## 1. Introduction

Processes that generate turbulence in the surface layer of the ocean rarely occur in isolation: generally, multiple forcings act simultaneously. The question of which forcing (if any) dominates turbulent production at any given time is of importance to vertical and horizontal transports of heat, salt, momentum, and any materials (plankton, sediment, bubbles, etc.) present within the range of turbulent structures. In shallow coastal oceans, this range can include the entire water column depth

It is believed that winds generate turbulence in the upper ocean both through direct action of wind stress on the surface and through an indirect process involving surface waves. A term in the wave-averaged momentum equation incorporating the latter mechanism, first derived by Craik and Leibovich (1976), will be here termed the Langmuir vortex force to clearly identify the process represented as that leading to Langmuir circulations (LC; Langmuir 1938). Both effects of wind forcing may be present together, and may be further superimposed on convection forced by destabilizing surface buoyancy flux and, in the case of shallow seas, turbulence associated with a bottom boundary layer.

Because of the complexity of turbulence driven by multiple processes, much of the literature on surface layer turbulence understandably focuses on a single mechanism [e.g., Agrawal et al. (1992), Steffen and D’Asaro (2002), and Plueddemann et al. (1996), for stress-driven, convective, and Langmuir-driven systems, respectively]. Comprehensive reviews of theoretical (Leibovich 1983) and computational (Sullivan and McWilliams 2010) studies that focus on LC and their connection to the surface wave field are available. A few large-eddy simulations (LESs) have treated the combination of stress, convective, and single-wave Langmuir forcings (Skyllingstad and Denbo 1995; Li et al. 2005), while others (Harcourt and D’Asaro 2008; Sullivan et al. 2007) have treated Langmuir forcing by a modeled spectrum of surface waves in the absence of convection: none have yet done both. Although there are exceptions (e.g., D’Asaro 2001; Tseng and D’Asaro 2004), observational studies of LC, reviewed most recently by Thorpe (2004), frequently do not quantify possible contributions from a stress-driven boundary layer and/or from destabilizing surface buoyancy flux, nor is there an accepted method of assessing their importance relative to LC. The present analysis seeks to fill this gap.

We consider interactions among stress, Langmuir vortex, and destabilizing buoyancy forcings, asking whether it is possible to determine when dominance of a single generation process is assured, using basic knowledge of wind, wave, and buoyancy forcings. Post hoc justification will be provided for an initial assumption that bottom boundary layer turbulence is of minor importance in most of the data examined here because of weak currents at the measurement site. In addition, effects of surface wave breaking will not be considered separately from the presence of surface waves. For a broad range of wave age, the majority of wind momentum is converted into waveform stress and drives a mean current (Sullivan and McWilliams 2010). Spatially variable wave breaking plays two roles, feeding momentum to the current and generating vertical vorticity via horizontal variation in the mean current. Along with that generated by other mechanisms, breaking-induced vertical vorticity can be rotated into the downwind direction by mean vertical shear to generate Langmuir circulations: breaking is included in the Langmuir vortex force through its contribution to fluid vertical vorticity.

Because the ocean surface layer involves Langmuir vortex forcing in addition to stress and convection, scalings derived from the atmospheric boundary layer are not automatically relevant nor necessarily adequate. Section 2 presents a new nondimensionalization of the momentum equation that provides two independent nondimensional parameters suitable for determining dominance among the three forcing processes considered. A five-beam vertical-beam acoustic Doppler current profiler (VADCP) operated continuously for several months at the LEO15 cabled observatory on the continental shelf off New Jersey provides an extensive dataset for testing this technique; section 3 describes available data and provides relevant details of processing. Section 4 presents a suite of diagnostics describing distinctly different characteristics of turbulence extending fully over an unstratified water column and demonstrably dominated either by Langmuir forcing or unstable convection, allowing definition of Langmuir supercell (LSC; Gargett et al. 2004) and convection (CVN) archetypes representing these two cases. In section 5, the forcing conditions resulting in each archetype are described. Vertical velocity variances are then presented in the space of the two nondimensional parameters, using the LSC and CVN archetypes to identify characteristic regions in which turbulence generation is dominated by Langmuir and destabilizing buoyancy forcing, respectively. Once identification/sorting has been made in the nondimensional parameter space, in section 6 we check that scaling based on the identified single process is consistent with observed vertical velocity variances, for example, if cases identified as dominated by convection indeed have variances consistent with scaling by

