AUV Observations of Langmuir Turbulence in a Stratified Shelf Sea

Alexander W. Fisher aApplied Physics Laboratory, University of Washington, Seattle, Washington
bWashington State Department of Ecology, Lacy, Washington

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https://orcid.org/0000-0002-9059-4900
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Nicholas J. Nidzieko cDepartment of Geography, University of California, Santa Barbara, Santa Barbara, California

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Abstract

Measurements collected by a Remote Environmental Monitoring Units (REMUS) 600 autonomous underwater vehicle (AUV) off the coast of southern California demonstrate large-scale coherent wave-driven vortices, consistent with Langmuir turbulence (LT), and played a dominant role in structuring turbulent dissipation within the oceanic surface boundary layer. During a 10-h period with sustained wind speeds of 10 m s−1, Langmuir circulations were limited to the upper third of the surface mixed layer by persistent stratification within the water column. The ensemble-averaged circulation, calculated using conditional averaging of acoustic Doppler dual current profile (AD2CP) velocity profiles using elevated backscattering intensity associated with subsurface bubble clouds, indicates that LT vortex pairs were characterized by an energetic downwelling zone flanked by broader, weaker upwelling regions with vertical velocity magnitudes similar to previous numerical studies of LT. Horizontally distributed microstructure estimates of turbulent kinetic energy dissipation rates were lognormally distributed near the surface in the wave mixing layer with the majority of values falling between wall layer scaling and wave transport layer scaling. Partitioning dissipation rates between downwelling centers and ambient conditions suggests that LT may play a dominant role in elevating dissipation rates in the ocean surface boundary layer (OSBL) by redistributing wave-breaking turbulence.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: A. W. Fisher, afisher@apl.washington.edu

Abstract

Measurements collected by a Remote Environmental Monitoring Units (REMUS) 600 autonomous underwater vehicle (AUV) off the coast of southern California demonstrate large-scale coherent wave-driven vortices, consistent with Langmuir turbulence (LT), and played a dominant role in structuring turbulent dissipation within the oceanic surface boundary layer. During a 10-h period with sustained wind speeds of 10 m s−1, Langmuir circulations were limited to the upper third of the surface mixed layer by persistent stratification within the water column. The ensemble-averaged circulation, calculated using conditional averaging of acoustic Doppler dual current profile (AD2CP) velocity profiles using elevated backscattering intensity associated with subsurface bubble clouds, indicates that LT vortex pairs were characterized by an energetic downwelling zone flanked by broader, weaker upwelling regions with vertical velocity magnitudes similar to previous numerical studies of LT. Horizontally distributed microstructure estimates of turbulent kinetic energy dissipation rates were lognormally distributed near the surface in the wave mixing layer with the majority of values falling between wall layer scaling and wave transport layer scaling. Partitioning dissipation rates between downwelling centers and ambient conditions suggests that LT may play a dominant role in elevating dissipation rates in the ocean surface boundary layer (OSBL) by redistributing wave-breaking turbulence.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: A. W. Fisher, afisher@apl.washington.edu

1. Introduction

Turbulence dynamics in the upper ocean control the exchange of mechanical energy, momentum, heat, and gases across the air–sea interface and can dramatically affect the processes through which transport from the surface to depth occurs. Wind acts to generate turbulence directly through wind stress acting on the ocean surface and indirectly through the generation of surface gravity waves. The presence of waves fundamentally alters turbulence in the ocean surface boundary layer (OSBL) relative to classical wall shear layers resulting in turbulent dissipation rates ε that typically exceed wall layer scaling ε(u3/z) by up to two orders of magnitude (Agrawal et al. 1992; Drennan et al. 1996; Gerbi et al. 2009; Gemmrich 2010; Sutherland and Melville 2015; Thomson et al. 2016).

The turbulent kinetic energy (TKE) budget for a horizontally homogeneous flow at steady state that includes wave effects can be written as (Kitaigorodskii 1983; McWilliams et al. 1997)
uiw¯Uizuiw¯USiz+gρ0ρw¯z(12ui2w¯+1ρ0pw¯)=ε,
where primes denote the turbulent fluctuations of velocity (u=u1, υ=u2, and w=u3), pressure (p′), and density (ρ′) and overbars denote the time averaging. The coordinate system is defined such that x1 and x2 are horizontal and x3 = z is positive upward with z = 0 at the mean free surface. Capitalized variables indicate the Eulerian horizontal velocity Ui and Stokes drift velocity USi. The reference density of seawater is denoted as ρ0, and gravitational acceleration is denoted as g. The first two terms on the lhs of Eq. (1) are the Eulerian shear production and Stokes drift production, respectively. The third term on the lhs is the buoyancy flux and the fourth term on the lhs is the vertical divergence in total TKE transport, which is the sum of the turbulent TKE fluxes driven by turbulent velocity (e.g., turbulent TKE flux) and pressure (e.g., pressure work) fluctuations.
Within a shallow wave transport layer just below the surface, the TKE dissipation rate is balanced by a divergence in total TKE transport (Terray et al. 1996; Scully et al. 2016), such that dissipation rates have been shown to scale as a power-law decay (Terray et al. 1996):
εHsF0=A(zHs)λ,
where Hs is the significant wave height of the wind sea (Gerbi et al. 2009), F0 is the surface TKE flux generated by wave energy dissipation via breaking, and A and λ are the constants. A lack of consensus regarding the exact value of λ persists, but prior work has generally reported values between −2 < λ < −1 (Drennan et al. 1996; Gerbi et al. 2009; Gemmrich 2010; Sutherland and Melville 2015; Thomson et al. 2016; Zippel et al. 2018). By using the gradient diffusion hypothesis, Craig and Banner (1994) developed an analytical solution for the diffusive–dissipative balance within the wave transport layer:
εz0F0=A(1+zz0)λ,
where z0 is the surface roughness length, which scales with wave height (Zippel et al. 2018) and is related to the dominant length scale of injected surface-generated turbulence. The rapid decay of wave-breaking turbulence typically limits direct wave-breaking effects on OSBL turbulence to depths shallower than ∼10Hs (Terray et al. 1996; Sutherland and Melville 2015; Gerbi et al. 2009), such that wave breaking is likely a dominant pathway for exchange processes close to the air–sea interface, but may not play a significant role in driving entrainment near the base of the mixed layer [up to O(100) m deep].

