Steve Elgar

Observations of sand bar evolution on a natural beach

Waves, currents, and the location of the seafloor were measured on a barred beach for about 2 months at nine locations along a cross-shore transect extending 255 m from 1 to 4 m water depth. The seafloor location was measured nearly continuously, even in the surf zone during storms, with sonar altimeters mounted on fixed frames. The crest of a sand bar initially located about 60 m from the shoreline moved 130 m offshore (primarily when the offshore significant wave height exceeded about 2 m), with 1.5 m of erosion near the initial location and 1 m of accretion at the final location. An energetics-type sediment transport model driven by locally measured near-bottom currents predicts the observed offshore bar migration, but not the slow onshore migration observed during low-energy wave conditions. The predicted offshore bar migration is driven primarily by cross-shore gradients in predicted suspended sediment transport associated with quasi-steady, near-bottom, offshore flows. These strong (>50 cm/s) currents, intensified near the bar crest by wave breaking, are predicted to cause erosion on the shoreward slope of the bar and deposition on the seaward side. The feedback amoung morphology, waves, circulation, and sediment transport thus forces offshore bar migration during storms.

Observations of bispectra of shoaling surface gravity waves

Aspects of the nonlinear dynamics of waves shoaling between 9 and 1 m water depths are elucidated via the bispectrum. The biphase values associated with significant bicoherence levels in 9 m depth are consistent with Stokes-like nonlinearities, but as the water depth decreases the waves evolve through a slightly skewed shape somewhat asymmetrical to a vertical axis toward a highly asymmetrical unskewed sawtooth shape. The real and imaginary parts of the bispectrum are the contributions to skewness and asymmetry from individual frequency pairs.

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.

Generation and propagation of infragravity waves

The generation and propagation of infragravity waves (frequencies nominally 0.004–0.04 Hz) are investigated with data from a 24-element, coherent array of pressure sensors deployed for 9 months in 13-m depth, 2 km from shore. The high correlation between observed ratios of upcoast to downcoast energy fluxes in the infragravity (FupIG/FdownIG) and swell (Fupswell/Fdownswell) frequency bands indicates that the directional properties of infragravity waves are strongly dependent on incident swell propagation directions. However, FupIG/FdownIG is usually much closer to 1 (i.e., comparable upcoast and downcoast fluxes) than is Fupswell/Fdownswell, suggesting that upcoast propagating swell drives both upcoast and downcoast propagating infragravity waves. These observations agree well with predictions of a spectral WKB model based on the long-standing hypothesis that infragravity waves, forced by nonlinear interactions of nonbreaking, shoreward propagating swell, are released as free waves in the surf zone and subsequently reflect from the beach. The radiated free infragravity waves are predicted to be directionally broad and predominantly refractively trapped on a gently sloping shelf. The observed ratios FseaIG/FshoreIG of the seaward and shoreward infragravity energy fluxes are indeed scattered about the theoretical value 1 for trapped waves when the swell energy is moderate, but the ratios deviate significantly from 1 with both low- and high-energy swell. Directionally narrow, shoreward propagating infragravity waves, observed with low-energy swell, likely have a remote (possibly trans-oceanic) energy source. High values (up to 5) of FseaIG/FshoreIG, observed with high-energy swell, suggest that high-mode edge waves generated near the shore can be suppressed by nonlinear dissipation processes (e.g., bottom friction) on the shelf.

Infragravity-Frequency (0.005–0.05 Hz) Motions on the Shelf. Part II: Free Waves

Abstract In Part I, the energy levels of ocean surface waves at infragravity frequencies (nominally 0.005–0.05 Hz) locally forced by swell in 13-m water depth were shown to be predicted accurately by second-order nonlinear wave theory. However, forced infragravity waves were consistently much less energetic than free infragravity waves. Here, in Part II, observations in depths between 8 and 204 m, on Atlantic and Pacific shelves, are used to investigate the sources and variability of free infragravity wave energy. Both free and forced infragravity energy levels generally increase with increasing swell energy and decreasing water depth, but their dependencies are markedly different. Although free waves usually dominate the infragravity frequency band, forced waves contribute a significant fraction of the total infragravity energy with high energy swell and/or in very shallow water. The observed h−1 variation of free infragravity energy with increasing water depth h is stronger than the h−1/2 dependence pre...

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.

Reflection of Ocean Surface Gravity Waves from a Natural Beach

Abstract The energy of seaward and shoreward propagating ocean surface gravity waves on a natural beach was estimated with data from an army of 24 bottom-mounted pressure sensors in 13-m water depth, 2 km from the North Carolina coast. Consistent with a parameterization of surface wave reflection from a plane sloping beach by Miche, the ratio of seaward to shoreward propagating energy in the swell-sea frequency band (0.044–0.20 Hz) decreased with increasing wave frequency and increasing wave height, and increased with increasing beach-face slope. Although most incident swell-sea energy dissipated in the surf zone, reflection was sometimes significant (up to 18% of the incident swell-sea energy) when the beach face was steep (at high tide) and the wave field was dominated by low-energy, low-frequency swell. Frequency-directional spectra show that reflection of swell and sea was approximately specular. The ratio of seaward to shoreward propagating energy in the infragravity frequency band (0.010–0.044 Hz) v...

Nearshore sandbar migration

Field observations suggest that onshore sandbar migration, observed when breaking-wave-driven mean flows are weak, may be related to the skewed fluid accelerations associated with the orbital velocities of nonlinear surface waves. Large accelerations (both increases and decreases in velocity magnitudes), previously suggested to increase sediment suspension, occur under the steep wave faces that immediately precede the maximum onshore-directed orbital velocities. Weaker accelerations occur under the gently sloping rear wave faces that precede the maximum offshore-directed velocities. The timing of strong accelerations relative to onshore flow is hypothesized to produce net onshore sediment transport. The observed acceleration skewness, a measure of the difference in the magnitudes of accelerations under the front and rear wave faces, is maximum near the sandbar crest. The corresponding cross-shore gradients of an acceleration-related onshore sediment transport would cause erosion offshore and accretion onshore of the bar crest, consistent with the observed onshore migration of the bar crest. Furthermore, the observations and numerical simulations of nonlinear shallow water waves show that the region of strongly skewed accelerations moves shoreward with the bar, suggesting that feedback between waves and evolving morphology can result in continuing onshore bar migration.

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.

Statistics of bicoherence

Numerical simulations are used to investigate statistics of biocoherence for the special case of a linear random process. Smoothed bicoherence statistics are shown to be independent of both the normalization used to form the bicoherence and of whether statistical stability is obtained by ensemble-averaging short records, or frequency merging within a long record. >