The goal is to understand the forms and dynamics of the flows near shore. These flows are forced by a combination of wave breaking, winds, pressure gradients, and topographic effects (Coriolis is of secondary importance, but its role increases moving offshore). Of particular interest here is the occurrence, form, and dynamics of rip currents. (Here, rip currents are loosely defined as narrow, offshore-directed flows extending some distance seaward from the shore through the surf zone.) Given the forcing and topography, we wish to predict the flow regime, in terms of the occurrence and strength of instabilities and rip currents, and the net effect on horizontal mixing and diffusion.
When do rip currents occur, and which aspects of the environment are most relevant to their dynamics? For example, they are often (but not always) associated with cuts in nearshore bars or channels oriented perpendicular to the coast. They are often associated with waves incident nearly normally onto the beach, being less common when the waves are at a steep angle. They vary irregularly in strength and location, making it difficult to formulate a sampling strategy. Thus, at a practical level, the first objective of this project was to make horizontal velocity measurements over an area of sufficient size to resolve the time-space variability of these phenomena. These observations were also coordinated with measurements of the bottom topography, incident wave field, and wind, and extended in time through a variety of conditions from calm to stormy.
The current objective is to classify the various flow conditions observed at SandyDuck in terms of some (as yet to be rigorously defined) measures of the nonlinear regime of the flow. Two complementary approaches are in terms of (1) the occurrence and strength of "rip currents" (narrow jet-like current structures extending more or less continuously from shore) and (2) the occurrence and strength of "shear waves" (instabilities associated with the alongshore flow especially along the crest of a sandbar). The next objective is to related these classifications to the forcing, in order to determine the important parameters controlling the flow. The final objective is detailed comparison and refinement of models of nearshore flow, in order to refine our understanding of the links between forcing and flow.
Two "Phased-Array Doppler Sonars" (PADS) were deployed at Duck, NC, as part of a major near-shore experiment in 1997, "SandyDuck" (see figure 1). This took place at USACE's "Field Research Facility" near Duck, North Carolina. Both systems were operational by September 7th, and operated through to November 1 (with some intermittent problems). Some 58 days worth of data were collected, including 41 days with both systems working.
Summary of when PADS were operational during SandyDuck (in html)
The PADS each provide a radially-directed component of velocity over an area up to 450m radius by 90 degrees in azimuth. The spatial resolution is about 6 m in range by 6 degrees; so (for example) at 200m range the sample area is about 6 by 20 meters. The sonars transmit every 0.75s, with each ping simultaneously sampling over all angles; thus surface waves as well as the mean flow can be resolved. Two-ping averages were recorded, providing a usable sample rate of 2/3 Hz. Simultaneously, one-minute averages were formed, sampled, and stored at 30 second intervals; these averages resolve the background flow, including infragravity waves, shear waves, and rip currents. All data were coordinated, via GPS time-stamping, with other measurements of waves, currents, bottom topography, etc., as carried out by other participants at SandyDuck. This will enable detailed comparisons between the quasi-continuous coverage from the PADS and the currents measured at a variety of points in or near the PADS area (see figure 1, circles). Efforts have begun to compare currents measurements with R. Guza, S. Elgar, and F. Fedderson (all at SIO), and also with A. J. Bowen and A. Hay (Dalhousie). Vertical current profiles were measured in a couple locations within the sonar field of view as well, one by J. Haines (USGS), and another by P. Howe (USF). In addition to the current and wave measurements of these groups, there are winds and directional wave spectra provided by C. Long (FRF staff, USACE). Bottom topography was measured each day (weather permitting) by M. Leffler and crew (also at the FRF/USACE).
Figure 1. SandyDuck experimental site, showing the (maximum) area covered by the Phased Array Doppler Sonars (PADS). The circles show locations of frames with current meters near or in the area. North is about 20 clockwise of left. The location is the Field Research Facility of the US Army Corps of Engineers, in Duck, North Carolina. The larger blue box shows the region covered in the following figures.
Within the overlapping area covered by both systems, both horizontal components of velocity can be estimated. Algorithms to combine the data were implemented and tested in the field (this link describes a method), and the first ever dual-Doppler views of horizontal flows were produced on October 8th, 1997 (figure 2, below). Sequences of these combined estimates produce movies of the 2-dimensional flow field, along with the associated fields of acoustic backscatter intensity (bubble cloud density), and estimates of vorticity. Such movies were routinely produced in near-real-time as the experiment proceeded. The software has been refined to incorporate dynamic estimates of the signal-to-noise levels, permitting the viewed area to vary in time as the good data retrieved varies. Additional refinements include the ability to compute and view the vertical component of vorticity and the horizontal divergence fields. The data are well behaved, so spatial derivatives can be taken; for the lower frequency data, sensible-looking vorticity estimates can be made. "External data" such as the wind speed and direction, wave height and direction, tidal elevation, and bottom contours are time-coordinated and incorporated into the plots. Coordinated elevation and bottom contours permit calculation of the "transport divergence" and potential vorticity from the estimated 2D velocity fields. Work on the verification and calibration of the instruments, a notoriously "invisible yet time-consuming" endeavor, is well underway.