The interaction between Stokes drift and wind-forced surface shear provides another mechanism through which waves can act to modify OSBL turbulence through the conversion of vertical vorticity into streamwise vorticity in a process predominantly attributed to the Craik–Leibovich (CL2) vortex force (Craik and Leibovich 1976; Leibovich 1983). The resulting Langmuir circulations (Langmuir 1938) are characterized by large, horizontal counterrotating vortices that are generally aligned downwave, which often have visible signatures (e.g., windrows) associated with surface-convergent downwelling zones (Weller and Price 1988). In a fully turbulent, weakly stratified OSBL, transient Langmuir cells form and dissipate episodically across a range of scales in a regime known as Langmuir turbulence (LT; McWilliams et al. 1997). Numerical studies of LT-based large-eddy simulations (LESs) have reproduced coherent wave-aligned vortices that are generally consistent with field observations (Skyllingstad and Denbo 1995; McWilliams et al. 1997; Min and Noh 2004; Sullivan et al. 2007; Grant and Belcher 2009); however, as noted by D’Asaro et al. (2014), comprehensive measurements of OSBL dynamics needed to characterize the dependency of mixed layer turbulence on surface waves are rare (Plueddemann et al. 1996; Smith 1998; Sutherland and Melville 2013). In contrast to open studies (D’Asaro et al. 2014; Li et al. 2009; Kukulka et al. 2009), detailed comparisons of data and theory made using shallow-water observations (Gargett et al. 2004; Gargett and Wells 2007; Tejada-Martínez and Grosch 2007; Gerbi et al. 2008; Kukulka et al. 2012; Scully et al. 2015; Zippel et al. 2020) have reported full-depth Langmuir cells (Gargett and Wells 2007), and significant distortion by tidal shear or bottom boundary layer turbulence (Kukulka et al. 2011; Gargett and Wells 2007; Scully et al. 2015) has been reported. Previous observations have shown that LT acts to enhance vertical turbulent velocity variance 〈w2〉 by up to a factor of 2 relative to comparable measurements made near a rigid boundary (Tseng and D’Asaro 2004; D’Asaro 2001) and that vertical motions associated with LT tend to be strongly negatively skewed (Scully et al. 2015).

The relative roles of wave breaking and Stokes production in energizing the near surface and structuring TKE within the mixed layer remain an open question. LES simulations that include representations of wave breaking and the vortex force have shown that energetic whitecapping may disrupt LT development (Sullivan et al. 2007; Kukulka and Brunner 2015) and that the redistribution of wave-breaking turbulence by large-scale LT cells can lead to locally enhanced short-term dispersion rates under convergence zones (Kukulka and Veron 2019). In the absence of wave breaking, TKE dissipation is thought to be balanced by Stokes production for |z/Hs| < 0.3, below which the turbulent TKE flux driven primarily by LT downwelling jets plays a dominant role in transporting near-surface turbulence deeper into the mixed layer (Grant and Belcher 2009). In contrast, Scully et al. (2016) showed that for observations collected in Chesapeake Bay in which LT was detected (Scully et al. 2015), TKE dissipation was balanced by a vertical divergence in pressure work consistent with wave-breaking turbulence dominating the vertical transport of TKE at |z/Hs| < 7, where the Eulerian shear was an order of magnitude less than expected by wall layer scaling (Fisher et al. 2018b) and LT was significantly distorted by tidal shear (Scully et al. 2016).

In this study, we present observations of LT in a stratified shelf sea including a characterization of the strength and geometry of near-surface circulation as well as the spatial heterogeneity of TKE dissipation. This work contributes to a small number of studies that have documented differences in turbulent quantities measured inside and outside of LT convergence zones and the role(s) of bubbles in structuring that spatial signature (Thorpe et al. 2003b; Gemmrich 2012; Zippel et al. 2020). The observations and analysis framework are described in section 2; we show in section 3 that the large-coherent vortices consistent with LT result in a distribution of elevated TKE dissipation rates in the OSBL that generally falls between law-of-the-wall and wave transport layer scalings. Finally, the specific nature of LT-driven turbulent transport of surface-generated TKE is examined in the context of wave breaking and Stokes production in section 4.

2. Methods

a. Data collection

Data were collected using a Hydroid–Kongsberg Remote Environmental Monitoring Units (REMUS) 600 autonomous underwater vehicle (AUV). The 4-m-long, propeller-driven AUV conducted a 20-h mission on 11–12 May 2022 approximately 1.5 NM south of Santa Barbara Point, California (34°22′38″N, 119°42′35″W) in a ∼52-m-deep region of slowly varying bathymetry. The vehicle was deployed in the vicinity of Santa Barbara Harbor and was initially tasked with an alongshore ingress to the sampling location under front-seat (REMUS) control. Once on station, vehicle control was transferred to the backseat robust multi-sensor technology for status monitoring in Industry 4.0 applications (ROMULUS) autonomy computer running Mission Oriented Operating Suite-Interval Programming (MOOS-IvP) software. ROMULUS was used to execute 15 transits of the stacked bowtie circuit shown in Fig. 1c, which consisted of 750-m horizontal legs oriented 10° apart at three vertical levels (z = −2, −6, and −10 m) followed by a profiling leg in which the vehicle collected a sawtooth profile between −45 < z < −2 m to resolve the mixed layer density structure. At the end of each circuit, a behavior timer was used to acquire a GPS fix prior to the next circuit. Traveling at a constant speed of 1.5 m s−1, the vehicle completed each circuit in approximately 1 h.

