Long-Range Acoustic Doppler Array Measurements of Surface Velocities
Jerome A. Smith and R. Pinkel
Scripps Institution of Oceanography, La Jolla, CA 92093, USA
Email: email@example.com, web: http://jerry.ucsd.edu/
Langmuir circulation (figure 1) has significance across the marine disciplines. Enhanced deepening and inhibited re-stratification can alter the surface temperature and hence net air-sea exchanges. Organization of bubbles into windrows introduces dramatic sound speed variability and also affects air/sea gas fluxes. Organization of seaweed and plankton affects marine life, including pelagic fisheries. Dispersal by Langmuir circulation is an important component in models for oil-spill tracking and for search-and-rescue operations. Previous studies have striven to parameterize the strength and size of Langmuir circulation as a function of wind, waves, and stratification. However, it has also been noted that the circulation patterns seem less regular in the open ocean than in lakes or other smaller bodies of water. To investigate the hypothesis that this may be due to interactions with the internal wave field, large-area measurements were needed in a region of strong internal wave generation. To this end, a 50 kHz acoustic Doppler sonar system was developed to obtain sequences of surface velocity measurements over a km-sized area of the oceanic near-surface layer. The system was deployed and operated between Oahu and Kuaui, Hawaii, and mapped backscatter intensity and Doppler shift (radial velocity) over an area typically extending more than 1.5 km in range by 42° in bearing (azimuth). The 32 element array yields resolutions of roughly 10 m in range by 1.3° bearing, sampling every 2.5 s, with single-sample variances of order 10 cm/s. The Hawaii data set, taken in conjunction with the Hawaiian Ocean Mixing Experiment (HOME), includes both high-frequency internal waves and Langmuir circulation. The former are associated with the strong internal tides generated nearby, while the latter are driven by the trades and/or storm winds, together with the (rather complex) directional wave field. The system also resolves the dominant waves (i.e., with periods longer than the Nyquist value of 5 seconds), revealing several discrete directional "modes," as is typical of mid-pacific conditions. Preliminary results appear to support the hypothesis qualitatively. However, a surprising finding is that evidence of mixing in the thermocline just below the mixed layer is stronger on a calm day (no LC) than on a corresponding time during moderate winds (LC present).
The mixed layer at the surface of oceans and lakes exerts significant influence on the exchanges of energy, momentum, and materials between the air and water. On the open ocean, it is also typically comparable to the extent of light penetration the "euphotic zone" where phytoplankton can grow and provide a basis for marine life. The air-sea exchanges affect climate and weather, providing both moisture and nucleation particles critical to rain and storm evolution, and controlling processes of concern such as sequestering of carbon dioxide and other green-house gases. Mixing below and across the base of the mixed layer provides nutrients for phytoplankton blooms, and is also critical to the net fluxes and sequestering of gases. The existence of large coherent structures in the mixed layer (e.g., "Langmuir circulation" as illustrated in figure 1) can also have other profound impacts on life at the ocean surface, perhaps leading to morphological and behavioral adaptations [Woodcock, 1944; Stommel, 1949; Woodcock, 1950].
Figure 1. Cartoon of Langmuir circulation, first described by [Langmuir, 1938]. As the wind blows on the surface, the mixed layer forms alternating rolls: as the water moves downwind, it spirals toward covergence lines roughly parallel to the wind, sinks to the base of the mixed layer, moves apart and rises again in between the convergences. Floating materials tend to gather at the surface convergences, often forming visible streaks or windrows.
