Research Article

Enhanced Turbulence and Energy Dissipation at Ocean Fronts

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Science  15 Apr 2011:
Vol. 332, Issue 6027, pp. 318-322
DOI: 10.1126/science.1201515

Abstract

The ocean surface boundary layer mediates air-sea exchange. In the classical paradigm and in current climate models, its turbulence is driven by atmospheric forcing. Observations at a 1-kilometer-wide front within the Kuroshio Current indicate that the rate of energy dissipation within the boundary layer is enhanced by one to two orders of magnitude, suggesting that the front, rather than the atmospheric forcing, supplied the energy for the turbulence. The data quantitatively support the hypothesis that winds aligned with the frontal velocity catalyzed a release of energy from the front to the turbulence. The resulting boundary layer is stratified in contrast to the classically well-mixed layer. These effects will be strongest at the intense fronts found in the Kuroshio Current, the Gulf Stream, and the Antarctic Circumpolar Current, all of which are key players in the climate system.

Although the basic characteristics of ocean circulation have been well known for many decades, a detailed understanding of its energetics has emerged only recently (1). The energy sources are well understood: Wind stress acting on surface currents (or “wind-work”), particularly in the Southern Ocean, is the dominant energy source, with little net input from heating/cooling or precipitation/evaporation. The energy sinks, however, are less well understood. Energy dissipation requires a cascade of energy through nine orders of magnitude, from the size of the ocean to the centimeter scales of viscous dissipation. A cascade of processes supports this flux. Instabilities of the large-scale circulation lead to the generation of a rich field of eddies with typical scales of 100 km at mid-latitudes. The dynamics of these eddies are highly constrained by Earth’s rotation such that their currents are nearly geostrophic (that is, the flow is governed by a balance between Coriolis and horizontal pressure forces). A turbulent, geostrophic eddy field tends to flux energy to larger rather than smaller scales, thus providing no obvious path to dissipation. Recent simulations (24) with very-high-resolution models suggest a new path from the eddy field toward dissipation through the formation of submesoscale fronts, regions of strong lateral gradient in the upper ocean, with horizontal scales of 1 to 10 km. Instabilities of these fronts could then cascade energy from the frontal scale to dissipation.

The simulations also suggest that the surface “mixed-layer” of the ocean is greatly modified in the presence of fronts. For one, the boundary layer is stratified, not mixed, and deepens by the action of turbulent motions that derive part of their energy from the frontal circulation as opposed to atmospheric forcing (4, 5). This is a shift from the classical paradigm of a surface boundary layer driven by the atmosphere, with implications for climate dynamics. The surface boundary layer is the mediator for air-sea interaction and therefore influences processes that play an integral role in the climate system such as the oceanic sequestration of carbon and the subduction, or transfer, of heat, salt, and dissolved gasses from the ocean’s surface to its interior. Oceanic sequestration of carbon and subduction occur to a large degree in the proximity of the ocean’s main currents: the Gulf Stream, the Antarctic Circumpolar Current, and the Kuroshio Current (6, 7). These currents are regions of strong lateral density gradients; therefore, their surface boundary layers could be substantially affected by frontal dynamics. Here, we present experimental evidence from a front in the Kuroshio showing that this is indeed the case.

Evolution of the front. Measurements were taken from 18 to 21 May 2007 (days 137 to 140) near the start of the Kuroshio extension off the coast of Japan. Here, the cold subpolar gyre waters of the Oyashio Current meet the warm subtropical gyre waters of the Kuroshio Current to form the Kuroshio front (Fig. 1A). The region is rich in eddies, as illustrated by the sea surface height contours in Fig. 1A (8). Measurements focused on an exceptionally sharp front [the “sharpest front” (SF), blue arrow in Fig. 1] formed by a strongly confluent flow between two eddies acting on the contrast between the warm Kuroshio water and the cold Oyashio water. Measurements were made by deploying a subsurface, neutrally buoyant Lagrangian (water-following) float (9) in the frontal region, acoustically tracking it from the ship, and surveying a ~5-km region around the float using the Triaxus profiling vehicle towed behind the R/V Melville (10). An example of the sampling strategy is shown in Fig. 1B. The float provided a reference frame moving with the frontal water, so that changes in frontal structure can be interpreted as attributable to its temporal evolution. The vertical motion of the float within the boundary layer also provided estimates of the turbulence intensity and dissipation rate. Measurements included temperature, salinity, and pressure on both platforms and velocity profiles obtained by combining ship and Triaxus data (fig. S3) (10).