Fig. 1.
Fig. 1.

(a) Schematic of REMUS 600 instrumentation. (b) Event-averaged directional wave spectra shown with the orientation of mission bowtie legs (solid lines) and mean wave direction (dotted line). (c) Diagram of AUV circuit showing stacked bowtie configuration of 750-m legs.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

A moored Sofar Ocean’s Spotter wave buoy was deployed 150 m east of the northern terminus of the AUV circuit and recorded 2.5-Hz GPS-based displacement measurements, from which hourly directional wave spectra were calculated using similar methods to Herbers et al. (2012). Local surface meteorological conditions were recorded by an Airmar 200WX WeatherStation mounted approximately 1.25 m above the water line on a gateway transponder buoy (GB4A) used for acoustic communication with the vehicle during sampling. The Airmar recorded 10-min averages of wind speed, wind direction, barometric pressure, and air temperature continuously during the experiment.

To maximize the resolution of cross-wave flow structure, bowtie legs were oriented perpendicular to the predominant mean wave direction of 250°N (Fig. 1b). Swell directions in the northern reaches of the Santa Barbara Channel are largely limited to a narrow angular range out of the west due to blocking and refraction induced by the presence of Point Conception and the Channel Islands. The irregular coastline, combined with high angles of incidence along the east–west coastline, results in rapid variations in wave energy arrival (Rogers et al. 2007; Crosby et al. 2019; Romero et al. 2020). Wave–current interactions associated with strong currents and complex mixed seas in the area can also lead to spatially heterogeneous wave breaking (Romero et al. 2020). Additionally, the complex topography of the Santa Ynez Mountains acts to shelter the region from prevailing northwest winds and increase the spatial heterogeneity of local forcing. These combined effects often result in complex mixed seas where both wind seas and swell are predominantly out of the west–west-southwest (W–WSW) (O’Reilly et al. 2000).

The standard payload of the vehicle includes upward- and downward-looking 600-kHz ADCPs that are sampled at 1 Hz with a vertical bin size of 0.5 m. The downward-looking ADCP is used as both a current profiler and a Doppler velocity log (DVL) to measure the vehicle’s altitude and horizontal velocity over the bottom. At operating depths used in this study, the DVL maintained constant bottom lock resulting in high-fidelity estimates of speed over ground and geographic position. A nose-mounted Neil–Brown C-T sensor and tail-mounted Paroscientific pressure sensor recorded conductivity, temperature, and pressure, respectively, at 5 Hz. The AUV is equipped with a 9-degree-of-freedom Kearfott T24 inertial navigation system (INS) that samples vehicle attitude and motion at 100 Hz and records 1-Hz extended Kalman-filtered output.

In addition to house instrumentation, the AUV was equipped with a Rockland Scientific MicroRider-1000 microstructure package and Nortek Signature 1000 acoustic Doppler dual current profile (AD2CP) (Fig. 1a). The microstructure package includes two orthogonal shear probes that measured vertical and transverse velocity fluctuations, a FP07 fast thermistor, and SBE7-6000 microconductivity sensor that sampled at 512 Hz. Two orthogonal accelerometers provided synchronous measurements of transverse and vertical translational motion, also at 512 Hz. The upward-looking five-beam Signature 1000 was mounted in the wet payload of the vehicle and configured to sample along-beam velocity profiles at 4 Hz continuously at 0.5-m vertical resolution. In addition to broadband current profiles, the instrument was configured to sample in echosounder mode to collect high-resolution (5 mm) profiles of acoustic backscatter intensity at 4 Hz using the vertical fifth beam. An integrated attitude heading reference system (AHRS) recorded synchronous measurements of instrument motion and attitude.

b. Analysis

To distinguish circulations associated with Langmuir cells from nonturbulent fluctuations induced by surface waves, elevated volume backscattering strength Sυ associated with entrained bubble clouds was used to map velocity measurements to cell structure assuming that observed bubble clouds were primarily structured by the strength of surface-convergent downwelling at depths > 1 significant wave height. A modified implementation of the sonar equation was used to estimate backscattering strength relative to ambient surface mixed layer conditions S˜υ, which assumed a constant gain factor of the configured transducer. A sample record of backscattering strength is shown in Fig. 2 for a 10-m-deep leg of the bowtie circuit in which Langmuir cells were detected. Similar to recent results shown by Derakhti et al. (2024), the acoustic near field of the AD2CP is approximately ∼1 m as indicated by increased attenuation in the vicinity of the upward-looking transducer head in Fig. 2. As shown in Fig. 2b, observed bubble plumes with depths denoted Dlc resulted in backscattering intensities that were on average between 5 and 20 dB above ambient conditions, calculated as the median backscattering strength outside bubble plumes, that decayed with depth within the plume. This is similar to bubble cloud measurements reported by Farmer and Li (1995) and corresponds to a 3–100-fold increase in void fraction assuming a constant bubble size distribution (Vagle and Farmer 1992).

Fig. 2.
Fig. 2.

