Measurements of the Generation and Evolution of Langmuir Circulations

Langmuir circulations are commonly observed on the surface of natural water bodies as a quasi-regular pattern of streaks or windrows. These are the surface signature of underwater counter rotating vortices roughly aligned with the wind direction and are often made visible by the accumulation of foam, slicks or detritus in the regions of convergence. Over the years, many observations of Langmuir circulations have been reported; these include observations of large-scale circulations (Thorpe and Hall 1983, Weller and Price 1988, Smith 1992), as well as intermediate to small-scale circulations (Owen 1966, Scott et al. 1969, Kenney 1993). The smaller scale circulations, along with breaking waves, may play an important role in the vertical transport of momentum, mass (gas), heat and biota within the mixed layer of the oceans (Melville et al. 1998).

We have conducted experiments in the large wind-wave facility at Scripps Institution of Oceanography. The water surface was monitored using a color imaging slope gauge for wave slope measurements, along with an Infrared camera to monitor the surface temperature and image the Langmuir circulations and the subsequent surface turbulence.

surface temperature
Figure 1 A) Surface temperature field for a final wind speed of 5 m s-1 and a fetch of 10.72 m. Times shown are 16.8, 18.3, 19.8, 21.3, 22.8, and 24.3 s. The temperature is given by the color code in degrees Celsius. B) Summary time series for the momentum flux at the surface, surface temperature, gas transfer velocity normalized to a Schmidt number of 600, and surface slope variance. The data shown is taken for a final wind speed of 5 m s-1 and a fetch of 10.72 m

The flow evolves in four stages from the initial acceleration and deepening of a shear-driven surface flow, which becomes unstable to surface waves and subsequently LCs. The LCs initially appear on the surface as streaks which are easily visualized with the thermal imager. Regions of surface convergence and divergence associated with local surface jets and wakes, respectively, are also clearly apparent. The surface jets eventually become unstable and the flow evolves to fully developed turbulence. In summary, the four stages progress from initial instability associated with divergence of the transverse velocity field, quasi-two-dimensional streak formation, streak dislocation or bifurcation, and transition to fully turbulent flow (figure 1A). In figure 1, the vertical (cross-wind) warm lines are the thermal markers laid down by the scanning beam of the CO2 laser with a 50 ms pulse length and a 2 Hz repetition rate. The line marker on the surface distorts, indicating regions of fast downwind motion, or jets, and regions of slower motion, or wakes. At t=19.8 s, the Langmuir circulations appear clearly as a series of along-wind streaks. The surface thermal markers permit the measurement of the streamwise velocity at the surface and identification of the jets and wakes. Shortly thereafter, the regions of increasing shear between the jets and wakes develop instabilities and the entire flow evolves into a turbulent regime. Once the flow is fully turbulent, the surface velocity can no longer be clearly segregated into jets or wakes, and after the Langmuir circulations have efficiently mixed down the momentum from the surface shear layer, the average surface velocity stabilizes at a somewhat lower velocity (figure 1B).

From figure 1A and 1B and our earlier work it is clear that Langmuir circulations disrupt the momentum and thermal boundary layers and provide rapid mixing of the surface layer.

Figure 1B) shows a summary of the time series for the surface momentum flux, temperature, gas transfer velocity normalized to a Schmidt number of 600 (that of CO2) and surface slope variance. The data shown is taken for a final wind speed of 5 m s-1 and a fetch of 10.72 m. It is clear that Langmuir circulations provide a very efficient mechanism for disrupting the momentum and thermal surface boundary layers. The gas transfer rates also are affected by the transition to Langmuir circulations. For the case presented here, a 70% increase in gas transfer velocity is observed to be directly correlated with the inception of the Langmuir circulations and the subsequent turbulence.

We have shown that for a wind-driven flow starting from rest, both the surface velocity and temperature evolve monotonically up to the inception of the Langmuir circulations. The instability then mixes heat and vorticity at rates greater than those of molecular diffusion. The data show that the Langmuir cells appear at a constant Reynolds number (based on the surface velocity and the shear layer depth) indicating that the mechanism for the instability is mechanical rather than thermal. Also, we have shown that the waves are necessary for the instability of the surface flow to the Langmuir circulations.

The period of significant coherence of the cells is transient and the flow rapidly evolves to fully developed turbulence. Yet, after the transition, it appears that the coherent structures still remain embedded in the turbulent flow and can be extracted by averaging. The observed instability is a transition phenomenon from a laminar to turbulent for the surface shear flow. It is possible that the inverse cascade observed during the transition might be involved in the development of the larger-scale Langmuir circulations observed at sea.