In assessing air-sea exchanges of heat and momentum, one-dimensional "slab-models" of the mixed layer have been found to perform remarkably well [Pollard et al., 1973; Price et al., 1986; O'Brien et al., 1991; Large et al., 1994; Li et al., 1995]. In these models, entrainment of deeper water into the mixed layer is driven mainly by inertial velocity shear across the pycnocline forming the base of the mixed layer [Pollard et al., 1973]. Surface stirring by wind and waves can cause continued slower erosion [Niiler and Krauss, 1977], and inhibits restratification. Surface stirring has been parameterized in the energy budget as proportional to the third power of wind friction velocity, (u*)3. However, the constant of proportionality appears to vary with location, and even at a single location the results are quite scattered. In the late 1970s, a mechanism for the generation of Langmuir circulation was identified a combination of waves and wind-induced shear [Craik and Leibovich, 1976; Garrett, 1976; Craik, 1977; Leibovich, 1977; Leibovich, 1980]. This suggests that where Langmuir circulation is involved, deepening should depend on a combination of wave Stokes' drift and wind stress [Li et al., 1995; Plueddemann et al., 1996; Smith, 1996; Li and Garrett, 1997]. With great optimism, it was ventured that wave climate variations would explain the remaining variability in mixed layer evolution.
Figure 2. Experiment sites. The ocean depths at the MILDEX, PATCHEX, and SWAPP sites are about 4000 m; depths at the HOME and MBL-1 sites about 1000 m.
LC Studies and Horizontal-Looking Doppler Sonars
In the 1980s, attempts were made to obtain horizontal "transects" of velocity through the middle of the oceanic mixed layer. Although the initial motivation was to help define the direction of propagation of internal waves, it was quickly realized that this provides a useful tool for studying mixed layer motion and Langmuir circulation (LC) [Smith et al., 1987], and also surface waves [Pinkel and Smith, 1987]. Indeed, an "inverted side-scan" system had already been employed to study LC in Loch Ness and the North Sea [Thorpe and Hall, 1983], and the backscatter-intensity-only information provided valuable insight into the kinematics of the circulation and some characteristics of the advection and diffusion of surface-active materials (such as bubbles or oil). Further development of "surface-skimming" Doppler sonar systems was motivated largely by investigations into the dynamics of the oceanic surface mixed layer.
In particular, a series of experiments were carried out from the research platform FLIP (FLoating Instrument Platform) to help improve our understanding of the development and evolution of the mixed layer and surface waves to the driving by wind, waves, buoyancy-fluxes, etc. The following is a brief summary of experiments conducted from FLIP by our group at SIO, the "Ocean Physics Group" (OPG) of the Marine Physics Lab (MPL). Included also are summary findings from each (see figure 2 for locations):
This summary focuses on our work from FLIP, and is far from a balanced review of studies into Langmuir circulation. A more comprehensive (but still far from balanced) review may be found in [Smith, 2001].
An Instrument With a Larger Field of View
The degree of organization of Langmuir circulation (e.g., how long the "streaks" remain coherent in the alongwind direction), and even the direction or orientation of the surface features relative to the wind, remains difficult to estimate objectively, particularly in stormy, cloudy, or foggy conditions. This motivated the development in the mid-1990s of the phased-array system that was used in MBLEX (1995), permitting acoustic backscatter strength (generally related to the number of bubbles just under the surface) and Doppler shift (proportional to radial velocity) to be mapped every second or so over a pie-shaped area some 450 m radius by 90° in bearing [Smith, 1998].
A larger area of the sea surface than that covered in MBLEX will enable examination of larger scale spatial variations of LC, as well as helping to define the high-frequency, short wavelength internal waves that may cause LC in the open ocean to be less regular than in lakes. To this end, a revised sonar system was developed and deployed as part of the Hawaiian Ocean Mixing Experiment (HOME nearfield leg, September-November 2002). Lower frequency sound attenuates less rapidly in sea water, and hence the signal stands above the noise floor out to longer ranges. At 50 kHz center frequency, the array provides 1.5 km range. Conversely, however, the array must be physically larger to obtain the equivalent angular resolution. To resolve the signal to 1.3° beamwidth, for example, requires an array about 2 m long (at 50kHz). With 32 receive elements, this permits a system covering about 42° in azimuth with this resolution. Using repeat sequence coding with 7 kHz bandwidth (roughly 15% of the center-frequency), range resolution of order 10 m is feasible with ±10 cm/s rms velocity error [Pinkel and Smith, 1992]. Backscatter intensity and Doppler shift are estimated over this area every 2.5 seconds.
