variable indicate that large‐scale eddies ((100) m) may be enhanced by surfzone bathymetric variability, whereas small‐scale eddies ((10) m) are less dependent on bathymetric variability. The simulated vertical dependence of the magnitude and mean length scale (centroid) of the alongshore wavenumber spectra of vertical vorticity and very low‐frequency (f ≈ 0.005 Hz) currents is weak in the outer surf zone, and decreases toward the shoreline. The vertical dependence in the simulations may be affected by the vertical structure of turbulence, mean shear, and bottom boundary layer dynamics.

Inhomogeneous Turbulent Dispersion across the Nearshore Induced by Surfzone Eddies

AbstractIn various oceanic regions, drifter-derived diffusivities reach a temporal maximum and subsequently decrease. Often, these are regions of inhomogeneous eddies, however, the effect of inhomogeneous turbulence on dispersion is poorly understood. The nearshore region (spanning from the surfzone to the inner shelf) also has strong cross-shore inhomogeneous turbulence. Nearshore Lagrangian statistics are estimated from drifter trajectories simulated with a wave-resolving two-dimensional Boussinesq model with random, normally incident, and directionally spread waves. The simulation is idealized and does not include other (wind, tidal, Coriolis) processes. The eddy field cross-shore inhomogeneity affects both the mean cross-shore drift and cross- and alongshore diffusivities. Short-time diffusivities are locally ballistic, and the mean drift is toward the eddy velocity variance maximum. The diffusivities reach a maximum and subsequently decrease, that is, are subdiffusive. The diffusivity maximum and time to maximum are parameterized taking into account the eddy field inhomogeneity. At long times, the cross- and alongshore diffusivities scale as t−1/2 and t−1/4, respectively, which is related to the offshore decay of the eddy intensity. A diffusion equation, with a space-dependent Fickian diffusivity related to the eddy velocity variance, reproduced the short-, intermediate-, and long-time behavior of the mean drift and cross-shore diffusivity. The small Middleton parameter, indicating fixed float dispersion, suggests the Eulerian time scale can parameterize the Lagrangian time scale in this region. Although this idealized simulation had no mean currents, and thus no shear dispersion or mixing suppression, inhomogeneous turbulence effects may be relevant in other regions such as the Antarctic Circumpolar Current (ACC) and western boundary current extensions.

Extremely Low Frequency (0.1 to 1.0 mHz) Surf Zone Currents

AbstractLow‐frequency surf zone eddies disperse material between the shoreline and the continental shelf, and velocity fluctuations with frequencies as low as a few mHz have been observed previously on several beaches. Here spectral estimates of surf zone currents are extended to an order of magnitude lower frequency, resolving an extremely low frequency peak of approximately 0.5 mHz that is observed for a range of beaches and wave conditions. The magnitude of the 0.5‐mHz peak increases with increasing wave energy and with spatial inhomogeneity of bathymetry or currents. The 0.5‐mHz peak may indicate the frequency for which nonlinear energy transfers from higher‐frequency, smaller‐scale motions are balanced by dissipative processes and thus may be the low‐frequency limit of the hypothesized 2‐D cascade of energy from breaking waves to lower frequency motions.

Controls on Flash Rip Current Hazard on Low-Tide Terraced Tropical Beaches in West Africa