Fig. 1

(A) Sea surface temperature (SST) map (37) of experimental area with sea surface height (SSH) (8) shown as contours (0.1-m interval). The thick black line denotes the ship track. Blue and red arrows mark sections shown below in blue and red boxes (C to F), respectively. L and H mark low- and high-pressure centers, respectively. (B) Triaxus and float data around SF2 [blue box (C and E)], with Triaxus density shown as a colored curtain hanging beneath the ship track and float trajectory shown as a ribbon colored by density beneath the surface track (dashed line). Sections show along-front velocity [(C) and (D)] and total PV [(E) and (F)] for SF2 (left, blue box) and for a later section (right, red box). Black contours plot potential density in each section, with the thick line marking σθ = 25.0 kg m–3 and thinner lines plotted at 0.05 intervals. Gray lines denote the Triaxus profile track.

Confluent flow (evident in Fig. 1A) concentrates the large-scale north-south temperature and salinity gradients into a smaller region, thus forming the SF. During day 137, estimates from the large-scale velocity field derived from satellite altimetry show a north-south convergence of north velocity ∂v/∂y < 0 (v, northward velocity; y, northward distance) and an east-west divergence of east velocity ∂u/∂x > 0 (u, eastward velocity; x, eastward distance), both of magnitude ~0.5 × 10−5 s–1. Estimates from direct velocity measurements (fig. S3) (10) along the front and ±3 km to either side confirm the north-south convergence and the acceleration of the along-front velocity (∂u/∂x ≈ –∂v/∂y ~ 1.2 ± 0.7 × 10−5 s–1). The observed front thinned laterally by about a factor of 2 during this period (Fig. 2A), a rate close to that predicted from these velocity gradients, thus forming and maintaining the SF through day 137. Both confluence components dropped to zero by day 138.5 and then become divergent with a magnitude of 0.5 ± 0.5 × 10−5 s–1. Thus, the SF is a transient region of strong density gradient generated by strong local confluence and embedded within the larger-scale Kuroshio front.

Fig. 2

(A) SST anomaly (relative to SST along the front) from ship surveys plotted relative to float position. Vertical axis is cross-frontal distance. (B) Depth-time section of along-front velocity following the float with potential density contoured at 0.2–kg m–3 intervals where available in the upper 150 m. (C) Wind stress (22, 23) magnitude and along-front component in pascals. (D) Vertical shear (UZ) of zonal velocity as a function of depth and time along the front.

A section across the SF (Fig. 1C) shows it to be less than 1 km wide in surface density and ~20 m deep (11). A surface-velocity maximum, the frontal jet, is found on the warm side of the front (Fig. 1C). The shear below this jet extends across the frontal region and has a substantial geostrophic component, but with a shear magnitude that is roughly half that expected geostrophically from the horizontal density gradient. A similar section taken 2 days and 220 km downstream (Fig. 1D) shows a much wider (4 km) and deeper (60 m) frontal zone. The large horizontal density gradients across the front have eroded, although the net contrast remains about the same, and the volume of water with intermediate properties has increased (Fig. 1, C and D). Thus, the decay of the SF appears to be due to a combination of local difluence and mixing.

Turbulence and mixing at the front. Measurements collected by the Lagrangian float at the SF quantify the rate of turbulent mixing. The float interspersed periods of Lagrangian drift with profiles and surfacing for communication. During the 16 drifts, the float was water-following in three dimensions, with its vertical velocity measuring the vertical velocity of the water. During profiles and surfacings, the float purposefully moved relative to the water and was thus not Lagrangian. The float sampled the SF during two of the drifts, which will hereafter be called SF1 and SF2. During these drifts, especially SF2, the float was exactly at the front, as indicated by: (i) its track (Fig. 1B), which follows the frontal interface mapped by the Triaxus; (ii) its density (Fig. 3B), which is intermediate between that of the warm and cold sides of the front; and (iii) its location at the maximum in horizontal density gradient (Figs. 1B and 3A). During these drifts, the float repeatedly cycles across the upper-ocean boundary layer (Fig. 3E), tracing the trajectories of boundary-layer water parcels and thus measuring their vertical velocity. Numerous other measurements in both convection (12, 13) and wind-forced boundary layers (1417) confirm that the vertical motion of these floats is due to upper-ocean turbulence.