For underwater sound near 50 kHz, a reasonable compromise between efficiency and bandwidth is obtained with tuned elements having a conical front-mass bonded to a smaller piezo-electric ceramic part. The elements used for the 50 kHz system are about 2 cm in diameter. These were laid out in an array 4 elements tall by 64 elements wide (figure 3). They were potted with a compliant filler, and the front face covered with urethane to waterproof the assembly (figure 4). On the back of the assembly is a built-in pressure case containing the electrical tuning and preamps (figure 5), connected directly to the transducers, resulting in 32 independent receivers each consisting of a 2 by 4 element block of elements. The array and underwater control and acquisition electronics were mounted on the hull of FLIP (figure 6), where they are positioned 15 m below the surface when FLIP goes into vertical orientation (see http://www-mpl.ucsd.edu/facilities/flip/index.html for more information on FLIP).
Figure 3. Tyler mounting the transducer assembly for the 50 kHz receive array.
Figure 4. The final, potted array face. Ready to connect to the electronics!
Figure 5. Rob, Eric, and Tyler prepare assembled receiver array for connection to the rest of the system. The preamp/tuning electronics are visible in the back-side pressure case, facing the camera.
Figure 6. E. Slater (Sr. Eng., MPL/SIO) and the new 50 kHz array on FLIP. The transmitters are sitting on the receiver face, to see whether the array "comes to life" when turned on from the lab aboard FLIP.
Figure 7. (Left) FLIP in horzontal position, being towed. Acoustic arrays are visible down the hull. (Right) FLIP in the vertical postion. The arrays are underwater.
HOME and LC
The primary objective of the Hawaiian Ocean Mixing Experiment (HOME) is to look at deep ocean mixing that results from the conversion of a large amount of barotropic tidal energy (the part most people are familiar with, that makes the sea surface rise and fall twice per day) into baroclinic energy (an internal tide, where the thermocline rises and falls, sometimes by very large distances, but with relatively little surface elevation). For more information on HOME, see http://chowder.ucsd.edu/home/home.html. The near field leg took place in September through November 2002, with FLIP moored between Oahu and Kauai, just South of the Kaena Ridge (figure 8). The large internal waves are also ideal for studying the effect of such waves on Langmuir circulation.
Figure 8. FLIP site near the Kaena Ridge, HOME nearfield, showing also the mooring line locations. Strong tidal currents flow along the channel between Oahu and Kauai, running roughly NNE to SSW, almost orthogonal to this ridge. As they do, they generate extreme internal waves, some several hundred meters in amplitude. This make the site apt for the study of internal wave induced mixing and possible interactions with the mixed layer.
The purpose of the adjunct project discussed here is to study the interactions between the internal waves and the mixed layer, including both interactions with Langmuir circulation during active wind-mixing and the "unmixing" that may occur during calm periods.
Here we focus on a small but representative sample of 2.5 days, from the start of October 3 to noon on October 5, 2002. First, it is useful to describe the environmental conditions. The wind is calm over the first half, increasing to 10 to 12 m/s over the second half (figure 9). The tides, visible in the time-depth density plots from the CTD system (figure 10), are increasing as we approach a full moon.
Figure 9. Windspeed observed aboard FLIP over the focus segment. Times are Hawaiian Daylight Time; i.e. day 3.5 corresponds to local noon on October 3, 2002. The first half provides a "no LC" scenario, while the second provides both "initial LC" and "sustained mixing" conditions. Highlighted segments are analysed in further detail.
Figure 10. Density profiles over the 2.5 day segment. Note the clear diurnal tide signal in the isopycnal depths, especially below 200 m. In the upper layer, there are clear signals of high-mode internal waves (e.g., isopycnal spreading near day 4.7 at 70 m depth).