The length and time scales associated with the generation of the surface waves and the Langmuir circulations are comparable. In the context of the CLII mechanisms, the problem studied here is clearly of order unity where the surface drift velocity is comparable to the surface-wave phase speed. This leads to a clear coupling of the Langmuir cells with the surface wave field. To our knowledge, these are the first observations of a modulation of the surface-wave field by the flow associated with the underlying Langmuir circulations.

Importantly, it is the Langmuir circulations and not wave breaking that first destroy the cool surface skin. It is possible that the phenomenon described here is a controlling factor of the temperature amplitude of the cool skin at low wind speeds. It is anticipated that these small-scale circulations, if present in the field, under developing seas or diurnal sea breeze conditions, for example, may play an important role in heat, gas, and momentum transfer from the atmosphere to the upper layer of the oceans.

Wind-wave generation

As described in the preceeding section, prior to the transition to turbulence of the surface flow, wind waves are generated. We have observed the first wavelet generated using a imaging slope gauge. A system which permits te retreaval of the two dimensional surface slope using the refractive properties of the water.

In each run, the stress provided by the increasing wind speed accelerates the surface of the water. During this early stage of the flow, momentum is transferred to depth by viscous diffusion and a laminar boundary layer develops in the water column. The surface then becomes unstable to surface-wave modes. Figure 2 shows the along-wind and cross-wind slope of the surface wave field at t=17, 25, 34, and 50 s for a final wind speed of 5 m s-1 at a fetch of 10.72 m.

Figure 2 Along-wind, Sx, and cross-wind, Sy, slope of the surface wave field at t=17, 25, 34, and 50 s for a final wind speed of 5 m s-1 and at a fetch of 10.72 m.
The slope images show the downshift of the dominant surface-wave wavenumber as the wave field grows. At t=34 s, the waves show some sign of nonlinearity as parasitic capillary waves appear on the front face of the dominant gravity wave (Longuet-Higgins, 1995; Fedorov and Melville, 1998). Shortly after the generation of the first waves, the surface flow becomes unstable and develops Langmuir circulations. Windrows or streaks then become apparent on the thermal images (figure 1) which exhibit regions of surface convergence and divergence associated with local surface jets and wakes. Figure 3 shows the directional wavenumber spectra, averaged between t=45 to 55 s, for Sx and Sy at a 5 m s-1 wind speed, for a fetch of 10.72 m. The spectra exhibit a bi-modal shape. The lowest peak is the signature of the long surface gravity waves with an approximate 12.5-cm wavelength. These waves are indeed observed in figure 2. The second peak at around 800 rad m-1 corresponds to a wavelength of 0.78 cm and is believed to be caused by parasitic capillary waves riding on the longer gravity waves (see Ebuchi et al. 1987 for an example). The dip separating the two peaks thereby separates two distinct regimes: the gravity and the capillary wave regimes. The so-called “Bond number” gives the ratio of surface tension forces to gravity

with a Bond number of unity yielding the length scale at which gravity and surface tension are equally important:

where T is the surface tension, ρ the density of water, and g the acceleration of gravity. This scale also corresponds to the waves with the minimum phase speed. As shown in figure 3 the dip in the wavenumber slope spectra lies at the scale given by the Bond number thereby separating the regions dominated by gravity and surface tension. This was previously observed by Zhang (1995) who also noted that the dips become filled at higher wind speeds (< 8 m s-1). As expected, the waves in the along-wind and cross-wind slope images mainly propagate in the x direction and y direction respectively.

Figure 3 Directional saturation slope spectra B(k) for a) Sx and b) Sy for a final wind speed of 5 m s-1 and a fetch of 10.72 m. &theda; is the angle of propagation relative to the along-wind direction x.
In this case, the waves with slopes in the cross-wind direction appear to primarily propagate at 40-50 degrees from the wind direction. The directional saturation slope spectra compare well with those of Jahne and Riemer (1990).

The wave field evolves as the flow develops with time. The initial generation of surface waves by the wind has long been a problem of interest (Miles 1957, Phillips 1957, Miles 1959), and remains an active area of research (Wheless and Csanady 1993, Belcher et al. 1994, Miles and Ierley 1998). Of interest are the initial scales of the observed wave properties. The CISG yields such information and we present it here for completeness. Table 1 shows the initial wave parameters for the first detectable waves.

The data shown in table 1 compare favorably with those of Kawai (1979). However, they should be compared with caution. Kawai’s experiment was designed to study the initial generation of waves where wind stress was rapidly increased to a constant value in order to be easily modeled by a step function; thus, the velocity shear layer in the water could be approximated by a constant-stress similarity solution. The experiments presented here were designed to study the instability of the flow to Langmuir circulations that accompany this classical wave-generation problem. In these experiments, the wind stress cannot be approximated by a step function and the resulting flow in both the air and the water are driven by a more complex surface boundary condition than that usually considered for the initial generation of surface waves.