Edge waves in the presence of strong longshore currents

A form of the linear, inviscid shallow water wave equation which includes alongshore uniform, but cross-shore variable, longshore currents and bathymetry is presented. This formulation provides a continuum between gravity waves (either leaky or edge waves) on a longshore current, and the recently discovered shear waves. In this paper we will concentrate on gravity wave solutions for which V(x)/c < 1, where V(x) is the longshore current, and c is the edge wave celerity. The effects of the current can be uniquely accounted for in terms of a modification to the true beach profile, h'(x) = h(x) [I - V(x)/c]¯², where h(x) is the true profile and h'(x) is the effective profile. This is particularly useful in conceptualizing the combined effects of longshore currents and variable bottom topography. We have solved numerically for the dispersion relationship and the cross-shore shapes of edge waves on a plane beach under a range of current conditions. Changes to the edge wave alongshore wavenumber, K, of over 50% are found for reasonable current profiles, showing that the departure from plane beach dispersion due to longshore currents can be of the same order as the effect of introducing nonplanar topography. These changes are not symmetric as they are for profile changes; IKI increases for edge waves opposing the current flow (a shallower effective profile), but decreases for those coincident with the flow (a deeper effective profile). The cross-shore structure of the edge waves is also strongly modified. As lkl increases (decreases), the nodal structure shifts landward (seaward) from the positions found on the test beach in the absence of a current. In addition, the predicted variances away from the nodes, particularly for the alongshore component of edge wave orbital velocity, may change dramatically from the no-current case. Many of the edge wave responses are related to the ratio V max/c, where V max is the maximum current, and to the dimensionless cross-shore scale of the current, lkl x(V max), where x(V max) is the cross-shore distance to V max. This is most easily understood in terms of the effective profile and the strong dependence of the edge waves on the details of the inner part of the beach profile. Inclusion of the longshore current also has implications regarding the role of edge waves in the generation of nearshore morphology. For example, in the absence of a current, two phase-locked edge waves of equal frequency and mode progressing in opposite directions are expected to produce a crescentic bar. However, in the presence of a current, the wavenumbers would differ, stretching the expected crescentic bar into a welded bar. A more interesting effect is the possibility that modifications to the edge waves due to the presence of a virtual bar in the effective profile could lead to the development of a real sand bar on the true profile. These modifications appear to be only weakly sensitive to frequency, in contrast to the relatively strong dependence of the traditional model of sand bar generation at infragravity wave nodes

Observations and a model of undertow over the inner continental shelf

Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 2341-2357, doi:10.1175/2008JPO3986.1.Onshore volume transport (Stokes drift) due to surface gravity waves propagating toward the beach can result in a compensating Eulerian offshore flow in the surf zone referred to as undertow. Observed offshore flows indicate that wave-driven undertow extends well offshore of the surf zone, over the inner shelves of Martha’s Vineyard, Massachusetts, and North Carolina. Theoretical estimates of the wave-driven offshore transport from linear wave theory and observed wave characteristics account for 50% or more of the observed offshore transport variance in water depths between 5 and 12 m, and reproduce the observed dependence on wave height and water depth. During weak winds, wave-driven cross-shelf velocity profiles over the inner shelf have maximum offshore flow (1–6 cm s−1) and vertical shear near the surface and weak flow and shear in the lower half of the water column. The observed offshore flow profiles do not resemble the parabolic profiles with maximum flow at middepth observed within the surf zone. Instead, the vertical structure is similar to the Stokes drift velocity profile but with the opposite direction. This vertical structure is consistent with a dynamical balance between the Coriolis force associated with the offshore flow and an along-shelf “Hasselmann wave stress” due to the influence of the earth’s rotation on surface gravity waves. The close agreement between the observed and modeled profiles provides compelling evidence for the importance of the Hasselmann wave stress in forcing oceanic flows. Summer profiles are more vertically sheared than either winter profiles or model profiles, for reasons that remain unclear.This research was funded by the Ocean Sciences Division of the National Science Foundation under Grants OCE-0241292 and OCE-0548961

Predicting seabed burial of cylinders by wave-induced scour : application to the sandy inner shelf off Florida and Massachusetts

Author Posting. © IEEE, 2007. This article is posted here by permission of IEEE for personal use, not for redistribution. The definitive version was published in IEEE Journal of Oceanic Engineering 32 (2007): 167-183, doi:10.1109/JOE.2007.890958.A simple parameterized model for wave-induced burial of mine-like cylinders as a function of grain-size, time-varying, wave orbital velocity and mine diameter was implemented and assessed against results from inert instrumented mines placed off the Indian Rocks Beach (IRB, FL), and off the Martha’s Vineyard Coastal Observatory (MVCO, Edgartown, MA). The steady flow scour parameters provided by Whitehouse (1998) for self-settling cylinders worked well for predicting burial by depth below the ambient seabed for Ο (0.5 m) diameter mines in fine sand at both sites. By including or excluding scour pit infilling, a range of percent burial by surface area was predicted that was also consistent with observations. Rapid scour pit infilling was often seen at MVCO but never at IRB, suggesting that the environmental presence of fine sediment plays a key role in promoting infilling. Overprediction of mine scour in coarse sand was corrected by assuming a mine within a field of large ripples buries only until it generates no more turbulence than that produced by surrounding bedforms. The feasibility of using a regional wave model to predict mine burial in both hindcast and real-time forecast mode was tested using the National Oceanic and Atmospheric Administration (NOAA, Washington, DC) WaveWatch 3 (WW3) model. Hindcast waves were adequate for useful operational forcing of mine burial predictions, but five-day wave forecasts introduced large errors. This investigation was part of a larger effort to develop simple yet reliable predictions of mine burial suitable for addressing the operational needs of the U.S. Navy.This work was supported by the grants from the U.S. Office of Naval Research Marine Geosciences Program. The work of A. C. Trembanis was supported by the USGS/WHOI Postdoctoral Fellowship

