Do Internal Waves and Langmuir Circulation Interact?


J. A. Smith and R. Pinkel, Scripps Institution of Oceanography, La Jolla CA

In conjunction with the Hawaiian Ocean Mixing Experiment (HOME), an order 1 square kilometer area of the ocean surface was monitored for velocity (Doppler shift) and backscatter intensity, using a novel 50 kHz multi-beam acoustic Doppler system (the work was supported by a combination of funding from ONR and NSF). The pie-shaped area is 43 degrees wide, extending out 1.5 to 2 km in range. The area is resolved to 10 m in range by 1.3 degrees in bearing (~5000 cells), sampled every 2.5 to 3 s. The data exhibit distinct surface expressions of high-frequency internal waves, Langmuir circulation, and other phenomena. The intense high-frequency internal waves are probably associated with the strong internal tides generated over the Hawaiian mid-ocean ridge. Langmuir circulation is driven by the trade- or storm- winds and surface waves. Surface waves are also resolved, typically revealing several discrete directional modes. In addition, rapid-profiling CTDs and a combined up/down-looking sonar ("deep-8 sonar") are used to describe the profiles of density and velocity associated with the internal wave field. The data are used to investigate interactions between Langmuir circulation and the internal wave field, focusing particularly on ultra-high-frequency internal waves (periods of order one minute) that are seen to have surprisingly large velocity signatures at the surface.


Figure 1. Conceptual picture of Langmuir circulation (as idealized vortices) interacting with internal waves (interfactial waves). Thorpe’s simple model suggests that this interaction can plausibly have a large effect on the stability of the LC system. (Figure from Thorpe, S. J. Phys. Oceanogr. 27(1):62-71, 1997.)



  1. Define "less organized"
  1. Define "Comparable forcing conditions"


Comprehensive LC measurements were added to the already comprehensive measurements being made in a region of strong IW forcing: near the Hawaiian mid-ocean ridge (i.e., as an add-on to the Hawaiian Ocean Mixing Experiment, Near-field leg, Sept-Oct. 2002). Thus we have:

Figure 2. Experiment site, roughly 20 mi WNW of Oahu, on the south flank of the mid-ocean ridge (white arrow).


Figure 3. Rob Pinkel, Eric Slater, and Tyler assembling the back-plane of the 64-element sonar receive array.


Figure 4. One "frame" of imaged (left) intensity and (right) radial velocity from the LRPADS system. The system resolves these fields to about 10 m in range by 1.3° in angle, sampling all angles simultaneously. This permits an area up to 1.8 km by 44° to be imaged every 2 to 3 seconds (limited only by the speed of sound). Click on image to see movie.

Figure 5. 30-second averaged fields. Now "streaks" can be seen in both the bubble field (left) and surface velocity (right) that correspond to LC. Click on image to see movie.

Figure 6. 30-second averaged fields of (left) intensity and (right) radial velocity, showing a set of very high frequency internal waves. These propagate from left to right across the field of view, going 100 m in about 3 minutes (~0.5 m/s). With about 150 m wavelength, that corresponds to wave periods of order 5 minutes.

This is a large internal wave signal, especially at the high-frequency limit: 5 to 10 cm/s horizontal current amplitudes at the surface. Yet the component measured is nearly orthogonal to the wave propagation direction. Where & how do these get generated? First they go north (toward the ridge), then later to the south. They could be related to "mixing events" in the uppermost thermocline (the only place where N2 is large enough to permit such high frequencies), or they could be high-frequency "spin-offs" from tidal internal wave scattering & interactions. They seem to be related to tidal phase.

These relatively clean views of such internal waves occur during calm periods. Simultaneous existence of LC and such HF IWs was also seen, under conditions appropriate to the existence of both phenomena. The pictures are somewhat confused before separation of the types of phenomena via spectral techniques.

Figure 7. A sample time-depth plot of the density profiles over a 12-hour period. Active mixing is indicated by the occurrence of overturns (e.g., detached "blobs" of contours near 40 m depth, hours 8 to 12).

Figure 8. One measure of mixing is the net difference in potential energy between the observed and sorted density profile, corresponding to "available overturn potential energy" (uppermost curve). This may be related to tide (middle) or wind (lowest curve) forcing.

Figure 9. Spectral density of vertical velocity vs frequency and yearday. To estimate net Stokes’ drift, wave direction is also needed. The LRPADS observations provide directional information for waves below 0.2 Hz (sampling every 2.5 s). For waves over 0.2 Hz, a reasonable assumption is that the mean direction is downwind. In the range 0.2 to 0.5 Hz or so, directional spread of the waves also acts to reduce the net downwind magnitude of the surface drift; for conditions similar to those considered here, the net reduction is by a factor of order 0.6, decreasing slowly with frequency .

Figure 10. In terms of Stokes’ drift, the high-frequency tail (f > 0.2 Hz, green) accounts for about 2/3 of the total (black). However, the HF tail is thought to stay close to equilibrium with respect to the local wind; thus, the non-equilibrium part of the wave field is effectively captured in the low-frequency portion (red line).

Figure 11. Ignoring directionality for a moment, we can crudely test the hypothesis that the waves over 0.2 Hz are approximately in equilibrium. This figure compares a combination of 0-0.2 Hz plus a constant times the wind to the actual total Stokes drift magnitude.