(a) Sample bubble plume detection in Signature 1000 echogram collected during 10-m circuit leg. Horizontal black lines indicate the average depth of plumes Dlc. (b) Average profile (thick line) of residual volume backscattering strength S˜υ as a function of normalized depth within bubble plumes. Shaded area represents one standard deviation from the mean.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Following the removal of low-frequency (<1/20 Hz) platform motion, Earth-relative AD2CP velocity profiles were rotated into a wave-relative coordinate system using average wave directions measured by the Spotter during each bowtie circuit. The near-neutral AUV closely follows isobars while sampling in a constant depth mode, such that vertical platform excursions within the wave frequency band are dominated by orbital motions (A. W. Fisher and N. J. Nidzieko 2023, unpublished manuscript), reducing aliasing of velocity signals by wave orbitals through sampling in a nearly wave-following vertical reference frame. Using estimates of acoustic backscatter, the downwelling centers were identified in 10-m-deep horizontal transects and used to map velocity measurements to locations within individual Langmuir cells. As noted by Plueddemann et al. (1996), the direct use of backscattering intensity may introduce additional uncertainty in the estimation of circulation because stronger circulation likely entrains higher densities of bubbles in convergent downwelling zones than weaker cells. In a similar approach to that used in Zippel et al. (2020), a binary classification of backscatter profiles was made using a threshold of S˜υ=6.5dB and downwelling centers were estimated as the mean cross-wave location of individual bubble clouds (e.g., Fig. 2a). Conditional averaging was then performed to calculate an ensemble velocity field based on a 2D spatial grid defined using a uniform 0.5-m vertical spacing and a 10-point discretization of spanwise distance normalized by estimated cell width.

The methods above provide a framework for characterizing observed turbulent circulation in shallow, horizontal AUV transects. To assess the relative roles of wind and waves as sources of turbulent energy driving those motions, we use the turbulent Langmuir number (McWilliams et al. 1997):
Lat2=u*US0,
where u* is the water-side friction velocity and US0 is the surface Stokes drift velocity. The surface value of Stokes drift in the average direction of wave propagation was calculated from measured directional wave spectra following Kenyon (1969). Due to the attenuation of wave motion due to buoy size, a f−4 tail was fit to the observed wave spectra for f > 0.8 Hz. The turbulent Langmuir number represents the ratio of wind-driven shear production to the production of TKE by Stokes shear via the vortex force (e.g., Leibovich 1983) in a shallow layer where Stokes shear is significant. Alternative definitions of Lat have been suggested due to the sensitivity of US0 to high-frequency surface gravity waves (e.g., Kukulka and Harcourt 2017). However, due to the tight coupling between wind stress and short waves within the equilibrium subrange, previous work has shown that Lat does not vary widely over realistic ocean conditions and generally falls between 0.2 and 0.5 for equilibrium conditions in the open ocean (McWilliams et al. 1997; Belcher et al. 2012). Shallow water observations have reported slightly larger values of Lat (Gargett and Wells 2007; Scully et al. 2015).
When there is sufficient heat loss at the ocean surface, the surface buoyancy flux can provide a dominant source of energy for turbulent exchange through the generation of Rayleigh–Bernard convective instabilities (Shay and Gregg 1986). To quantify the relative importance of buoyancy forcing to wave forcing, Li et al. (2005) define the Hoenikker number, which may be expressed as
Ho=2B0US0βu*2,
where B0 = αgQ/Cpρw is the surface buoyancy flux out of the ocean, 1/2β is the Stokes e-folding depth, α is the thermal expansion coefficient, Q is the net surface heat flux, and Cp is the specific heat capacity of water. Under stabilizing conditions, Ho < −1, it has been suggested that near-surface stratification prevents the generation of Langmuir turbulence. Similarly, the transition to a convection-dominant regime is thought to occur at Ho > 1.
Bulk air–sea fluxes were estimated from surface measurements, in combination with subsurface temperature observed by the AUV in the upper 2 m of the water column, using the COARE 3.5 algorithm (Fairall et al. 2003; Edson et al. 2013). Net shortwave and longwave radiation were not measured directly; instead, estimates were obtained from the NCEP North American Regional Reanalysis model for the grid cell closest to the study domain. In addition to bulk wind stress, the momentum flux required to maintain a balance between wind energy input and dissipation within the equilibrium subrange of the wave field was calculated using the Phillips (1985) analytical expression for the wave energy spectrum within the equilibrium subrange:
F(f)=4βI(p)gueq8π3f4,
where F(f) is the wave displacement spectra as a function of cyclic frequency f, β is an empirical constant, I(p) is a directional spreading function, and ueq is the air-side friction velocity required to maintain the wave field. Assuming stationary and homogeneous wind forcing, spectral levels within the equilibrium subrange are entirely determined by the balance between generation, dissipation, and redistribution by nonlinear wave–wave interactions such that the tail of the wave spectrum responds rapidly to changing wind conditions and is thought to support the majority of aerodynamic drag (Janssen 1989). Contained within this assumption, this approach presumes that wave direction within the equilibrium subrange closely follows wind direction. The equilibrium stress therefore provides an alternative estimate of the momentum flux transmitted to the water column through the wave field and has been shown to capture momentum sinks associated with the growth of young sea states (Fisher et al. 2017).

Following Banner (1990), the equilibrium subrange is defined here as f > 2fp, where fp is the peak wave frequency. Uncertainty in the empirical growth rate β (Plant 1982) is a principal source of uncertainty in the application of Eq. (6) as previously reported values vary by approximately a factor of 2 (Phillips 1985; Juszko et al. 1995; Voermans et al. 2020). By comparing observed wind speed and wave spectra, Voermans et al. (2020) found that for 10-m wind speeds > 6 m s−1, observations were reasonably approximated using a constant value of β = 0.009, which is slightly less than the originally proposed value of 0.012 (Phillips 1985; Thomson et al. 2013). To estimate ueq, Eq. (6) was fit to measured wave spectra within the equilibrium subrange assuming β = 0.011 and I(p) = 2.44. The value of the spreading parameter was determined from spectral moments following Thomson et al. (2013) and averaged for periods when wind speeds exceeded 5 m s−1.