## 2. Nondimensionalization of the equations of motion

In cases where all three turbulence-generating processes are present, we seek a nondimensionalization of the momentum equation to identify situations in which only one of the three dominates the production and ensuing characteristics of the turbulent field; by default, this also identifies situations that do not have a dominant forcing, that is, that must be accepted as produced by a mixture of forcings.

*i*th component of (total) wave-averaged velocity,

*n*th component of fluid vorticity, and

For

Appropriate nondimensionalization of the momentum equation, involving specification of any two of time, length, and velocity scales, should yield parameters gauging relative strengths of the three forcing mechanisms. Because surface wind stress drives both “ordinary” and Langmuir turbulence, *e*-folding depth of the Stokes velocity associated with a single wave of wavenumber

It has become generally accepted that the presence of Langmuir circulations decreases mean shear in the bulk of the mixing layer [McWilliams et al. (1997); Gargett and Wells (2007), hereafter GW07; Tejada-Martinez and Grosch (2007), hereafter TMG07, and subsequent LES studies]. We consider this decreased mean shear as an effect rather than a cause, interpreting

Previous deep-water single-wave scalings involve an additional parameter

Summary of velocities and velocity scales: parameters defined in text. Stokes shear, required for computation of

*O*(10

^{4}) or larger; hence, viscous effects are subsequently ignored].

## 3. Observational data

Nearly continuous observations were taken from mid-May through October 2003 at Node B of the LEO15 cabled observatory, a shallow (15 m) site approximately 6 km off of the coast of New Jersey (39°27.69′N, 74°14.68′W). Here, homogeneous water columns are normally associated with downwelling winds and surface buoyancy fluxes that are destabilizing or at most weakly stabilizing, conditions occupying a significant fraction of the annual cycle, from early fall through late spring.

Velocities

Horizontal velocities and turbulent stresses were calculated under respective assumptions of first- and second-order homogeneity over beam spread (GW07). The response function analysis of Gargett et al. (2009) shows that horizontal scales associated with the full-depth turbulent structures considered here are large enough that beam separation effects do not significantly affect first-order estimates of horizontal velocity variances for retained scales. “Mean” flow

A fundamental metric used to classify turbulence is

Atmospheric data were taken at a meteorological tower located on the beach to the west of Node B. Backed by an extensive marsh, the tower has excellent exposure: tower wind speed and direction are highly correlated with those measured at a nearby offshore buoy (Münchow and Chant 2000). Before computing derived quantities such as

Because of the focus on competition among Langmuir, stress, and destabilizing buoyancy forcing, records with destabilizing surface buoyancy (heat) flux were selected from all available periods when the water column was effectively unstratified, as defined above. Records used cover a wide range of forcing, from nearly calm through typical 1–2-day storm conditions. Record-averaged winds range from nearly 0 to 13 m s^{−1} and wave conditions range from gentle swell to fully developed seas. A final selection criterion required that the peak of the Stokes function should be resolved below the maximum frequency used in the band-limited estimate of

## 4. Archetypes of full-depth Langmuir circulation and unstable convection

A suite of large-eddy characteristics is used to define “archetypes” for two end members of mixed forcing, one case in which the large-eddy turbulent structures are LSC, the full-depth Langmuir cells termed Langmuir supercells by Gargett et al. (2004), and another (CVN) in which they demonstrate characteristics of convection in a bounded domain. Although only a single record is presented in detail in each case, records with similar forcing conditions have similar characteristics.