Scott, T.; Castelle, B.; Almar, R.; Senechal, N.; Floc'h, F., and Detandt, G., 2018. Controls on flash rip current hazard on low-tide terraced tropical beaches in West Africa. In: Almar, R.; Almeida, L.P.; Trung Viet, N., and Sall, M. (eds.), Tropical Coastal and Estuarine Dynamics. Journal of Coastal Research, Special Issue No. 81, pp. 92–99. Coconut Creek (Florida), ISSN 0749-0208.Flash rip currents are transient non-fixed offshore-directed jets of water often associated with migrating surf-zone eddies. They can occur on featureless (alongshore-uniform) beaches and are essentially hydrodynamically controlled. Due to their unpredictable nature, they represent one of the most significant hazards to bathers across surf zones worldwide, especially in Tropical West Africa, where high levels of flash rip activity and a lack of a lifeguard service lead to high drowning rates. Recent work has shed light on two contrasting driving mechanisms for non-fixed rips: (1) cascading vortices generated by wave breaking, and (2) shear instabilities of the longshore current. This research provides the first quantitative scientific understanding of wave-driven currents in Tropical West Africa. Specifically, the study focussed on the dynamics of flash rips occurring along alongshore-uniform beach morphology, through the collection of unique Lagrangian field measurements of flash rips. During two periods, February 2013 and March 2014, 13 days of field data collection occurred at Grand Popo beach on the southerly-facing Bight of Benin coast (Gulf of Guinea, West Africa). The experiments measured flash rip currents, nearshore hydrodynamics and morphology at a moderately energetic (long-term average significant wave height, Hs = 1.36 m, and peak wave period Tp = 9.4 s), sandy alongshore-uniform low-tide terraced beach exposed to South Atlantic groundswells and local wind-waves. A suite of GPS drifters, dye-tracking and video confirmed the presence and characteristics of low–high energy flash rips (up to 0.7 m/s) in the surf zone, while in-situ acoustic wave and current measurements from the surf zone and inner-shelf provided metocean forcing conditions (0.8<Hs<1.6 m; 8<Tp<14 s; 1°<Dp<21° (from shore normal)) and longshore current velocities (0.2–0.8 m/s in surf zone). Throughout a range of wave conditions (height/period/angle/directional-spreading) contrasting flash rip behavioural responses were observed (surf zone exits/offshore extent/offshore-directed velocities). This study (1) supports findings of the first rip experiment conducted at this site (Feb 2013) suggesting that flash rip activity is likely to be driven by wave breaking vorticity generation (flash rip activity high under shore-normal wave forcing) and (2) provides further quantitative insights into the role of specific wave/tide forcing characteristics on flash rip activity, specifically the importance of reduced directional spreading and tidal level in controlling increases in offshore extent of flash rip currents. Finally, (3) the observed ubiquity of significant hazardous transient flash rip activity and identification of key behavioural controls can provide a foundation for any future development of rip hazard prediction tools and effective lifeguarding in West Africa.

Rip current circulation and surf zone retention on a double barred beach

Rip currents have an important control on the exchange of water and advected materials such as sediment and pollutants, between the surf zone and inner shelf. Concurrent in situ Eulerian and Lagrangian (GPS drifter) data of surf zone waves and currents were combined with video data on wave breaking patterns over the inner and outer bars on a high energy, double-barred beach. The data collectively show how the occurrence of wave breaking over the outer bar changes the behavior of a channel rip current, and the exchange process. On both days, there was a prominent clockwise eddy in the surf zone, for which the seaward-heading portion formed a rip current in a well-defined channel rip, incised into the inner bar. Exit rate (measured with drifters) from the surf zone to inner shelf decreased significantly with increased wave breaking over the outer bar, from 71% exits to 6% over the two days. Exit rate appears to be driven by the balance between wave breaking over the inner and outer bars and pulsing of currents within the surf zone. Under higher wave conditions, there were stronger pulsations in surf zone currents and more surf zone exits. However, higher wave conditions caused wave breaking over the outer bar. This breaking increases vorticity around the outside of the surf zone eddy, which increases surf zone retention. This is in contrast to previous studies showing that vorticity is highest at the center of surf zone eddies. Under such conditions, drifter exits were rare, and occurred due to vortex shedding. During lower incident wave conditions, eddy vorticity was lower, and drifters could relatively freely exit the surf zone. This is one of the few studies that investigate surf zone circulation on a high energy, double-barred beach.

The suppression of surfzone cross‐shore mixing by alongshore currents

AbstractMixing by horizontal surfzone eddies is important to the cross‐shore exchange of material through the surfzone. Surfzone cross‐shore mixing for normally and obliquely incident waves, with very similar incident significant wave heights and directional spreads, is quantified using Boussinesq modeled drifter trajectories. For t &lt; 100 s, surfzone cross‐shore diffusivities K(t) are independent of incident wave angle owing to similar eddy velocities m s−1. For 600 &lt; t &lt; 10,000 s, K(t) is maximum for normally incident waves and decreases with incident wave angle. Thus, the mixing parameterization is not completely applicable to the surfzone, because and LE do not change for these experiments. Reduced mixing for obliquely incident waves results from large eddies (wavelengths &gt;200 m) propagating at a velocity C different than the mean current velocity V(x)—the same mechanism that reduces mixing for mesoscale eddies.