LT effects on turbulent exchange within the surface mixed layer were evaluated through analysis of dissipation rates estimated from measured microstructure shear spectra. Assuming isotropy in the inertial subrange, the rate of turbulent kinetic energy dissipation is related to shear as follows (Oakey 1982):
ε=152ν(υx)2¯=152ν(wx)2¯=152ν0Ψ(k)dk,
where ε is the turbulent kinetic energy dissipation rate, ν is the kinematic viscosity, Ψ(k) is the wavenumber shear spectra, and υ and w are the transverse and vertical turbulent velocity fluctuations, respectively, measured along an x axis aligned with the vehicle’s centerline. The following methods are similar to previously reported results using this platform (Fisher et al. 2018a). Shear spectra were estimated from measured shear signals over 3-s data increments via ensemble averaging of five 512-point FFTs using a 50% overlapped cosine window. The corresponding FFT spatial length of 1.5 m adequately resolves the inertial subrange even at low dissipation rates and ensures high degrees of freedom for the observed range of dissipation rates; the resulting ensemble-averaged spectra have a spatial resolution of 4.5 m. Spatially averaging due to the finite size of the airfoil shear probes was adjusted following Macoun and Lueck (2004) using a half-power wavenumber response of 48 cpm. Prior to integration, the adjusted shear spectra were despiked and detrended using a 0.5-Hz high-pass Butterworth filter. The integrated MicroRider accelerometers were used to correct vehicle motion following the spectral method outlined in Goodman et al. (2006). Using the Rockland Scientific International (RSI) ODAS v4.2 MATLAB code, dissipation rates were then estimated from Nasmyth empirical spectra (Oakey 1982) by first integrating observed shear spectra for wavenumbers < 10 cpm. Based on this initial estimate, dissipation rates were calculated using either an integration (variance) method or fitting the inertial subrange of the observed spectra to Nasmyth spectra. The variance method was used for dissipation rates < 1 × 10−5 m2 s−3, which applied to nearly all of the data. The upper limit of integration was determined by the initial dissipation estimate and was restricted to wavenumbers between 10 and 150 cpm (e.g., Lueck 2016).

At approximately 0400 UTC 12 May, the responsiveness of both the orthogonal shear probes and FP07 suddenly degraded, possibly due to the probes hitting an object in the water column. The resulting microstructure shear and temperature signals collected during the 7th–15th AUV circuits were nonphysical and omitted from the analysis. To assess the quality of the remaining data, the goodness of fit between observed shear spectra and Nasmyth curves was evaluated using the figure-of-merit parameter, FoM = MAD × DOF1/2, which combines degrees of freedom (DOF) and the mean absolute deviation (MAD) into one misfit estimate that generally captures conditions when observations agree well (FoM < 1) with the Nasmyth shape and when they do not (FoM ≫ 1). Observations departed significantly from Nasmyth curves when FoM > 1.1, which is slightly more conservative than the criterion previously reported (Fer et al. 2022). Additionally, any spectra that passed the FoM criterion for which the ratio Ψ(k) to the Nasmyth curve differed by at least one order of magnitude within the inertial subrange were omitted. Approximately 5% of the data failed to meet these criteria and were omitted from further analysis.

3. Results

a. Wind, wave, and buoyancy conditions

The May 11 event was driven by sustained 10 m s−1 westerly winds that lasted 10 h and rotated from 230° to 330°N following the passage of an atmospheric warm front (Fig. 3). The event built mixed seas with significant wave heights that reached 1.5 m with average wave periods of 4 s. Following Wang and Hwang (2001), wave spectra were partitioned into wind sea and swell components by finding a separation frequency defined using wave steepness:
α(f*)=8πf*fmaxf2F(f)dfg[f*fmaxF(f)df]1/2,
where α is a frequency-dependent steepness function that describes the average steepness or waves at frequencies above f* (Hz). The characteristics of α(f*) are strongly related to short wind waves as reflected by the dependency on f2 in Eq. (8), and their cumulative nature reduces sensitivity to spectral irregularities. A separation of frequency fs that separates wind sea from dominant swell is then defined as the peak frequency of the steepness function.
Fig. 3.
Fig. 3.

(a) Ten-meter neutral wind speed estimated using COARE 3.5 colored by wind direction. The UN10 values estimated using ueq and COARE 3.5 wave-slope-dependent roughness also shown as markers. (b) Bulk air-side shear velocity (circles) shown with equilibrium shear velocity estimated from observed wave spectra (solid line). Gray shaded area corresponds to ueq values resulting from uncertainty in β as reported by Juszko et al. (1995). Asterisks indicate the bulk flux estimate which has been corrected for wave-induced pressure fluctuations as described in the text. (c) Significant wave height. (d) Peak (markers) and energy-weighted (line) wave period. (e) Bulk wave steepness of wind sea (white markers) and mixed wave field (black markers). (f) Turbulent Langmuir number estimated via Eq. (4) (solid line) and using relative angle between wind and waves (markers). Solid black bars indicate periods when Langmuir cells were detected in Signature 1000 echograms. Vertical dotted lines in all panels indicate the mean time of AUV circuits labeled sequentially C1–C15.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Throughout the wind event, in which measured wave spectra exhibited a clear f−4 spectral slope at high frequencies (Fig. 4), the equilibrium subrange estimate of the air-side friction velocity u*a was less than the COARE 3.5 estimate and exhibited less temporally variability (Fig. 3b). The event-averaged wave age, defined as cp/u*a, where cp is the phase speed associated with the peak frequency of the wind sea, was 18.2 with the youngest recorded wave age being 11. A common threshold that is used to define the point at which a wave field can be considered fully developed is cp/u*a32 (Donelan 1990; Edson et al. 2013), such that young wave ages measured in this event suggest that the wind sea was in an active state of growth toward equilibrium.

Fig. 4.
Fig. 4.