### a. Vertical velocity variance and backscatter patterns

Figure 2 depicts fields of fluctuation vertical velocity and backscatter amplitude

### b. Horizontal velocity variances and horizontal anisotropy

The two turbulent flows seen in Fig. 2 have very different associated mean flows, velocity variances and stresses, and degrees of horizontal anisotropy. Defining total velocity

In contrast, record 161.008 has small mean velocities (Fig. 3d) and turbulent velocity variances (Fig. 3e) that are much weaker than those of LSC (note scale changes). All three shear stresses are near zero and the turbulence is approximately horizontally isotropic throughout the water column. Vertical velocity variance is smaller than horizontal variances.

### c. Profile traces in the Lumley triangle

Measurement of profiles of the three-dimensional turbulent velocity field enables calculation of the depth map of Lumley invariants [Lumley 1978; Simonsen and Krogstad 2005; the form shown in Fig. 4 is that of Pope (2000)]. As seen in TMG07, stress-driven turbulent boundary layers have a depth trajectory that begins (at the wall, where

The CVN record is characterized by a very different Lumley map (Fig. 4b). The trajectory begins well away from the upper two-dimensional boundary, indicating persistence (relative to stress or Langmuir-dominated flows) of significant vertical velocity variance near the bottom, and subsequently remains within the interior of the triangle. Although the trace “jumps” from one side to the other of the central axis of the triangle as a result of noise in the weak shear stresses, there is a left-hand (

All of the characteristics described above for record 043.024 are consistent with identification as full-depth Langmuir circulations (as detailed further in the coupled observational and computational studies of GW07 and TMG07). Identification of record 161.008 as an archetype for convective dominance (i.e., CVN) rests on a number of features. First, the large-eddy structures are horizontally isotropic, as in the convective atmospheric boundary layer. Vertical velocity variance that is smaller than horizontal, unlike the atmospheric case where it is of the same order of magnitude, Lenschow et al. (1980), is nevertheless consistent with the continuity relationship

The horizontal scale of turbulent structures in each case can be estimated using known features, wavelet analysis, and measurements of an appropriate advection velocity to predict apparent periods as a function of time. GW07 showed that apparent period in the LSC event of Fig. 6 was well predicted by an assumption of structures with large downwind scale and fixed crosswind scale, advected by mean crosswind velocity. Crosswind scale thus predicted was ~(4–6)*H*, in rough agreement with horizontal scales of *H*.

## 5. Identification of dominant forcing

In this section, forcing regimes giving rise to the two archetypes defined above are described using a suite of derived variables. Turbulence in these fundamentally different regimes is then shown to occupy distinctive regions in the space of

### a. Characteristics of forcing fields associated with LSC and CVN archetypes

*Q*> 0) at night and stabilizing gain during the day; characteristically, daytime heat gains are minimal during the storm event marked by arrows, presumably the result of cloud cover. Filled circles denote qualified records used in subsequent analyses. Figure 6d shows various velocity scales plotted on a (discontinuous) common scale. Bottom stress velocityis calculated as

^{−1}in record 043.022) that is an order of magnitude larger than

The session containing the convective archetype 161.008 has very different forcing characteristics (Fig. 7). Although

### b. Location of archetypes in the plane

Figure 8 illustrates how the space of the nondimensional parameters

The remaining qualified records in each session lie at intermediate values, occupying a continuum between LSC and CVN end members in terms of both location in the

### c. The complete dataset in the plane

Figure 9 shows the distribution of 170 qualified records in the *e*-folding depth

Also of note in Fig. 9 is the relative paucity of points near the CVN archetype, relative to those near the LSC archetype. Dependence of

## 6. Scaling of turbulent vertical velocity variance

We have used the parameters La and Ra that result from the scaling of Eq. (14) to identify records that should be dominated by a single type of turbulence forcing. Once that identification has been made, one expects that velocity and length scales will be those appropriate to the single process thus identified. We now consider whether such a single process scaling velocity indeed provides acceptable normalization of observed vertical velocity variance in those cases identified as dominated by either convection or Langmuir forcings (in the absence of any identified as dominated by stress forcing).