Fig. 3

(A) Horizontal buoyancy gradient, proportional to minus the density gradient (represented by color), computed from R/V Melville’s hull-mounted temperature sensor plotted as a function of time and potential density. The black line denotes the float trajectory, whereas the white line plots the position of maximum buoyancy gradient. (B) Density profiles at SF2 from float (blue) and Triaxus (gray) used in Fig. 1B. Two Triaxus profiles are highlighted (black). (C) Vertical velocity variance from floats (1417) for wind-forced upper-ocean boundary layers as a function of wind speed. Confidence intervals (95%) were computed as in (14). SF2 lies well above all other data. U10, the wind speed at 10-m height. (D) Time series of boundary-layer–integrated dissipation estimated from the float-acceleration spectrum (black solid circle), float VKE averaged over each float drift (open circles), 1-hour–averaged float VKE (gray line with dashed line interpolating between drifts), EBF computed at float averaged over drifts (red circles), and EBF computed at maximum density gradient (red line, 1.5-hours running average). (E) Float depth during Lagrangian drifts (yellow filled areas) and boundary-layer depth (black bars) estimated as twice the mean float depth.

What is the energy source for this turbulence? Numerous float observations of the average vertical kinetic energy (VKE) in the upper-ocean boundary layer show a remarkably good correlation between VKE and the 10-m wind speed (Fig. 3C). This correlation indicates that wind is usually the major source of energy for upper-ocean turbulence (18). However, the VKE during SF2 (gray in Fig. 3C) lies far (a factor 6) above these values, suggesting that wind cannot explain the anomalously high turbulence levels at SF2.

In Fig. 3D, the anomalously high turbulence at SF2 is shown in terms of energy dissipation rate; that is, the flux of energy through the turbulence. The average dissipation in the boundary layer is estimated from the frequency spectra of float vertical acceleration (Fig. 3D, black circles, and fig. S4) (10, 19) and plotted as depth-integrated dissipation by multiplying by the boundary-layer depth (Fig. 3E) (20). Dissipation rate and energy are closely linked so that a second estimate with higher time resolution can be formed from the VKE (Fig. 3D, solid and dashed gray traces and open circles) (21). The average dissipation at SF2 rises by a factor of ~10 to 20 above the nonfrontal values with the VKE estimate suggesting that even higher values occurred just before the measurements began.

Cooling of the ocean by the atmosphere drives boundary-layer turbulence with an average dissipation rate given by the surface buoyancy flux (12). At SF2, very weak cooling occurs (22, 23), with a buoyancy flux of less than 0.3% of the measured dissipation. Atmospheric cooling cannot explain the anomalously high turbulence levels at SF2.

In summary, SF2 is unremarkable in wind stress (Fig. 2C) or in velocity (Fig. 2B), but is highly anomalous in turbulence level (Fig. 3, C and D) and in lateral gradient (Fig. 2A).

Potential vorticity and frontal instability. We hypothesize that a flux of energy from the front itself accounts for the enhanced turbulence levels at SF2. The boundary layer at SF2 is stably stratified (Fig. 3B) yet highly sheared in the vertical direction due to the presence of a strong jet along the front (Fig. 2, B and C). This latter condition makes the flow potentially susceptible to symmetric instability (SI) (4), which extracts kinetic energy from the geostrophic frontal jet. The Ertel potential vorticity (PV) (24) is the key quantity for diagnosing this instability; a flow is unstable to SI when the PV is negative (25). PV can become negative due to the combination of a sufficiently strong vertical shear and lateral density gradient and a sufficiently weak vertical density gradient. These conditions can occur within the boundary layer of a strong front, with the front providing the shear and lateral gradient and the boundary layer having a reduced stratification. Simulations (4, 5) indicate that under these conditions SI will grow, become unstable to secondary, smaller-scale instabilities (26), and feed a turbulent cascade to dissipation, resulting in a fully turbulent boundary layer drawing its energy from the front.

We used velocity and density data taken by the ship to evaluate the PV on each of the nearly 100 crossings of the front (fig. S5) (10, 24). We found negative PV near the surface (Fig. 1E) for 0.2 days at SF2 and nowhere else (Fig. 1F). The front at SF2 is therefore unstable to SI, suggesting that the turbulence at SF2 is drawing energy from the frontal shear.

The simulations indicate that SI at a front occurs when the wind blows perpendicular to the frontal gradient (27, 28), which is typically in the direction of the frontal velocity (Fig. 4). Such a “down-front” wind drives a net transport of water perpendicular to the frontal jet to carry heavy water across the front, from the cold side to the warm side. This Ekman transport advects heavy water over light water, reducing the stratification, and thus reducing the PV and promoting SI. The Ekman buoyancy flux (EBF) (27), computed from the product of the down-front wind stress (Fig. 2C) and the cross-frontal density gradient (Fig. 3A), is a measure of this effect. Simulations (4) suggest that turbulence in a fully developed boundary layer of depth H and driven by down-front winds extracts kinetic energy from the frontal jet at a depth-integrated rate given by H(EBF)/2 and dissipates it within the boundary layer. This quantity (29) peaks at SF2 (Fig. 3D, red) with a value comparable to the measured dissipation rate, thus providing quantitative evidence supporting the hypothesis that the boundary layer at SF2 was driven primarily by SI induced by a down-front wind.