Spotter surface displacement spectra colored by observed wind speed. During the wind event, a clear f−4 equilibrium subrange is present.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Comparison of COARE 3.5 estimates of UN10 with other available nearby observations (NDBC stations NTBC1 and 46053) indicates that the high-frequency variation present between 22 and 27 h after midnight 5/11 was inconsistent with other regional time series of the wind event and exceeded offshore wind speeds (NDBC 46053). In contrast, estimates of UN10 based on ueq using COARE 3.5 wave-dependent formulations of roughness defined by Edson et al. (2013) and calculated following Voermans et al. (2020) did not exceed 15 m s−1 or exhibit similar large peaks. Given the measurement height of the Airmar (1.25 m), which was comparable to the significant wave height during the experiment, it is possible that bulk estimates of UN10 were biased high by preferentially sampling wave-coherent airflow in the atmospheric wave boundary layer (WBL; Janssen 1989) and periodic sheltering of the anemometer by large wave crests. Previous studies have demonstrated that mean wind profiles within the WBL can decrease more rapidly than expected for a log profile leading to an overestimation of 10-m conditions when adjusted from the measurement height (Babanin et al. 2018; Husain et al. 2022).

Corresponding air-side friction velocity estimates are shown in Fig. 3b. Equilibrium stress values corresponding to previously reported uncertainties in the empirical growth rate (β = 0.0122 ± 3.6 × 10−3 Juszko et al. 1995) are shown as well as u*a estimates that have been corrected for wave-coherent airflow following Hristov and Ruiz-Plancarte (2014) [Eq. (25) therein]. We note that, like mean wind speed measurements, parameterized β values do not account for changes in the ratio of wind curvature to shear (Miles 1957) or other modifications to an assumed logarithmic near-surface wind profile (Plant 1982; Janssen 1989, 1991). The Janssen (1999) formulation of the pressure work term within the atmospheric TKE budget was used to specify a reasonable wind deficit that decayed exponentially with height. Following the subtraction of the estimated wind deficit from measured wind speed, COARE 3.5 was rerun on the adjusted time series to produce new estimates of u*a. Uncertainty in β corresponds to an approximately 30% change in estimates of ueq, and correcting for wave-induced pressure effects reduced bulk u*a (UN10) estimates by 15% (10%). We note that during the beginning of the record, both estimates largely overlap; however, wind–wave misalignment contributed to increased uncertainty in both parameters at the end of the wind event (26–29 h). Additionally, the unusual peaks in bulk estimates of UN10 could not be accounted for using a constant height adjustment for wave-induced pressure effects. Without direct, spectral wind stress measurements and given the possible bias in GB4A wind measurements, ueq was used as a direct proxy of u*a for the remainder of analysis.

Values of Lat calculated using ueq averaged 0.4 during the wind event (Fig. 3f). Because the relative angle between average wave direction and wind direction θww varied by as much as 60° during the event, an estimate of Lat that accounts for wind–wave misalignment Lat2=u*cos(θww)/US0 is also shown. During periods when Langmuir cells were detected, both formulations of Lat resulted in similar ratios of wind to wave forcing. As such, Eq. (4) was used in the scaling analysis for the remainder of the paper. Estimates of Ho based on COARE 3.5 bulk fluxes indicate that generally |Ho| < 0.1 during periods when Lat < 0.5, with values of 0 < Ho < 0.01 associated with destabilizing surface buoyancy fluxes. As winds relaxed and the surface buoyancy flux became negative, Ho < −0.1, indicating that a stabilizing surface heat flux was generally not strong enough to prevent LT generation during the latter half of the event (not shown).

Direct measurements of breaking waves are difficult, often requiring the visual detection of individual whitecaps at the sea surface, which were not collected during this study. Rather, bulk wave steepness was used to estimate breaking rates based on spectral observations utilizing a parametric breaking model. Bulk steepness was calculated based on both the full spectrum and the wind sea following Eq. (9):
s=Hskmtanh(kmd).
The mean wavenumber km in Eq. (9) is calculated using linear wave theory given water depth d. Results shown in Fig. 3e indicate that throughout the event, s < 0.4 consistent with limiting steepness values reported in previous studies (Drazen et al. 2008; Filipot et al. 2010; Zippel and Thomson 2017) conducted in deep-to-intermediate wave environments. Bulk steepness ranged between 0.2 and 0.35 for the full spectrum and 0.28–0.39 within the wind sea during periods of sustained wind forcing, which corresponds to an average breaking fraction of 7.5 × 10−3 and 1.5 × 10−2, respectively, when estimated using the Chawla and Kirby (2002) single-parameter breaking model. These relatively high breaking fraction estimates indicate that energetic whitecapping was likely occurring throughout the event, serving as a dominant pathway for the transfer of momentum and energy into the water column.
Throughout the wind event, the upper 40 m of the water column remained weak to moderately stratified (Fig. 5a) and exhibited nearly linear stable stratification during the first 4 h of the experiment. Surface mixed layer depth Hm, estimated as the minimum depth for which N2 > 9 × 10−5 s−2, deepened from 19 to 26 m between 1900 and 2300 UTC 11 May before rapidly shoaling to 4 m when a well-mixed, deep-water mass moved north onto the shelf (Figs. 5b,c). The observed deepening rate of ∼2 m h−1 was consistent with the simple analytical model proposed by Trowbridge (1992) for a wind-forced, rigid-lid OSBL with linearly varying stable stratification:
HmHmt=CRic1/2u*2N,
where C = 1.22 is an empirical constant and Ric = 1/4 is the critical value of the gradient Richardson number. Average values of u* and N¯20 over the first four AUV circuits were used in Eq. (10), where N¯20 is the depth-averaged value of the Brunt–Väisälä frequency N over the upper 20 m of the water column. In contrast to observations by Smith (1992) and Plueddemann et al. (1996), this suggests that wave-driven mixing did not play a significant role in deepening the mixed layer during this experiment. Current speeds within the surface mixed layer exceeded 35 cm s−1 near the surface with significant shear (Fig. 6) near the base of the mixed layer that changed rapidly in response to wind and baroclinic forcing.
Fig. 5.
Fig. 5.

(a) Density structure shown with mixed layer depth (white line) estimated using a threshold of N2 = 9 × 10−5. The Trowbridge (1992) analytical solution for mixed layer deepening is shown as a black line. (b) East/west (c) and north/south water velocities shown with density anomaly contours.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Fig. 6.
Fig. 6.