*u**, (Fig. 10b) Langmuir velocity scaleand (Fig. 10c) convective velocity scale

A successful scaling is one that produces constant scaled variance with minimal scatter. The color-coded results of Fig. 10, where values of scaled variance of *O*(1) are blue, suggest that convective scaling with

Mean and std (% of mean) of

^{−1}is associated with

^{−1}, in reasonable agreement with an anecdotal value of 3 m s

^{−1}necessary for generation of LC [Pollard (1976) and references therein]. The slope agrees with that found in the Lake Ontario measurements of Kitaigorodskii et al. (1983) and with the relationship

When a linear relationship like (21) exists, scaling with *C* = 1.4–1.7 (Panofsky 1973). The observed value of *C* = ~3 (Table 2, LC Region) might thus imply velocities significantly in excess of stress driven. However while present results are suggestive, error bounds (~50%) are sufficiently large that *C* = 1.4–1.7 cannot be ruled out. The question of the relevance of

Note that

## 7. Discussion

All qualified data are presented in the three-dimensional space of *n* = ~2.

A second, implicit, assumption made in the present analysis is that the observed turbulence is steady state, that is, adjusts instantly to changes in forcings (instantly is defined here as within the record period of ~2.2 h over which both are averaged). It is widely accepted that turbulence adjusts to forcing change within one to a few large-eddy overturning time scales; for full-depth turbulent structures, this time scale ^{−1} for these events yields ^{−1},

## 8. Conclusions

Using an extensive set of data characterizing the large eddies of full-depth turbulence under a wide range of surface-forcing conditions, it has been demonstrated that situations dominated by either Langmuir vortex forcing or destabilizing surface heat flux can be identified by distinct locations in the plane of

The above conclusions hold only if bottom boundary layer turbulence associated with pressure gradient forcing like tides is negligible. A third nondimensional number

For values of

Examination of possible normalizations of turbulent vertical velocity variance

Similar observations in locations with different depths, tidal magnitudes, et cetera, are required to discover whether the present results at an inner-shelf location characterized by weak tides are applicable to other depth-limited systems. Preliminary results from a deeper (26 m) site with stronger tides (Savidge et al. 2008) show a similar distribution of data in

Another question is whether results obtained in a depth-limited system are applicable to the deep-water ocean surface layer. In a depth-limited system, coherent full-depth LC (LSC) are obtained both in steadily forced LES (TMG07) and in observations (GW07). LES of this case show that steady state is achieved rapidly because a depth-limited stress-driven flow contains large scale coherent but weak structures called Couette cells (Papavassiliou and Hanratty 1997; TMG07) that transition quickly to larger, stronger and highly coherent Langmuir structures upon imposition of Langmuir vortex forcing.

In deep-water LES (Skyllingstad and Denbo 1995; McWilliams et al. 1997; Tejada-Martínez et al. 2009), surface wind stress is balanced primarily by the Coriolis force and “mean” and turbulent velocities achieve a statistical steady state only when averaged over several inertial periods (Tejada-Martínez et al. 2009). Moreover while deep-water LES typically show early development of distinctly structured small-scale LC, under steady forcing these eventually transition to less structured “Langmuir turbulence” while increasing in horizontal and (to a lesser extent) vertical scale (Skyllingstad and Denbo 1995; McWilliams et al. 1997; Tejada-Martínez et al. 2009).