Figure 11. North-South component of velocity (colors) over the same time-depth range as figure 10, with isopycnal depths superimposed (black contour lines). Sidelobes hitting the surface disrupt the velocities above 70 m depth or so. As the surface is approached, the velocity field looks distinctly high-mode (e.g., the velocity at 90 m depth is distinctly different from that at 150 m).
Technologically the experiment is a success. The new 50 kHz sonar system was deployed, switched on, and routinely provided measurements over an area 1.5 km range by 42° in bearing, resolved into 32 beams and 10 m range bins. Backscatter intensity and Doppler shift are estimated over this area every 2.5 seconds, resolving the dominant surface waves (figure 12). The data are suitable to look for direct links between LC and internal waves, and to describe MLD and LC evolution under steady strong winds (trades) in the presence of complex multi-directional waves (swell from several directions).
Figure 12. Surface waves observed with the new sonar (1717 HDT, October 4, 2002). A single frame (ping) of backscatter intensity (left) and radial velocity (right) from the new 50 kHz system. Up is toward the West; wind is from lower right to upper left (from ENE). Roughly 10 s seas going downwind are seen in both fields. Intensity (left) also shows hints of smaller scale streaks parallel to the wind, visible from 200 to 1000 m. Click on the image to see an animation.
To examine the underlying surface expression of Langmuir circulation, time-smoothing is applied. The smoothing employed is a 30-second box-car average of a 30-second exponential average, yielding an effective 1 minute smoothing sampled every 30 seconds. This smoothing is an effective compromise between side-lobe suppression and computational efficiency (the latter being important with the quantity of data dealt with here). The results are shown in figure 13 for the time segment surrounding the sample of figure 12 (from 1900 to 2100 HDT, Oct 4 2002). Over this segment, the features are noticeably anisotropic with significant elongation parallel to the wind. There is also significant time evolution, however, supporting the allegation that LC is less steady in oceanic conditions.
Figure 13. Langmuir circulation. Data from roughly the same time period as in figure 12, but with the surface waves time-averaged out (~40 second smoothing, or 16 pings). Elongated features parallel to the wind are now seen in both the intensity (left) and velocity (right), indicating active Langmuir circulation. Wind is about 10 m/s, from lower right to upper left. Note expanded scale relative to figure 12. Click on image to view animation.
Some 12 hours later, the wind has increased from 10 to 12 m/s, yet the LC-related features appear less well organized (click here to see the animation). In this segment, the features are significantly less anisotropic, as well as evolving rapidly in time relative to previous experience.
The Langmuir circulation observed off Hawaii is unsteady, with "along-stripe" coherence lengths not much larger than in the "cross-stripe" direction. It is not clear that the degree of disorganization is significantly larger than seen in, for example, the MBLEX (1995) data set.
Mixed Layer Motion in Calm Weather
Next we consider what happens in and just below the mixed layer in a calm period with strong internal wave forcing. Near the end of October 3, while the wind was still below 3-4 m/s, the steep internal tides gave rise to high-frequency motions visible in both intensity and velocity maps of the surface (figure 14). A reasonable question is whether this internal wave activity helps to "unmix" the mixed layer, and how the sub-mixed layer mixing compares between this calm time and a corresponding time with wind forcing present (i.e., between 1700 to 2400 on October 3, without wind, versus on October 4).
Figure 14. Data similar to figure 13 (40 second smoothing), but for a calm period near the peak tidal flows (1824 HDT, 3 Oct 2002). High-frequency internal waves are seen to propagate across the field from left (South) to right (North). The signal is seen in both intensity and velocity. Click image for movie.
To seek indications of mixing, it is useful to look more closely at the density profiles (or equivalently here, the temperature profiles). Figure 15 is a close-up view of the top 200 m over the calm period, showing evidence of mixing in the form of overturns and "detached bubbles" of heavier or lighter water in the sub-mixed layer thermocline.
