Observations of Vorticity Near Shore

Dr. Jerome A Smith, Scripps Inst. of Oceanography, La Jolla CA 92093-0213

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. Here is a summary of when the PADS were operational during SandyDuck.

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, simultaneously sampling over all angles; surface waves as well as the mean flow are resolved. Two-ping averages were recorded, providing a usable sample rate of 2/3 Hz. All data were coordinated via GPS time-stamping, including measurements of waves, currents, bottom topography, etc., carried out by other participants at SandyDuck. This permits comparisons between the quasi-continuous coverage from the PADS and the currents measured at a variety of points in or near the PADS area (figure 1, circles). There are also wind measurements, and directional wave spectra (provided by C. Long of the FRF, USACE). Bottom topography was measured each day (weather permitting) by M. Leffler and crew (also at FRF/USACE).


Figure 1. SandyDuck experimental site, showing the approximate areas covered by the Phased Array Doppler Sonars (PADS; pie-shaped areas). The circles show locations of frames with current meters (etc.) 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 blue box indicates the region covered in the following figures and movies.

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). 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). Such movies were routinely produced in near-real-time as the experiment proceeded. The software incorporates estimates of the signal-to-noise levels, permitting the viewed area to vary in time as the good data retrieved varies. The data are well behaved, so spatial derivatives can be taken, and sensible-looking vorticity estimates can be made. Time-coordinated measurements of wind speed and direction, wave height and direction, tidal elevation, and bottom contours are incorporated into the movies.

Figure 2. (quicktime movie, 2 MB) This movie shows a particularly well isolated "vortex pair," entering from the left (North), moving quickly across the field of view, and leaving behind a trail of mostly reddish (negative) vorticity. The wind speed and direction are indicated by the red arrow near the lower left corner, and the wave direction and rms height are indicated by the co-located blue arrow. As indicated, the conditions were pretty calm during this period, with winds under 2 m/s and waves around 0.5 m significant height.

To get a rough idea of the time-scale for decay of vorticity, the mean-square vorticity (enstrophy) over the area offshore of 385 m is examined (closer to shore, the signal-to-noise varies somewhat erratically). The vorticity stripe left behind displays a fairly well defined exponential decay with a time scale of 10 minutes (for vorticity-squared; hence 20 minutes for the frictional decay time scale of vorticity):


Figure 3. Plot of mean-square vorticity over a well-defined event (0100 to 0200 UTC, 10/14/97). The outer area (offshore of 385 m) displays a roughly exponential decay of mean-square vorticity with about a 10 minute time scale. The area closer to shore, while much more noisy and less reliable, does appear to have a shorter time scale for vorticity decay, of order twice as fast. Units of vorticity used here are actually arbitrary- divide by about 3000 to convert to inverse seconds squared.

Figure 4. (quicktime movie, 3.2 MB) This movie shows a more commonly observed scenario, with a lot of vorticity activity advecting through with the mean flow (from left to right). The wind speed and direction are indicated by the red arrow near the lower left corner, and the wave direction and rms height are indicated by the co-located blue arrow. The wind was in the process of shifting; it was previously stronger from the North, and is slowing. The mean flow alongshore as yet remains from the North. The waves are bigger than in the above example, about 1.3 m significant wave height.

At the beginning of this sequence, from 0645 to 0700 UTC, there is a broad "surge-like" front extending from lower-right to upper left, which propagates up and to the right across the field of view at 15-20 cm/s. Such convergent fronts were observed fairly often over the two-month deployment; during the moderately stormy period around 10/18, they sometimes occurred several times per hour.

In the midst of all this activity, there are a few "vorticity events" of sufficient size to dominate the field temporarily, and introduce "spikes" of mean-square vorticity which appear to decay in a roughly exponential fashion:


Figure 5. Plot of mean-square vorticity from 0700 to 0800 UTC, 10/18/97 (Note that this plot starts at 0700, not at 0645 as for the movie above). The outer area (offshore of 385 m) again displays a roughly exponential decay of mean-square vorticity with about a 10 minute time scale. The area closer to shore (again much more noisy and less reliable) appears to have a shorter time scale than the offshore area, but longer than on 10/14: of order two-thirds the offshore value. Again, the units of vorticity used here are actually arbitrary- divide by about 3000 to convert to inverse seconds squared.

It is interesting that the time-scales appear similar between the two events shown here, in spite of a factor two or three difference in the significant wave height. Although the rms values of mean-square-vorticity are larger in this second case, the peak values appear to be comparable.

This work was funded by ONR.

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This page last updated March 9, 2000.