One of the greatest challenges in the study of the air-sea interface is presented by breaking waves. Entrainment of gases and the expulsion of droplets and particles by breaking waves are of primary importance to gas fluxes in particular and air/sea exchanges in general. The surface roughness and turbulence near the surface are key to understanding the kinematics and dynamics of this elusive interface. Unfortunately, it is nearly impossible to obtain measurements closer than a meter or two below actively breaking wave crests.
Here, high-resolution ultrasound measurements from an up-looking phased-array system are presented. The system provides digitally beamformed measurements over "pies" about 22 degrees wide by 16 m maximum range, with resolutions of about 1.5 degrees by 5 cm. The instrument was mounted 13.5 m below the mean surface, so the cell size near the surface is about 5 cm (vertical) by 30 cm (along-wind). Sequences of intensity images form a "movie" that can be analyzed for motion as well as for relative scatterer (bubble) density.
Data presented were obtained as a wave of about 2.5 m height crest to trough passed through the field of view while breaking (one of several breakers captured over a two-week deployment from R/P FLIP). Figure 1 shows a frame from a PADS movie of acoustic intensity, from data taken between 16:24 and 16:25 UTC, 9/16/1999 (9:24 am local time) on the open ocean (~4000 m deep) about 200 km west of San Diego, CA.
By tracking features in time and space over the 2D sample area, the background velocity field can be estimated (Figure 2). One significant feature is the surface. However, by its nature only the vertical velocity can be estimated there. The surface is located in each frame as follows: Beamforming is over-resolved, producing 31 beams from the 16 receivers (the Nyquist wavenumber is not processed). Analysis is restricted to the center 13 beams, ranges 8 to 16 m. Along each beam, the nearest range after the maximum that falls 13 dB below the maximum is identified. The 3 farthest outliers from the median of the 13 values are rejected. A line is fitted to the remaining points, providing the surface location and slope directly above the sonar. Finally, the time series of height and slope are de-spiked (median filtered using 15 points). Dropouts introduced by dense bubble clouds are an issue, and this procedure was developed to minimize the effect.
Figure 1. One frame from a time series (see the movies here!) of vertical-slice images under a breaking wave. The wave is propagating from right to left. The upper edge of the region of highest backscatter (red) provides a good estimate of the surface location, illustrated by the line segment crossing x=0, y=15 m. The red "wedge" extending down and to the right from the highest point on the surface is produced by a cloud of bubbles being actively injected by the breaking wave. Over time this bubble cloud penetrates to between 2 and 3 m depth. A time-delayed correlation technique (PIV) was used to track the mean motion of 2 m squares in the vertical. A set of 16 squares were tracked, centered on the locations indicated by asterisks (*). Arrows indicate estimated vertical velocities of each square at the time of the picture.
This prototype "coherent mode" deployment shows promise, and performance could be improved significantly with a few modest adjustments: (1) A transmitter with much narrower beampattern in the cross-pie direction is needed, to bring that dimension of the sample area into line with the other two spatial dimensions. (2) A position closer to the surface would both reduce the along-wave cell size and increase the permissible sample rate. For example, from 5 m below the surface horizontal resolution at the surface becomes 10 cm, and sample rates up to 150 frames per second are possible. At these rates, coherent phase changes from one ping to the next could be used to refine vertical velocity estimates (actually radial velocity from the sonar) after an initial estimate from feature tracking. The ambiguity velocity would be around 30 cm/s for 200 kHz sound. (3) More receivers would also help to refine the angular resolution; doubling the number and reducing the range to 5 m would result in 5 cm resolution in both vertical and horizontal. It would appear that much could be learned about the velocity and turbulence structure under breaking waves by this approach.
Figure 2. Time-series of (equivalent) vertical displacements at and below the surface. The uppermost trace is from a "surface finder" threshold-based routine. Intense bubble clouds can cause dropouts (jagged red line), so that de-spiking is needed to produce a more reasonable surface estimate (superimposed black line). This trace is characterized by motions near 8 and 5 second periods. Time-delay correlations produce velocity estimates from the heterogeneous intensity fields; these were integrated to synthesize equivalent displacements versus location below the surface ("Displacement from PIV", red lines). The pressure at 13 m mean depth was also recorded (lowest red line). For comparison, an equivalent trace at each depth is computed from the surface track (black lines) using exponential decay versus frequency computed from linear dispersion. Breaking occurs for the second peak, near T = 24.5 s.