Figure 15. Time-Depth plot of temperature over the calm period with strong internal waves. Note the evidence of overturns and isolated "bubbles" of heavier or lighter water indicated especially in the contours (e.g., near hour 23 at 40 to 80 m depth). This is strong evidence of active mixing in the sub-mixed layer thermocline region.
For comparison, figure 16 shows the corresponding close-up view for October 4, with 10 m/s wind and active Langmuir circulation. There is still evidence of mixing (e.g., steep contours in the last hour), but it appears weaker than during the calm period shown in figure 15.
Figure 16. Time-depth plot of temperature for October 4 2002, with 10 m/s winds and active Langmuir circulation. There is still evidence of mixing (e.g., steep contours in the last hour), but it appears weaker than during the calm period shown in figure 15.
It is curious that the mixing appears weaker with combined wind and internal wave forcing. If further analysis confirms this, an explanation is in order. A hypothesis is offered: the internal waves are generated from below, and are incident on the surface layer. In calm weather, they reflect efficiently, hence roughly doubling the extreme shears in the sub-mixed layer thermocline, and promoting enhanced mixing. When LC are there, forced by the wind and waves, the mixed layer has a much higher effective viscosity this, in turn, could damp the internal wave reflections, and hence (somewhat unexpectedly!) reduce the shear and net mixing below the mixed layer. In this case, energy that would have gone into mixing below the mixed layer is absorbed within it instead.
The time of enhanced mixing on Oct 3 does not occur with the high-frequency waves of figure 14, but at a "slack time" between internal waves. From 1800 to 1930 on the 3rd, the internal waves (as in figure 14) propagate from South to North. From 0030 to 0130 the next morning, they are seen propagating from North to South. In between, from about 2230 to 2400 on the 3rd, there are not discernable internal waves in the surface intensity or velocity data; however, there are some curious "spots," especially in the intensity data, that seem to come and go quickly (see animation here).
The Langmuir circulation observed off Hawaii is unsteady, with along-stripe coherence lengths not much larger than in the cross-stripe direction. However, it is not clear that the degree of disorganization is significantly larger than seen in, for example, the MBLEX (1995) data set.
In addition, The time-depth plots from the rapid-profiling CTD systems indicate enhanced upper thermocline mixing (just below the mixed layer) during a period of calm winds and increasingly strong baroclinic tides. One day (two tidal cycles) later, after resumption of trade winds, there appears to be less mixing below the mixed layer, even though tidal amplitudes increase. Perhaps the enhanced eddy-viscosity of the turbulent mixed layer acts to damp the high-mode internal waves responsible for the enhanced mixing?
Acknowledgements. This work was supported by ONR (C/G# N00014-02-1-0855 and N00014-00-1-0159) and NSF. Thanks also to T. Golfinos and the crew of FLIP, and to the OPG engineering team of E. Slater, M. Goldin, M. Bui, and A. Aja.
Craik, <A.D.D>., The generation of Langmuir circulation by an instability mechanism, J. Fluid Mech., 81, 209-223, 1977.
Craik, <A.D.D>., and S. Leibovich, A rational model for Langmuir circulations, J. Fluid Mech., 73, 401-426, 1976.
Garrett, C., Generation of Langmuir circulations by surface waves- A feedback mechanism, J. Mar. Res., 34, 117-130, 1976.
Langmuir, I., Surface motion of water induced by wind, Science, 87 (2250), 119-123, 1938.
Large, W.G., J.C. McWilliams, and S.C. Doney, Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization, Rev. Geophys., 32 (4), 363-403, 1994.
Leibovich, S., Convective instability of stably stratified water in the ocean, J. Fluid Mech., 82, 561-581, 1977.
Leibovich, S., On wave-current interaction theories of Langmuir circulations, J. Fluid Mech., 99, 715-724, 1980.