Modeling surfzone to inner‐shelf tracer exchange

AbstractA near‐shoreline, continuous dye release at an approximately alongshore‐uniform beach (IB09 experiment) is simulated with the wave‐resolving Boussinesq model funwaveC. The model generates surfzone eddies and transient rip currents but does not resolve inner‐shelf vertical variation or stratification. The funwaveC model reproduces well the observed surfzone and inner‐shelf dye observations over roughly 350 m cross‐shore and 2 km alongshore. Dye is advected alongshore by wave‐ and wind‐driven currents similarly in the observations and model. Near‐shoreline mean dye concentration decays downstream as a power law with similar observed (−0.33) and modeled (−0.38) exponents. Observed and modeled cross‐shore mean dye profiles are similar, though modeled inner‐shelf dye is somewhat elevated. Observed and modeled alongshore dye transports agree, though with compensating surfzone and inner‐shelf errors later in the release. For times &lt;3.5 h (before observed and modeled dye advects beyond the model alongshore domain), observed and modeled dye budgets are similar to each other and close to within 10%, and half the observed and modeled dye is exported to the inner‐shelf. Later in the release, surfzone and inner‐shelf dye masses are under and overpredicted, respectively. Model‐data differences may be due to the model's lack of vertical variation, stratification, or tide. The good overall model‐data agreement indicates that nearshore tracer transport and dispersion are realistically simulated over 5 h and 2 km alongshore, and that the model transient rip currents accurately induce cross‐shore exchange between the surfzone and inner‐shelf.

Bathymetric controls on very low frequency rip current motions

McCarroll, R.J.; Brander, R.W., and Turner, I.L., 2016. Bathymetric controls on very low frequency rip current motions. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 418-422. Coconut Creek (Florida), ISSN 0749-0208.Time-averaged mean rip currents are forced by persistent gradients in dissipation over shallow bars and deep rip channels. Time-variable horizontal surfzone eddies, at the ∼10 min or very low frequency (VLF) range, are forced by stochastic wave breaking injecting vortical energy into the surfzone. Previous observations note that deep channel rips have greater variability of velocity while shallow channel rips exhibit greater variability in trajectory, this suggests a continuum of flow states that at present are poorly understood. This paper investigates the degree of bathymetric control on VLF motions illustrating how VLF motions manifest on different morphologies. Three field sites are investigated using low-pass filtered: (i) mean velocity; (ii) variable eddy velocity; (iii) directional standard deviation; and (iv) instantaneous vorticity. A VLF flow-type parameter is introduced to differentiate flow regimes, based on degree of bathymetric control. A novel classification scheme is introduced: (i) strong bathymetric control, with high mean velocities and rip cell oscillation; (ii) moderate control, with high mean velocities and variable VLF trajectories; and (iii) weak control, with low mean velocities and mobile eddies. Level of bathymetric control may be related to channel orientation, in addition to relative depth. This study improves our understanding of rip flow variability over short times frames, with implications for sediment transport and beach safety.

Modelling the alongshore variability of optimum rip current escape strategies on a multiple rip-channelled beach

Rip currents are a leading cause of drowning on beaches worldwide. How bathers caught in a rip current should attempt to escape has been a subject of recent debate. A numerical model of human bathers escaping from a rip current flow field is applied to a 2-km-long section of the open beach of Biscarrosse, SW France. The study area comprises 4 rip channels that visually appear similar from the beach, but exhibit different morphologies. Simulations are run for 2 representative hazardous summer wave conditions. Results show that small changes in the bar/rip morphology have a large impact on the rip flow field, and in turn on the alongshore variability of the optimal rip current escape strategy. The overall flow regime (dominant surf-zone exits versus dominant recirculation), which is found to be influenced by the alongshore dimensions of the sand bars adjacent to the rip channel, is more important to rip current escape strategy than rip velocity. Flow regime was found to dictate the success of the “stay afloat” strategy, with greater success for recirculating flow. By comparison, the dominant longshore feeder current and rip-neck orientation determined the best direction to “swim parallel” towards. For obliquely incident waves, “swim parallel” downdrift then swim onshore with breaking waves was highly successful and can become a simple safety message for beach safety practitioners to communicate to the general public. However, in SW France where rip spacing is large ( $$\sim$$ 400 m), surf-zone eddies have large spatial scales of the order of 100+ m, requiring a large distance (100+ m) to swim to reach safety, therefore requiring good swimming ability. This also shows that in addition to rip current intensity, rip flow regime and the depth of adjacent sand bars, rip spacing is important for defining rip current hazard and the best safety message. Our results also indicate that for normal to near-normal wave incidence, rip current hazard and best rip current escape strategy are highly variable alongshore due to subtle differences in bar/rip morphology from one rip system to another. These findings challenge the objective of developing a universal rip current escape strategy message on open rip-channelled beaches exposed to normal to near-normal wave incidence, even for seemingly similar rip channels.