Figure 2. One of the first dual-PADS images produced was of swell incident from the SE, generated by hurricane Erica. The arrows represent horizontal vector velocities estimated at a regular grid (15 m spacing) in the region where both PADS produced good data. With such extensive fields of velocity, together with the measured bottom topography, it is possible to estimate the horizontal transport divergence within this area too. An example movie of waves (quicktime, 1.8 MB) clearly shows propagation. The data from the sonars appears to resolve the waves easily.
Of central interest to this project is the vertical component of vorticity associated with the lower frequency flow field (and, hopefully, with rip currents). A zero-phase filter was applied in real time to the data, producing a second data stream of 1-minute low-passed (wave-free) velocities. The data acquisition system recorded both data streams continuously, day and night, through the experiment (aside from times of equipement failure). Some of these low-frequency vorticity fields are interesting:
Figure 3. Horizontal velocity vector estimates (small black arrows) and the associated field of vorticity (color contours), estimated over the area covered by both PADS. Two vorticity features are observed. The upper feature (#1) resembles a vortex pair as is sometimes seen in models. This moves through the domain from left to right, along the trajectory roughly described by the gray arrow. The intensity of the feature is fairly constant, and it appears to leave behind a trail of red (-) vorticity along the -4.5 meter depth contour. The lower feature (#2) is a small rip current, probably originating near the gap in the sandbar (as above); this extends some distance into the domain as suggested by the gray arrow, but then fades. These features can also be viewed in the original movie sequence (quicktime, 1.7MB) (the movie version also has wind and wave vectors, and the depth contours are dynamically adjusted for the tide).
Internal dynamics versus boundary flux of vorticity can be addressed using estimates of velocity and vorticity near the edge of the region to estimate the boundary-flux of vorticity. There is a sense that the dissipation of vorticity should be larger where wave breaking occurs, and smaller further offshore. To make a first-cut examination of this, the measurement area was further subdivided into two parts, inshore and offshore of the 4 m depth contour. The notion that the near-shore vorticity dissipates much more rapidly than that offshore is born out in this calculation. In the striking example shown above (feature #1), an offshore feature resembling a "vortex pair" propagates through along the 5 m contour, leaving behind a "tail" of negative vorticity; this remnant tail persists after the feature exits the other boundary, and decays with about a 20 minute time-scale. In contrast, the occasional offshore "squirts" associated with rip-current activity (e.g. feature #2) decay too rapidly to measure well, lasting only a few minutes. A first-pass survey of the data indicates that the former (a discrete offshore vorticity feature) is rare, while the latter (rip-current-like "squirts" coming off the inner bar) are sporadic but not uncommon.
Figure 4. Horizontal velocity vector estimates (small black arrows) and vorticity (colors) for another time period, after the wind blew and the waves increased to about 1.3 m significant height. The larger arrows at lower left indicate wind (red; here down to about 4 m/s from the N) and waves (blue; about 1.3 m significant wave height incident from the NE or upper left). The movie (3.3 MB) shows miscellaneous vorticity features advecting South, and occasionally stronger jets or vortex-pairs propagating offshore and South (up and to the right). The appearance and decay of some of the more prominent features permits a crude assessment of the frictional time scale of the flow (see "observations of nearshore vorticity").
Although the (Eulerian) velocities are generally directed slightly offshore, the true (Lagrangian) drift is more nearly parallel to shore, as seen by tracking bubble-clouds or vorticity features through the movie-sequences. The Stokes' transport of the incident waves contribute a significant amount to the overall balance, as the waves slow and steepen over the sloping bottom and eventually break.
The next step is to define objective measures of the flow regime that are useful yet practical. For example, some recent work [Slinn et al. 1998] has usefully characterized the flow regime in terms a horizontal "bulk Reynolds number": the ratio of (bottom) frictional to (horizontal) advective time-scales (which they call "Q"). However, reverse-engineering of "Q" from the observed velocity fields is uncertain and probably not really practical. The approach taken here is to examine averaged indicators of flow activity. For example, the average enstrophy (mean square vorticity) should be a good indicator of the occurrence of shear waves; in contrast, the kinetic energy (mean square velocity perturbations) over 1 to 10 minute periods should be a good indicator of the total flow perturbations, including both rip currents, shear waves, and other infragravity motions. Further analysis via time-space Fourier transforms may permit separation of motions according to the appropriate dispersion relations.