Fig. 4

Structure of the symmetrically unstable front. A wind blowing down the frontal boundary between warm and cold water induces an Ekman transport perpendicular to the wind and to the front. This carries heavy water from the cold side of the front over light water from the warm side, which, in the presence of the frontal jet and lateral density gradient, acts to reduce the stratification near the surface and makes the front unstable to symmetric instability. The instability draws energy from the frontal jet, leading to enhanced turbulence, and induces a circulation acting to bring warm water to the surface and cold water to depth, thus counteracting the effect of the Ekman transport and keeping the near-surface stably stratified, with warm water over cold water.

The structure of the boundary layer also supports this hypothesis. SI acts to reduce the anomalously negative PV by inducing a circulation that increases the stratification, thereby counteracting the effect of the EBF (Fig. 4). Simulated boundary layers within symmetrically unstable fronts are simultaneously stratified and turbulent (5), in contrast to those outside of fronts, which are generally well mixed. Indeed, the observed density profiles within the front (Fig. 3B) lack mixed layers and are instead stratified at all depths. The Lagrangian float trajectories repeatedly cross this stratification, indicating that the boundary layer at SF2 is both turbulent and stratified (30).

Although SF1 exhibits elevated EBF and dissipation, the thin (H ≈ 10 m) boundary layer precludes estimating PV and the towed surveys barely cross the front, making EBF errors large. An accurate evaluation of the hypothesis is not possible at SF1.

Near-inertial frequency waves. Sections of velocity and shear (Fig. 2, B and D) show that the above frontal processes are associated with deeper structures suggestive of internal waves. In particular, the depth-time section of shear (Fig. 2D) shows alternating diagonal stripes of positive and negative shear with upward phase propagation and a period close to the local inertial period (i.e., half a pendulum day: 0.84 days at this latitude). The north-south component of shear (not shown in Fig. 2) is in quadrature with the east-west component such that the velocity vector rotates clockwise with approximately constant magnitude as a function of both increasing depth and increasing time. This pattern is widely found in the ocean and interpreted as the signature of downward propagating near-inertial frequency internal waves (31). Given the observed stratification and estimating the vertical wavelength and period of the waves to be 200 m and 0.78 days, respectively (based on a least-squares fit on the shear field of the upper 150 m and first 2 days), theory predicts that the waves’ downward energy flux is ~6 mW/m2, which is similar to an estimate for the energy input to near-inertial waves from the winds of 9 mW/m2 (32), but only about 6% of the excess turbulent dissipation at the SF2. These calculations suggest that the waves are probably driven by the winds and minimally contribute to the energetics of the turbulence within the boundary layer at the front.

Surprisingly, however, the strong near-surface shear of the sharpest front appears to be part of the deeper near-inertial pattern. The boundary-layer depth (Fig. 3E) also appears to have variability on roughly the same time scale; that is, the increased depth at days 138.7 and 139.6. Thus, it is possible that these inertial motions could play a role in the rapid confluence and difluence that generate and dissipate the SF, as well as in producing its negative PV. We further speculate that the SI at the front could feed energy into the inertial waves and thus radiate energy into the ocean interior. Because the lateral scale of the near-inertial motions is probably much larger than that of the SF, their overall role in the SF energetics could be substantially larger than that implied by the small local flux density.

Implications. Traditionally, the upper-ocean boundary layer is thought to be driven by the atmosphere through fluxes of heat, moisture, and momentum (33, 34). The observations presented here break from this paradigm by suggesting that lateral density gradients and their geostrophic currents can also play a role in boundary-layer dynamics by supplying energy to turbulence at the expense of the circulation and permitting stratification and turbulence to coexist. Therefore, the greatly enhanced boundary-layer turbulence and dissipation described here in a very sharp Kuroshio front is likely an extreme example of a process that occurs much more widely in the ocean, potentially playing an important role in its dynamics and energetics. Furthermore, these results are consistent with recent theory on submesoscale processes and thus encourage incorporation of this theory into boundary-layer models. Such physics is not accounted for in present-day climate models. Fronts associated with the Kuroshio, Gulf Stream, and Antarctic Circumpolar Current are key players in the ocean-atmosphere climate system. Inaccurate representation of the boundary layer and flow energetics in frontal regions could thus substantially affect the predictive skill of climate models.