Figure 12. Another way to estimate Stokes’ drift is via comparison of "feature-tracking velocity" (a form of PIV) to that estimated from the Doppler shift. The former, which tracks the motion of bubble clouds across the field of view, is a Lagrangian velocity estimate. The latter is an approximately Eulerian velocity estimate, taken at a depth of order 1 m below the wave troughs. The difference is approximately the Stokes’ drift (black). For comparison, an estimate from the wind is also shown (red); as intimated above, the wind and overall Stokes’ drift generally correlate to a level of 90 — 95%. In contrast to the similar exercise performed previously , the present system has sufficient angular resolution and coverage to estimate both components.

Figure 13. Conversely, Feature-Stokes estimate corresponds to the Eulerian flow.

Figure 14. The full 3D spectrum is available for the 0 to 0.2 Hz band. This shows a slice at the local peak frequency at the time of the example shown in figure 4 (9/30/02). Vector directions on this slice correspond to wave propagation directions; a strongly bimodal directional spread is seen, with evidence of further complex structures splitting each peak into "clusters" that probably have more to do with statistics than physics. This spectrum is calculated from the radial velocity component alone, projected onto a regular grid and Fourier transformed in all 3 dimensions. The response is somewhat angle-dependent, with weak (but not vanishing) response to waves propagating exactly along the x-axis (across the field of view from right to left or left to right). No correction has been applied. A movie showing successive frequency planes is available by clicking on the figure.

Figure 15. Another way to view the 3D directional-frequency spectrum of waves is to examine the 2D k-f spectra taken along a particular direction (here, along "beam 33," which is just to the left of center on the pie-shaped plots like that of figure 4). In this view, patterns that propagate along the beam at fixed speeds appear as straight lines. For example, in the intensity spectrum (left panel), bubble-clouds advecting with the mean flow produce variance along the line just slightly tilted off vertical, corresponding to small apparent phase-speeds (of order 0.1 m/s). Surface waves propagating toward or away from the instrument follow a quadratic dispersion curve tangent to the x axis at the origin and curving away as the higher frequency waves move more slowly. Surface waves propagating at an angle have higher apparent phase-speeds (e.g., consider the intersection of wave crests crossing the beam at an angle), and so fill in the area across the x-axis somewhat. Variance corresponding to surface waves is clearest in the velocity spectrum (right panel), but visible in both.

The surprising feature here is the line of variance at a little over 45° seen in the velocity spectrum, corresponding to an along-beam apparent phase speed of around 5 m/s (roughly half the windspeed or, alternatively, at the group velocity of the peak waves). What does this "stuff" look like in regular space?

Figure 16. Two snapshots of the radial velocity field for variance near the "5 m/s line" referred to above. A spectral filter was applied to eliminate variance corresponding to speeds less than 4.5 m/s (to eliminate turbulence and LC "frozen" into the mean flow) and faster than 6.5 m/s (to eliminate the huge surface wave signal). The roughly uniform orange-green speckle corresponds to the noise level remaining after this filter. The right panel is 20 s later than the left panel. A band of blue-shift velocity (velocity toward the instrument, at the bottom of the panel) is seen that propagates about 100 m farther away in that time. The surprise here is that the unknown phenomenon is quite thin.


Figure 17. The see whether there is some relation between the 5 m/s patterns and wave groups, a wave-envelope analysis is carried out- essentially a Hilbert transform in time at each data point. This figure illustrates what the analysis produces: on the left is the wave amplitude envelope, contoured from 0 (white ) to 50 cm/s amplitude (dark blue). On the right is the original wave-field at the same time. Slightly inclined bands of large amplitude on the left (e.g. at 200, 350, and 900-1000 m range) are seen to correspond to large oscillations in the wave-field on the right, although the group size is not more than a wavelength or so. In addition, bands of higher and lower amplitude can be seen that run approximately vertically in the left hand panel (but are hard to discern on the right). These are not artifacts of the analysis or instrument response: they vary in location and strength, and do not appear except for bimodal directional distributions such as found during this particular time.

In terms of understanding the "5 m/s stuff," these longitudinal nodes are merely an interesting distraction. Its worth noting that they are not aligned with the wind or LC, and so probably do not interact with the latter. However, two questions do come up: (1) Is there a location along the lee side of the island where the LCs & wave nodes do line up and interact? (2) Is there any other significance (could there be an internal wave/wave group interaction)?

Figure 18. An example frame from the wave-amplitude/"5 m/s stuff" comparison movie. Some correlation is seen: particularly along the left side at 500, 850, and 1150 m range. The band at 250 on the right also has a corresponding feature on the left (more clear in the movie version. Click on image to see movie.)


What’s Been Learned So Far


Smith, J.A., Evolution of Langmuir circulation during a storm, Journal of Geophysical Research, 103 (C6), 12,649-12,668, 1998.

Smith, J.A., and G.T. Bullard, Directional Surface Wave Estimates from Doppler Sonar Data, Journal of Atmospheric and Oceanic Technology, 12 (3), 617-632, 1995.

Thorpe, S.A., Interactions between internal waves and boundary layer vortices, J. Phys. Oceanogr., 27 (1), 62-71, 1997.