Bin-averaged vertical shear normalized by wall layer scaling shown with standard error bars as a function of depth within the surface mixed layer. Horizontal dashed lines indicate sampling depths of 2, 6, and 10 m.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

b. Langmuir cell structure

Bubble clouds extending to 9 m deep were detected in AD2CP echograms during the first eight circuits of the AUV mission as depicted in Fig. 3f. Cell geometry was inferred from acoustic bubble signatures, such that the depth of individual plumes was estimated as the maximum depth for which the median backscatter at a given depth within a plume exceeded background levels by 4 dB. Plume depth Dlc was then determined from plume-averaged vertical backscatter profiles, which were spatially averaged using a 0.5-m-centered window. Horizontal cell spacing Wlc was calculated as the across-wave distance between adjacent downwelling centers, such that individual vortex widths were estimated as Wlc/2. Distributions of bubble plume depth and spacing measured during periods when LT was present are shown in Fig. 7. The median plume depth varied little during the first 6 h of the event when Ho was positive, deepening from 6 to 6.5 m before decreasing to 5.5 m during periods when −0.1 < Ho < 0. Horizontal cell spacing appeared lognormally distributed with the majority of observations falling below the average mixed layer depth a median value close to 14 m during the first 6 h of the experiment. These results are comparable to previously reported backscatter associated with Langmuir turbulence (Farmer and Li 1995; Thorpe et al. 2003a); however, no accompanying measurements of cloud depths were available in those studies. As stratification increased, Wlc increased to ∼30 m. Sparse ∼5-m-deep bubble clouds were detected during the ninth circuit, but were too few in number to estimate cell statistics. Favorable values of Lat and Ho during this period suggest that cell formation was suppressed due to rapid shoaling of isopycnals and/or a reduction in wave breaking resulting in a highly intermittent field of downwelling injections rather than a well-developed LT field. A summary of length scales associated with observed LT cells and mixed layer stratification is shown in Table 1.

Fig. 7.
Fig. 7.

Langmuir cell statistics during the 11 May wind event: (a) cell depth and (b) cross-wave cell spacing. Thick vertical lines in both panels indicate the median value of the distribution. The dashed line in (b) indicates the average mixed layer depth.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Table 1.

Summary of surface mixed layer length scales observed during C1–C6 shown in meters.

Table 1.

Conditionally averaged AD2CP vertical velocities indicate that observed bubble clouds were coincident with intensified downwelling jets flanked by broader, weaker upwelling zones consistent with surface-convergent counterrotating cells typical of Langmuir turbulence (Fig. 8). In an ensemble sense, the spanwise extent of downwelling regions was approximately 67% of upwelling regions with corresponding depth-averaged velocity magnitudes that were generally more than twice as strong. By assuming a balance between Stokes shear production and TKE dissipation, several studies have suggested that the appropriate velocity scaling for Langmuir turbulence is (Smith 1996; Min and Noh 2004; Harcourt and D’Asaro 2008; Grant and Belcher 2009; Belcher et al. 2012; Sutherland et al. 2014)
w*L=1Lat2/3u*=(u*2US0)1/3.
The vortex force acts to increase vertical and transverse turbulent kinetic energy variance above values expected for wall-bounded shear flows, which have been documented by a number of prior observational (D’Asaro 2001; Tseng and D’Asaro 2004; Scully et al. 2015) and numerical LES studies (Min and Noh 2004; Li et al. 2005; Sullivan et al. 2007; Grant and Belcher 2009). Depth-averaged vertical velocities shown in Fig. 8a agree well with w*L with normalized downwelling intensities close to 1 near the ocean surface, supporting the use of Eq. (11) as the appropriate scaling for Langmuir turbulence. Vertical turbulent kinetic energy (VKE) estimated as the spanwise-averaged vertical velocity squared w2/u*2 decayed rapidly with depth in a manner consistent with previous studies of Langmuir cells in homogeneous water (Fig. 8c). Observations agree well with recent LES results by Kukulka and Harcourt (2017) for monochromatic wave conditions defined using the peak wavenumber of the wind sea (k = 0.63 m−1) in the absence of stratification. In contrast to the monochromatic conditions simulated in that study, mixed seas present during this experiment had Stokes drift decay scales that were dominated by the wind sea near surface and increased with depth due to the presence of swell. A clear subsurface maximum was present below z = −1.5 m, suggesting that the peak of the VKE profile was not resolved and may have been closer to the surface as demonstrated by numerous LES studies (e.g., Fig. 8c).
Fig. 8.
Fig. 8.

Conditionally averaged vertical velocities as a function of transverse distance from the downwelling center. (a) Depth-averaged vertical velocity for zh˜ as a function of distance normalized by cell width. (b) Vertical velocity structure as a function of normalized cross-cell distance and depth. In both panels, vertical velocities have been normalized by w*L. (c) Normalized VKE profile shown with Kukulka and Harcourt (2017) LES results (black line) for monochromatic wave conditions (k = 0.63 m−1). Bars in (b) and (c) indicate one standard error.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

To determine the impact of stable stratification on the distribution of VKE, a critical mixing depth is calculated using a Langmuir Froude number [Eq. (12)] similar to that defined by Li and Garrett (1997):
Frlc=w*LNh˜.
When Flc is high, downwelling jets associated with LT may penetrate stable stratification and entrain water leading to a deepening of the surface mixed layer (e.g., Kukulka et al. 2010) before eventually reaching a stable limit (z=h˜) when wave-driven mixed layer deepening is arrested. A critical value of Frlc = 0.5, which is slightly less than Frlc = 0.6 originally suggested by Li and Garrett (1997), yields mixing depths that averaged 7 m and agreed well with observed distributions of Dlc shown in Fig. 7a as well as ensemble cell velocity profiles shown in Fig. 8. Critical mixing depths h˜ are generally consistent with the observed decay of VKE, indicating that LT penetration depth was arrested by stable stratification at |z/Hm| > 0.35.