Supporting Online Material

www.sciencemag.org/cgi/content/full/science.1201515/DC1

SOM Text

Figs. S1 to S7

References

References and Notes

  1. See supporting online material for details of instrumentation and calculations.
  2. Temperature measured continuously on the ship’s hull shows a SF that is ~500 m wide, substantially smaller than the sampling scale of the Triaxus towed profiler. Triaxus data show a tight linear relation between potential temperature and potential density in the upper 10 m so that potential density can be accurately predicted from potential temperature (fig. S6A) (10).
  3. For deep mixed layers, not shown in Fig. 3C, surface buoyancy flux can control the turbulence (12).
  4. Boundary layer depth is computed as twice the mean depth of the float. This will be exactly true for a float whose depth is uniformly distributed across the boundary layer.
  5. The kinetic energy in the boundary layer will be ~1.5H<w2>, where H is the boundary-layer depth, w is vertical velocity, and isotropic turbulence is assumed. This energy will dissipate in an eddy overturning time at approximately H/<w2>1/2, thus predicting a depth-integrated dissipation rate of 1.5<w2>1.5. Figure 3D shows a plot of 3<w2>1.5. The constant 3 was chosen to best fit the dissipation estimates from acceleration. The difference could easily be due to the expected anisotropy of the boundary-layer turbulence and exact overturning time. The constant could vary with the boundary-layer dynamics; this analysis does not account for this possibility.
  6. We computed surface fluxes of momentum, heat, and buoyancy from the IMET, Improved Meteorology measurements on the R/V Melville using the TOGA/COARE algorithms as implemented in the MATLAB air-sea toolbox (23). This results in estimates of the wind stress τ=ρu2 (where ρ is air density, and u is the friction velocity) and the buoyancy flux Jb.
  7. The Ertel PV is defined as Q = ωa · ∇b, the dot product of the absolute vorticity ωa=fk+ζ and the gradient of buoyancy b = –gρ/ρ0. The coordinates are (x, y, z) for the along-front (east), cross-front (north), and up directions with associated velocity components (u, v, w). The Coriolis parameter is f, gravity’s acceleration is g, potential density is ρ, ρ0 is a reference density, and ζ is the relative vorticity ×u. Computationally, the vertical vorticity is estimated as ζz = –∂u/y and the cross-front component of vorticity as ζy = ∂u/z. The PV can be split into two parts: Q = QV + QH, where QV = (f – ∂u/y)∂b/∂z and QH = (∂u/∂z)∂b/∂y. A geostrophic flow is symmetrically unstable when its PV is negative and QV > 0.
  8. More accurately, down-front winds are defined as winds that induce a positive wind-driven buoyancy flux: EBF=ρo1τwug/z, where τw is the wind stress and ug/z=f1k×b is the geostrophic shear. Thus, down-front winds have a component along the geostrophic shear.
  9. EBF and its statistical error are computed using a density gradient derived from temperature measured on the ship’s hull (figs. S6 and S7) (10). Error estimates are dominated by the variance of the temperature observations on either side of the front, the uncertainty in the float position, and the uncertainty of the wind direction.
  10. Three different measures of stratification—(i) the vertical density gradient measured from the Triaxus profiles (gray in Fig. 3B), (ii) the vertical density gradient from the float trajectories (blue in Fig. 3B), and (iii) the mean difference between CTDs on the top and bottom of the float (not shown in Fig. 3)—all indicate that the stratification is stable. Comparison of the two highlighted Triaxus profiles (black in Fig. 3B) with the float profile shows that although the deeper parts of the float profile differ from the mean Triaxus profile, some Triaxus profiles have a similar structure to that seen by the float.
  11. A simple slab model (35) with no damping and a 25-m-deep layer gains inertial energy at a rate of ~9 mW/m2 between days 135.5 and 137.5, mostly due to wind bursts near days 136.3 and 137.3. This is sufficient to drive the observed near-inertial energy flux, although the complexities of near-inertial wave generation and propagation in a frontal region such as this (36) make a more exact analysis difficult to conduct.
  12. Velocity differences across the bottom of the mixed layer also play an important role, but these are mostly driven by local winds (34).
  13. Acknowledgments: This work was supported by the Office of Naval Research as part of the Assessing the Effects of Submesoscale Ocean Parameterizations program (grants N00014-05-1-0329/30/31, N00014-08-1-0445/10446/10447, and N00014-09-1-0202). This work would not have been possible without the efforts of staff at the Integrated Observations Group, the Ocean Engineering Department at the University of Washington Applied Physics Laboratory, and the crew and officers of the R/V Melville.
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