Hydrodynamic Instability Mechanism for Rip Currents

On reexamining the hydrodynamic instability, Yu [1] showed that when the fully dynamical interactions are duly accounted for, and proper mathematical analysis is carried out, the positive feedback between the wave and evolving current can initiate and sustain rip current circulations with scales comparable to field observations on alongshore uniform beaches. In this study, we extend that analysis to consider nonplanar beaches, and to include a new branch of unstable modes that correspond to alongshore propagating horizontal circulations with the magnitudes of the flow growing in time. The latter has not previously been studied. These propagating unstable modes have typical time periods of tens of minutes and alongshore propagation speeds of a few centimeters per second. The physical implications of their spatial and slow time oscillations are discussed, as of relevance to occurrence and recurrence of transient rips, alongshore migration of rip currents and very low frequency pulsations in surf zone eddy circulations.

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 (&amp;lt;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 (&amp;gt;80%) of vorticity forcing occurring at short alongshore scales &amp;lt;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 ky.

Relating Lagrangian and Eulerian horizontal eddy statistics in the surfzone

AbstractConcurrent Lagrangian and Eulerian observations of rotational, low‐frequency (10−4 to 10−2 Hz) surfzone eddies are compared. Surface drifters were tracked for a few hours on each of 11 days at two alongshore uniform beaches. A cross‐shore array of near‐bottom current meters extended from near the shoreline to seaward of the surfzone (typically 100 m wide in these moderate wave conditions). Lagrangian and Eulerian mean alongshore velocities V are similar, with a midsurfzone maximum. Cross‐shore dependent Lagrangian (σL) and Eulerian (σE) rotational eddy velocities, estimated from low‐pass filtered drifter and current meter velocities, respectively, also generally agree. Cross‐shore rotational velocities have a midsurfzone maximum whereas alongshore rotational velocities are distributed more broadly. Daily estimates of the Lagrangian time scale, the time for drifter velocities to decorrelate, vary between 40 and 300 s, with alongshore time scales greater than cross‐shore time scales. The ratio of Lagrangian to apparent Eulerian current meter decorrelation times TL/TA varies considerably, between about 0.5 and 3. Consistent with theory, some of the TL/TA variation is ascribable to alongshore advection and TL/TA is proportional to V/σ, which ranges between about 0.6 and 2.5. Estimates of TL/TA vary between days with similar V/σ suggesting that surfzone Lagrangian particle dynamics vary between days, spanning the range from “fixed‐float” to “frozen‐field” [Lumpkin et al., 2002], although conclusions are limited by the statistical sampling errors in both TL/TA and V/σ.

Infrared Remote Sensing of Surf-Zone Eddies

<?Pub Dtl=""?> Airborne infrared imagery is used for the first time to investigate characteristics of surf-zone eddies, occurring along an along-shore uniform beach. Eddies are found to have diameters of 100 to 150 m, an alongshore spacing of about 375 m (2.5 times the surf-zone width), and lifetimes of 40 min and longer. Eddies travel alongshore at speeds of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\sim$</tex></formula> 0.3 to 0.5 m/s, at a distance from the shoreline of about 1.3 surf-zone widths. Eddies are also observed to move directly offshore, two surf-zone widths from the shoreline. Fine-scale thermal structure within an eddy includes <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\sim$</tex> </formula> 6-m-wide cold patches, possibly the surface imprints of bottom-induced turbulence, and a small ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$&lt;$</tex> </formula> 10-m wide) ‘cold core’, likely from accumulation of surfactant by radially inward surface flow. Visualization of an eddy is enhanced through flow deformation of surfactant slicks. In particular, narrow slicks appear to be wound-up by an eddy into spirals similar in form to those of a free vortex. In this sense, these nearshore eddies resemble ocean sub-mesoscale ‘spiral eddies’ as seen in synthetic-aperture radar and sunglint imagery.

