Jerome A. Smith

Marine Physical Laboratory, 0213

Scripps Institution of Oceanography

La Jolla, CA 93093-0213



The is to understand the physical mechanisms which mediate fluxes of energy, momentum, and matter between the air and sea. In particular, the form and dynamics of mixed layer motion can have a significant effect on these exchanges, and we hope to improve our ability to describe and predict these motions and their effects.


A Phased-Array Doppler Sonar (PADS) was deployed on the Research Platform FLIP off Pt. Conception in the spring of 1995, as part of MBLEX, an experiment aimed at improving our understanding of the Marine Boundary Layers on both side of the air/sea interface. A second was completed in time for the second leg of MBLEX, off Monterey CA. This instrument provides estimates of the radially-directed component of velocity over an area up to 400m radius by 35 degrees in azimuth (see figure 1). The spatial resolution is about 8 m in range by 3 degrees; so (for example) at 200m range the sample area is about 8 by 10 meters. The sonars transmitted every 0.75s, with each ping simultaneously sampling over all angles; thus surface waves as well as the mean flow are resolved in the raw data. 30s averages (40 pings) were recorded, providing about 3 cm/s RMS velocity error in each range-angle bin (in practice, additional errors arise from imperfect beamforming, etc.). All data were coordinated via GPS time-stamping. This enabled detailed comparisons between the quasi-continuous coverage from the PADS and the presumed forcing by wind, Stokes’ drift, inertial currents, and stratification.

The approach taken in this project was to compare the measurements to a simple "PWP" type mixed layer model, and to a similar model augmented by a "Langmuir circulation" parameter [Price et al., 1986, Li and Garrett, 1997]. Work on the CTD data (density profiles) and current profiles has been in collaboration with R. Pinkel and student M. Alford. Wind stress calculations for the first MLBEX leg were carried out by then-graduate-student K. Rieder (now Dr. Rieder).

A novel aspect of this data is that the intensity features can be tracked, yielding a direct measurement of the near-surface Lagrangian velocity. In contrast, the measured Doppler shift (frequency shift) is proportional to the Eulerian velocity. Thus, the difference is a direct measure of the Stokes’ drift due to surface waves. Over part of the time series, this difference was calculated and is compared to the Stokes’ drift estimated from wave-wire data in figure 2.

MBLEX was successful. The data are both novel and high quality. Almost all relevant forcing terms were well measured (with the exception of the radiation terms in the heat balance). In particular, the velocity jump across the thermocline at the base of the mixed layer is well estimated from comparison of the surface velocity (Eulerian) from the PADS to the deeper flow, estimated from an up-looking 4-beam janus-configuration Doppler sonar (see figure 3). This permits accurate assessment of the "bulk Richardson number instability," as described (for example) in Price, et al., [1986].

Figure 1. Four frames 15 minutes apart during strong forcing conditions. Note how the stripes alternate between well-defined and irregular. The arrows indicate the wind; a 50 m vector (on the image’s scale) represents a 10 m/s wind. North is up.

This segment may also be viewed as a movie (2.6MB). The vacillations occurred near the end of a gale-force storm in March, 1995. As above, the panel on the left shows bubble-density near the surface, while that on the right shows the "line of sight" surface velocity. The arrows in the lower right corners indicate the windspeed (50m -> 10m/s) and direction. Over this two-hour segment, the wind is nearly steady at 15 m/s (30 knots). There's one minute "real time" per frame, the movie plays at 4 fps.

Figure 2. The measured difference between intensity feature advection and Doppler velocity estimates, both based on the PADS data (red stars), and the surface wave Stokes’ drift calculated from wave wire data (black line). The agreement is remarkable. Y axis units are cm/s -- advection speeds (by inertial currents) reach 30 cm/s, and surface wave orbital velocities are up to 150 cm/s.

Figure 3. Mixing strength, parameterized by the density jump required to stop mixing, for (i) the bulk Richardson mechanism (thick line); (ii) Langmuir circulation, as estimated directly from the RMS velocity scale V (medium line); and (iii) LC mixing estimated from Us and nt via comparison with numerical model results, for developing waves (thin solid line) and for fully developed waves (thin dashed line).

Figure 4. Scaling of the RMS measured radial surface velocity takes the general form V~u*(Us/u*)n; n is sought as the slope of (V/u*) versus (Us/u*) on a log-log plot. This figure indicates a value for n of 1.0; i.e., V ~ Us, with no dependence on u* once Langmuir circulation is well formed. Values from times when there were no signs of Langmuir circulation are shown as red crosses.



• The observed mixed layer deepening is consistent with the "bulk dynamics" of shear across the thermocline due to inertial motion as the primary agent. Surface stirring by the combined action of wind and waves may have helped maintain the mixed layer after this, and may even have induced some additional slow deepening, but is clearly of secondary importance (figure 3).

• Langmuir circulation can vary significantly in strength, spacing, and peakiness over timescales of order 15 minutes (figure 1). Not the wind, waves, nor mixed layer depths vary significantly on this time scale. In these "vacillations," the strengths of velocity versus intensity features were 180° out of phase: strongest intensity features coincided with weakest RMS velocities. It is suggested that the buoyancy of bubbles may be non-negligible in the dynamics of these phenomena.

• The spacing and orientation of intensity versus velocity features can differ. Here, intensity features aligned within a couple degrees of the wind (favoring the right), while the velocity features averaged 10° to the right of the wind. The intensity spacing tracks 2 times the mixed layer depth, while the velocity feature spacing is closer to 2.5 times MLD. While this mismatch is puzzling, it would appear likely that the time/space-dependent behavior of bubbles in a time-varying flow should be investigated. Simulations with realistic bubble dynamics may help to understand these differences.

• The difference between mean feature-tracking and Doppler velocity estimates provides a direct estimate of the Stokes’ drift near the surface. Both estimates come from the same data stream, without explicitly resolving the waves. To my knowledge, this is an observational first for the open ocean.

• The surface velocity variance associated with the mixing observed here is smaller than in previously reported cases. It is suggested that this may be related to swell opposing the wind.

• Finally, when there is Langmuir circulation, the RMS velocities associated with the low-frequency features scale quite tightly with the Stokes’ drift alone, rather than with the wind or a combination of wind and waves (figure 4). This relation is nonlinear in that a threshold must be set for the existence of Langmuir circulation before it holds.


The scaling illustrated in figure 4 for mixed layer motion applies only after Langmuir circulation has been "turned on." The implication is that this non-linear transition (from no-LC to LC conditions) may have to be explicitly modeled. A transition criterion based on the "generation strength" (u* Us) is used in Smith (1997); however, it has not been established whether this is an optimal (or even widely acceptable) choice.

Parameterization of the mixed layer behavior is likely to be improved by incorporation of the results shown here. On the other hand, the gross difference in rms velocity scale here and that observed for equivalent conditions in earlier experiments indicates that there remains some "hidden variable" governing the strength of surface motions associated with wind/wave mixing.


Li, M., and C. Garrett, Mixed layer deepening due to Langmuir circulation, J. Phys. Oceanogr., 27, 121-132, 1997.

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, 8411-8427, 1986.

Smith, J.A., Evolution of Langmuir circulation during a storm, (pdf, 567k) Journal of Geophysical Research, 103(C1), 12,649-12,668, 1998.