3-D Surface Wave Spectra at SandyDuck

A pair of "phased-array Doppler sonars" (PADS) were deployed at Duck, NC in the fall of 1997, as part of the SandyDuck field experiment. In addition to observations of vorticity in the nearshore flow, the data can be used to estimate 3D (2 horizontal space + time) spectra of the velocity fields, roughly from .001 to 0.3 Hz. Waves over about 0.05 Hz (under 20 second period) tend to be incident windwaves and swell from storms. Waves from 0.01 to 0.05 Hz tend to be shore- trapped "edge waves" or nearly shore-trapped "leaky modes" or "surf beat," which still approximately obey the same dispersion relation as the incident surf (i.e., phase-speed and group speed is approximately root[gh]). More slowly evolving activity tends to be associated with meanders of the alongshore flow or "eddies" drifting past.

An interesting time to look at is 1900 UTC, 10 September 1997. Swell with about 19 second period (very long!) was arriving from the very distant hurricane Erica, to the SE across the Atlantic. This swell was partially reflected off the beach. There is also some swell incident from the NE near 12-13 second period.

Here 3D spectra of the velocity fields are shown. The movie shows one frequency at a time. The uppermost plot shows the 1D linear frequency spectrum, with a vertical line at the frequency being displayed in the other 4 plots. The corresponding period is written at the lower left corner for each frame.

The middle two plots show the spatial distribution of variance at that frequency (period) for the (left) shore-normal velocity component and (right) alongshore component. The array pattern of the two PADS is clearly seen. Note in particular the bands of light and dark which appear as the frequency cycles through 19 second period activity. The locations of these nodes and antinodes varies fairly smoothly with frequency, and have the right spacing to match the predicted gravity-wave speed (about 7 m/s for a mean depth near 5 m). The variance fields at each frequency are normalized by the maximum value of the shore-normal component (which is usually the larger, but not always).

The lower pair of plots show the corresponding 2D wavenumber spectra at the given frequency for the (left) shore-normal velocity component and (right) alongshore component. The wavenumber spectra at each frequency are normalized by the maximum value of the shore-normal component (which is usually the larger, but not always).

A growing red circle represents linear dispersion. Stuff outside the circle corresponds to motions propagating more slowly than gravity waves, inside the circle would correspond to faster propagation.

Here is the 3D spectrum 2 hours later. The swell from the NE increases, the 19-s swell from the SE decreases. Wind is still weak.

Here is the 3D spectrum 2 more hours later. The swell from the NE increases, the 19-s swell from the SE decreases, and new wind-waves from the North appear at the highest frequencies. A fresh wind from the North has sprung up.

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This page last updated 03/09/00.