Li, M., and C. Garrett, Mixed layer deepening due to Langmuir circulation, J. Phys. Oceanogr., 27 (1), 121-132, 1997.
Li, M., K. Zahariev, and C. Garrett, Role of Langmuir circulation in the deepening of the ocean surface mixed layer, Science, 270, 1955-1957, 1995.
Niiler, P.P., and E.B. Krauss, One-dimensional models of the upper ocean, in Modeling and Prediction of the Upper Layers of the Ocean, edited by E.B. Krauss, pp. 143-172, Pergammon, Tarrytown, N. Y., 1977.
O'Brien, M.M., A. Plueddemann, and R.A. Weller, The response of oceanic mixed layer depth to physical forcing - modelled vs observed, Biol. Bull., 181 (2), 360-361, 1991.
Pinkel, R., and J.A. Smith, Open Ocean Surface Wave Measurement Using Doppler Sonar, Journal of Geophysical Research, 92, 12967-12973, 1987.
Pinkel, R., and J.A. Smith, Repeat-sequence coding for improved precision of Doppler sonar and sodar, J. Atmos. Oceanic Technol., 9 (2), 149-163, 1992.
Plueddemann, A.J., J.A. Smith, D.M. Farmer, R.A. Weller, W.R. Crawford, R. Pinkel, S. Vagle, and A. Gnanadesikan, Structure and variability of Langmuir circulation during the surface waves processes program, J. Geophys. Res., 101 (C2), 3525-3543, 1996.
Pollard, R.T., P.B. Rhines, and R. Thompson, The deepening of the wind-mixed layer, Geophys. Fluid Dyn., 4, 381-404, 1973.
Price, J.F., R.A. Weller, and R. Pinkel, Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing, J. Geophys. Res., 91 (C7), 8411-8427, 1986.
Smith, J.A., Observed growth of Langmuir circulation, J. Geophys. Res., 97, 5651-5664, 1992.
Smith, J.A., Observations of Langmuir circulation, waves, and the mixed layer, in The Air Sea Interface: Radio and Acoustic Sensing, Turbulence, and Wave Dynamics, edited by M.A. Donelan, W.H. Hui, and W.J. Plant, pp. 613-622, Univ. of Toronto Press, Toronto, Ont., 1996.
Smith, J.A., Evolution of Langmuir circulation during a storm, Journal of Geophysical Research, 103 (C6), 12,649-12,668, 1998.
Smith, J.A., Observations and theories of Langmuir circulation: a story of mixing, in Fluid Mechanics and the Environment: Dynamical Approaches, edited by J.L. Lumley, pp. 295-314, Springer, New York, 2001.
Smith, J.A., and J.L. Largier, Observations Of Nearshore Circulation - Rip Currents, J. Geophys. Res., 100 (C6), 10967-10975, 1995.
Smith, J.A., and R. Pinkel, Improvement of Doppler estimation through repeat sequence coding, in Oceans '91/Proceedings, October 1-3, 1991, Honolulu, Hawaii, USA/Ocean Technologies and Opportunities in the Pacific for the 90's, pp. 977-984, IEEE, Piscataway, N.J., 1991.
Smith, J.A., R. Pinkel, and R. Weller, Velocity structure in the mixed layer during MILDEX, J. Phys. Oceanogr., 17 (4), 425-439, 1987.
Stommel, H., Trajectories of small bodies sinding slowly through convection cells, J. Mar. Res., 8, 24-29, 1949.
Thorpe, S., and A.J. Hall, The characteristics of breaking waves, bubble clouds, and near-surface currents observed using side-scan sonar, Cont. Shelf Res., 1, 353-384, 1983.
Woodcock, A.H., A theory of surface water motion deduced from the wind-induced motion of Physalia, J. Mar. Res., 5 (3), 196-205, 1944.
Woodcock, A.H., Subsurface pelagic sargassum, J. Mar. Res., 9 (2), 77-92, 1950.