Tejada-Martínez et al. (2009) suggest that the differences in both coherence and developmental time scales between deep- and shallow-water LES result from the different base structures present in the underlying stress-driven flows at the time Langmuir forcing is turned on. However, differences in boundary conditions may also contribute. Using the terminology of Pope (2000), the free-surface boundary condition is near wall resolved for the depth-limited case, but near wall modeled for the deep-water case, resulting in major differences in the role played by subgrid stress, hence potentially in characteristics of the computed turbulence. At the bottom boundary, turbulence in the depth-limited case is bounded by a solid, stress-supporting surface for which a well-established modeling framework exists. In the deep-water case, it interacts with a stratified interior below the mixing layer base, an interaction parameterized in a variety of ways. Skyllingstad and Denbo (1995), McWilliams et al. (1997), and Li et al. (2005) impose an internal wave radiation condition at the top of the stratified region, while Tejada-Martínez et al. (2009) set normal velocity to zero and tangential stresses to zero at the depth of the Ekman layer, preventing internal waves from reflecting back into the domain by a Rayleigh-damping term at the simulation base. However the actual stress at the bottom of deep ocean surface boundary layers, involving interaction with an existing internal wave field as well as local generation of internal waves, is essentially unknown. We conclude that the present results should not be applied to the deep-water case without further modeling and observational studies.

Stress exerted on the ocean is dominated by high

Research support from the National Science Foundation (OCE0136403 and OCE0927724) and NOAA (NA06RU0139) is gratefully acknowledged. The observations owe much to the skills of Christopher Powell and Shuang Huang. We gratefully acknowledge the substantial contributions made by the reviewers of this paper and those of an earlier version.

# APPENDIX

## Stokes Velocity and Stokes Shear Functions

*h*

In a multiwave case, it will be assumed that the surface wave spectrum depends only on frequency (wavenumber). Storm wind conditions at LEO15 usually involve winds from the NE, more rarely from the SE; in both conditions, locally generated seas are superimposed on swell propagating roughly westward toward the nearby shore, producing roughly symmetrical directional spectra. Although it can be argued that the geometric aspect of a directional surface wave spectrum decreases the downwind Stokes drift velocity, other mechanisms that could potentially increase it (Craik and Leibovich 1976; Garrett 1976) remain observationally unproven. Until uncertainties about the net effect of a directional spectrum are resolved, a unidirectional assumption is the most straightforward. This assumption also provides results more easily compared with LES driven by single-wave characteristics, results usefully compared with observations in previous identification of full-depth Langmuir circulations.

*e*-folding scales reduce the associated vertical velocity present at the necessarily deeper instrument depth. The magnitude of response corrections at low and high frequencies means that any underestimation of the noise level removed from the vertical velocity spectrum could potentially lead to large erroneous values in both regions, a point to which we return below.

Figure A2a presents results of Eq. (A2) for several records chosen to span the range of observed sea state, from strongly wind-forced states associated with LSC (top) to nearly calm conditions associated with CVN (bottom); Table A1 provides values of significant forcing parameters. In all panels, spectral values derived from vertical velocity spectral estimates below the average noise level are set to zero. As seen in the top two panels of Fig. A2a, the assumption involved in Eq. (A2) is verified observationally. Provided wave amplitude is significantly larger than the 0.4-m Doppler bin size,

Parameters for the records of Fig. A2:

However Stokes velocities of high-frequency (wavenumber) waves drop off rapidly with depth, hence are unlikely to contribute significantly to the generation of full-depth LC. We thus assume that a determinate Stokes velocity appropriate for assessing generation of the large-scale structures considered here can be calculated for arbitrary Stokes functions by low-pass filtering, either explicitly by band limiting the surface integral or implicitly either by evaluating Eq. (A4) at a small depth below the surface or by averaging Eq. (A4) from some small depth to the surface. Because it is desirable to use a surface Stokes velocity to facilitate numerical comparisons with most previous (single wave) observational and computational studies, the former option has been chosen. The value of *e*-folding depths, small Stokes shears, and small potential growth rates. While we assumed above that the missing contribution from high frequencies is unlikely to be important for generation of the large-scale LC considered here, the contribution to Langmuir forcing by very small–scale waves is presently not well determined by either theory or observation. However any potential contribution should scale with the band-limited value, because small-scale waves adjust rapidly to changes in forcing. It is encouraging that

The standard integration range described above is modified only in very low wind/wave conditions, when the Stokes function may consist of two peaks, a lower due to swell and a higher associated with locally generated seas, separated by a range of frequencies where

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