Wave variance partitioning in the trough of a barred beach

The wave-induced velocity field in the nearshore is composed of contributions from incident wind waves (f > 0.05 Hz), surface infragravity waves (f σ²/gβ), where ƒ is the frequency, σ = 2πf, k is the radial alongshore wavenumber (2π/L, L being the alongshore wavelength), β is the beach slope, and g is the acceleration due to gravity. Using an alongshore array of current meters located in the trough of a nearshore bar (mean depth ≈ 1.5 m), we investigate the bulk statistical behaviors of these wave bands over a wide range of incident wave conditions. The behavior of each contributing wave type is parameterized in terms of commonly measured or easily predicted variables describing the beach profile, wind waves, and current field. Over the 10-day period, the mean contributions (to the total variance) of the incident, infragravity, and shear wave bands were 71.5%, 14.3% and 13.6% for the alongshore component of flow (mean rms oscillations of 44,20, and 19 cm s¯¹, respectively), and 81.9%, 10.9%, and 6.6% for the cross-shore component (mean rrns oscillations of 92, 32, and 25 cm s¯¹, respectively). However, the values varied considerably. The contribution to the alongshore (cross-shore) component of flow ranged from 44.8- 88.4% (58.5-95.8%) for the incident band, to 6.2-26.6% (2.5-32.4%) for the infragravity band, and 3.4- 33.1 % (0.6-14.3%) for the shear wave band. Incident wave oscillations were limited by depth-dependent saturation over the adjacent bar crest and varied only with the tide. The infragravity wave rms oscillations on this barred beach are best parameterized by the offshore wave height, consistent with previous studies on planar beaches. Comparison with data from four other beaches of widely differing geometries shows the shoreline infragravity amplitude to be a near-constant ratio of the offshore wave height. The magnitude of the ratio is found to be dependent on the Iribarren number, ξ₀ = β(H/L₀)¯1/2. Shear waves are, as previous observation and theory suggest (Oltman-Shay et al., 1989; Bowen and Holman, 1989), significantly correlated with a prediction of the seaward facing shear of the longshore current

Beach foreshore response to long-period waves in the swash-zone

A field experiment designed to test the hypothesis that infragravity and lower frequency waves influence the patterns of erosion and deposition on the beach foreshore has been carried out. The data show coherent fluctuations in the foreshore sediment level which can be related to low frequency wave motions. The fluctuations have heights of up to 6 cm with typical time scales of 8 to 10 minutes. They can be characterized in two ways: by the progression of the fluctuations up the foreshore slope (landward), and by the decrease in the RNS height of the fluctuations as they progress landward. The velocity of migration also changes as the fluctuations progress landward. Analysis of runup time series obtained by time-lapse photography concurrent with the sediment level measurements reveals long-period waves of undetermined origin at frequencies and phases which strongly suggest that the waves force the original perturbation in sediment level. In order to better understand the characteristics of these sediment level fluctuations, a numerical model of sediment transport on the foreshore has been developed. Gradients in sediment transport define erosional and depositional areas on the foreshore. Runup velocities were modeled and the results were used in the sediment transport model. The model predicts that any perturbation in foreshore elevation will progress landward while decreasing in amplitude and in velocity, thereby matching the field observations. Relationships between beach slope and the profile response clarified by this model are used to explain the initial formation of the perturbations of sediment level

Beach and Nearshore Survey Data: 1981-1984 CERC Field Research Facility

Source: https://erdc-library.erdc.dren.mil/jspui/This report presents 4 years of highly accurate, approximately biweekly surveys of four selected beach profiles collected at the US Army Engineer Waterways Experiment Station, Coastal Engineering Research Center's Field Research Facility (PRF) in Duck, NC. These data are unique because they cover the most active region of the nearshore, from the dune out to a depth where net bottom changes appear to be negligible, and were collected coincident with detailed measurements of waves and water levels. The data were collected between 1931 and 1984 using the FRF's CRAB, a 10-m-tall motorized tripod, which, combined with an electronic "total station" surveying instrument, is capable of accuracies of a few centimetres in both elevation and position. The report discusses the data-collection methods, the sources of errors and data-editing procedures, and a brief summary of the actual profile data. Appendices contain the listings and plots of the survey data along with the tables and plots of the wave and water-level data

Radiocarbon dating, sedimentation rate, granulometry and organic carbon content of ODP Leg 182 sites

This data report presents sedimentological (grain size) and geochemical (X-ray diffraction, total organic carbon, accelerator mass spectrometry radiocarbon, and percent carbonate) information obtained from the western transect (Sites 1132, 1130, and 1134) and the eastern transect (Sites 1129, 1131, and 1127) in the Great Australian Bight during Leg 182. The purpose is to quantify changing rates of sediment accumulation and changes in sediment type from the late Pleistocene and Holocene, in order to relate these changes to the well-known sea level curve that exists for this time frame. Ultimately, these data can be used to more effectively interpret lithologic variations deeper in the Pleistocene succession, which most likely represent orbitally forced sea level events