On the technical side, a significant requirement is verification and calibration of the phased-array Doppler sonar (PADS) measurements. The existing model for transforming the "raw" acoustic data into maps of velocity and scatterer density is adequate to begin concurrent work on the above objectives. However, new obstacles to be considered and overcome include partial backscatter from the bottom and interference from acoustically bright structures. An exciting development in the use of these sonars is achieving the time-space-velocity resolution necessary to resolve the energy-containing surface waves. Questions concerning whether or not there is variation of the response in space and time (due, for example, to clouds of bright scatterers drifting over a relatively constant background of bottom-returns) can be addressed directly by examining surface waves as they propagate over well-known topography and currents. In addition to these "self-consistency checks," data from discrete locations within the PADS viewing area are being used for direct comparisons. Where there is strong vertical mixing, currents near the bottom can be used (e.g., Guza et al and Hay et al); at other times, the comparison is restricted to the smaller number of measurements taken through the water column (e.g., P. Howd).
Vortex generation and detachment apparently do occur near shore. While the former is fairly common, persistence of detached vortices appears to be rare. The early indications are that the highly nonlinear regime indicated by detaching vortex-pairs is more likely to occur during low winds and medium waves. The most striking example (figure 2) occurs during the unusual conditions of offshore flow opposing both wind and waves.
In well-mixed, wave dominated conditions (figure 4) the Eulerian velocity has a distinct offshore component. In contrast, the Lagrangian drift, as indicated by the motion of bubble clouds (not shown here) is quite tightly shore-parallel. The difference would likely match the computed Stokes' drift of the waves [cf. Smith 1998]. This is apparently a significant term in the nearshore mass balance.
Exchanges of mass and momentum between the surf-zone and water farther offshore are thought to occur mainly via horizontal flow patterns (Shepard and Inman 1950). The narrow offshore-directed portions of this flow pattern are often referred to as "rip currents. These phenomena are thought to influence the movement and sculpting of sand near shore (Holman and Bowen 1982), and could be important in the off-shore transport of sand (Smith and Largier 1995). The dynamics and form of rip currents are still not well known, despite decades of interest. It is thought that 5 factors are important in determining the form and dynamics of near shore flows:
These 5 factors should be well characterized by the combined effort of SandyDuck investigators, over times long enough to experience a variety of conditions. In particular, we experienced incident wave fields with a variety of incident angles, heights, and directional spreads, and at different angles to the wind.
One day it should be possible to predict the nonlinear regime of the flow: Will there be rip currents? How much on/offshore mixing may we expect? Are the conditions conducive to sediment transport? To build this ability, we need a data-base covering a variety of conditions, both in forcing and response, with sufficient time-space coverage to provide the needed measures of the flow.
The means by which we have viewed the velocity and vorticity fields in this study is novel. Patterns suggestive of vortex dynamics (e.g., a self-propagating vortex pair) have been observed in the nearshore environment for the first time. The PADS measurements are a natural complement to the discrete arrays of high-precision current meters, pressure sensors, (etc.) deployed within and near the surf-zone. As a data-base of conditions and response is built up, we can begin to extensively test our models and improve our predictive ability.
Holman, R. A., and A. J. Bowen, Bars, bumps, and Holes: models for the generation of complex beach topography., J. Geophys. Res., 87, 457-468, 1982.
Shepard, F. P., and D. L. Inman, Nearshore water circulation related to bottom topography and wave refraction, Trans. Am. Geophys. Union, 31, 196-212, 1950.
Slinn, D. N., J. S. Allen, P. A. Newberger, and R. A. Holman, Nonlinear shear instabilities of alongshore currents over barred beaches, Journal of Geophysical Research-Oceans, 103, 18357-18379, 1998.
Smith, J.A., Performance Of A Horizontally Scanning Doppler Sonar Near Shore, (pdf, 528k) Journal Of Atmospheric And Oceanic Technology, 10 (5), 752-763, 1993.
Smith, J.A., and J.L. Largier, Observations Of Nearshore Circulation - Rip Currents, (pdf, 536k) Journal Of Geophysical Research-Oceans, 100 (6), 10967-10975, 1995.
Thorpe, S. A., and A. J. Hall, Nearshore Side-Scan Sonar Studies, Journal Of Atmospheric And Oceanic Technology, 10, 778-783, 1993.