VORTICAL VLF MOTIONS UNDER SHORE-NORMAL INCIDENT WAVES

Field observations and numerical model simulations are examined to investigate the magnitude of vortical very low frequency (VLF) velocity fluctuations (i.e. large scale surfzone eddies) under different offshore wave forcing. Observations of vortical VLF motions under shore -normal wave incidence at Duck, NC, USA are re-analyzed and compared with the characteristics of the incident wave spectrum. Long wave periods and narrow frequency spread incident waves were found to coincide with stronger vortical VLF motions. Numerical model simulations investigating the effect of the incident wave parameters in a more isolated way confirm the observed effect of frequency spread and wave period on the magnitude of VLF motions. Variations in incident wave spectrum resulted in changes in the vortical VLF magnitude of the same order as the magnitude of the vortical VLF velocity fluctuations themselves. These results imply that under shore-normal incident waves strong vortical VLF velocity fluctuations in the surfzone are more likely under swell conditions and at swell dominated coasts.

A Lagrangian stochastic model of surf zone drifter dispersion

Drifter‐derived cross‐shore and alongshore surf zone diffusivities were previously estimated on an alongshore uniform beach over 1000 s for five Huntington Beach, California, 2006 (HB06) experiment release days. The cross‐shore diffusivity Kx had a nonmonotonic time dependence, potentially due to the shoreline or to weaker diffusivity seaward of the surf zone. The alongshore diffusivities Ky were qualitatively consistent with shear dispersion but differed from the classic Taylor laminar theory. Here, modeled and analytic diffusivities for the five release days are derived from a Lagrangian stochastic model (LSM) that uses the drifter‐derived bulk (cross‐shore averaged) velocity variance and cross‐shore‐dependent mean alongshore current. The LSM modeled and analytic cross‐shore diffusivities are nonmonotonic due to the shoreline and strongly suggest that the observed cross‐shore diffusivity is shoreline affected. The LSM typically reproduce well the observed Kx with Lagrangian time scale between 75 and 200 s, consistent with surf zone eddy time scales. HB06 drifter trajectories were too short to observe the analytic long‐time Kx limit, and weaker diffusivity seaward of the surf zone may be important at longer times (&gt;1000 s). On all release days, the LSM model and analytic alongshore diffusivity reproduce well the observed Ky with alongshore Lagrangian time scales between 95 and 155 s. The isolated shear‐induced diffusivity is very well represented by an analytic theory which incorporates a nonzero Lagrangian time scale. Many of the stochastic model parameters can be specified a priori with reasonable assumptions to predict surf zone dispersion of an initial value problem pollution spill.

Modeling surf zone tracer plumes: 2. Transport and dispersion

Five surf zone dye tracer releases from the HB06 experiment are simulated with a tracer advection diffusion model coupled to a Boussinesq surf zone model (funwaveC). Model tracer is transported and stirred by currents and eddies and diffused with a breaking wave eddy diffusivity, set equal to the breaking wave eddy viscosity, and a small (0.01 m2 s−1) background diffusivity. Observed and modeled alongshore parallel tracer plumes, transported by the wave driven alongshore current, have qualitatively similar cross‐shore structures. Although the model skill for mean tracer concentration is variable (from negative to 0.73) depending upon release, cross‐shore integrated tracer moments (normalized by the cross‐shore tracer integral) have consistently high skills (≈0.9). Modeled and observed bulk surf zone cross‐shore diffusivity estimates are also similar, with 0.72 squared correlation and skill of 0.4. Similar to the observations, the model bulk (absolute) cross‐shore diffusivity is consistent with a mixing length parameterization based on low‐frequency (0.001–0.03 Hz) eddies. The model absolute cross‐shore dispersion is dominated by stirring from surf zone eddies and does not depend upon the presence of the breaking wave eddy diffusivity. Given only the bathymetry and incident wave field, the coupled Boussinesq‐tracer model qualitatively reproduces the observed cross‐shore absolute tracer dispersion, suggesting that the model can be used to study surf zone tracer dispersion mechanisms.