Analysis of cell aspect ratios, defined as Wlc/2Dlc, indicates that LT cells had average aspect ratios close to 1 (Fig. 9) similar to previous observations made in deep-water wave conditions (Plueddemann et al. 1996; Zippel et al. 2020) prior to the arrival of the deep-water mass. As isopycnals shoaled, average cell aspect ratios increased to values 1.5<Wlc/2Dlc<3, indicating that an increase in near-surface stratification contributed to a horizontal stretching of the LT field in a similar manner to previous shallow-water observations of full-depth LT Gargett and Wells (2007).

Fig. 9.
Fig. 9.

Langmuir cell aspect ratio (black markers) and the ratio of overturning time scale to crosswind advective time scale (white markers) shown with 95% confidence limits.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

To determine the extent to which LT cell geometry was deformed by current shear, rather than suppression of vertical motions by stable stratification within the mixed layer, an advective time scale associated with cross-wave shear is defined as Tadv=(Wlc/2Dlc)(V/z)1 following Kukulka et al. (2011). By comparing the advective time scale to the time scale associated with LT overturning Tlc=Dlc/w*L, the relative importance of differential advection by cross-wave sheared currents in modifying cell geometry may be assessed. Results shown in Fig. 9 indicate that during times when LT was present, 0.4<Tadv/Tlc<1.8, indicating that energetic turbulent overturning was occurring at similar time scales to differential horizontal advection within the upper water column. It is therefore likely that variable near-surface stratification and cross-shelf current structure may have acted to distort Langmuir cells, particularly during the relaxation of the wind event.

c. The vertical distribution of TKE dissipation

To characterize the vertical structure of TKE dissipation rates in the presence of LT, distributions of shear probe ε estimates were calculated as a function of normalized depth z/Hs with Hs corresponding to the wind sea, using data from the first six AUV circuits when cell geometry statistics were relatively constant. The proportion of measurements collected at each horizontal level of the bowtie circuit is shown using stacked bar colors that denote the sampling depth. Results are shown in Fig. 10 with the corresponding law-of-the-wall and wave transport layer [Eq. (2)] scalings as well as LES results from Sullivan et al. (2007) that included stochastic wave breaking and vortex force effects. The surface TKE flux was estimated following Craig and Banner (1994) using Gt = 90, which is within the range of values used in previous studies of young seas at wave ages for which Terray et al. (1996) found Gt to be roughly constant. A majority of observations at z/Hs > −7 fell between law-of-the-wall and Terray et al. (1996) scalings with mean values generally exhibiting a similar decay rate to the LES results of Sullivan et al. (2007) and previous observations made below the wave-breaking layer (Thorpe et al. 2003b; Sutherland et al. 2014). At depths below z/Hs < −7, measured dissipation rates decayed with depth but generally exceeded all surface scaling, eventually increasing with depth for z/Hs < −15. Near the surface and at depths zh˜, TKE dissipation was generally lognormally distributed with kurtosis and skewness values of log-transformed data close to 3 and 0, respectively (Figs. 10b,c). Near the base of the wave mixing layer, ε distributions were markedly different and exhibited strong positive skew and large kurtosis values. We hypothesize that this departure from lognormality at the base of wave mixing layer is indicative of energetic mixing events associated with large cells acting to penetrate stable stratification and drive intermittent injections of TKE.

Fig. 10.
Fig. 10.

(a) Vertical distribution of dissipation rate as a function of normalized depth. Median (pluses) and standard mean (squares) values are shown for each distribution with bar color indicating depth of sampling. Scalings shown include surface wall layer (thin solid line), Terray et al. (1996) with Gt = 90 (thick solid line), and Sullivan et al. (2007) LES results for combined effects of wave breaking and stokes drift (dashed line; relative to Hm). (b) Kurtosis and (c) skewness of log-transformed ε distributions as a function of normalized depth. Vertical solid lines indicate Gaussian scaling.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

4. Discussion

TKE dissipation rates exhibited a high degree of heterogeneity along horizontal AUV transects with ε often varying by over an order of magnitude over distances comparable to Wlc (Fig. 11). Very few field studies have documented the horizontal variability of dissipation rates in the presence of Langmuir turbulence (Osborn et al. 1992; Thorpe et al. 2003b; Gemmrich 2012; Zippel et al. 2020), but those limited observations indicate similar heterogeneity as reported here. Similar to measurements made by Thorpe et al. (2003b) and Zippel et al. (2020), intermittent regions of elevated TKE dissipation generally coincided with elevated backscatter present in AD2CP echograms.

Fig. 11.
Fig. 11.

Sample time series of echograms and shear probe dissipation estimates collected at (a),(b) 2-, (c),(d) 6-, and (e),(f) 10-m depth during C1. Thin black lines in (a), (c), and (e) indicate the depth range of S˜υ used in conditional averaging of ε. In (b), (d), and (f), solid horizontal line indicates wall layer scaling and color indicates the magnitude of S˜υ measured 1–1.25 m above the transducer head.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Conditional averaging of dissipation estimates based on AD2CP backscattering strength measured between 1 and 1.25 m above the vehicle indicates that TKE dissipation rates were on average three times higher below downwelling centers than ambient conditions with a power-law relationship of the form ε/εambM˜υb, where S˜υ=10log10M˜υ. Logarithmic regression of the data indicates b was relatively insensitive to the depth at which measurements were taken with b approximately equal to 0.2 for data collected at 2- and 6-m depth (Fig. 12). Backscattering strengths between 9- and 8.75-m depth did not span a wide enough range of S˜υ to perform curve fitting. Because the record length used in shear probe dissipation estimates (4.5 m) is comparable to the median cell width Wlc/27m, the averaging procedure used here to report observed enhancement of ε within LT downwelling centers may be biased low.

Fig. 12.
Fig. 12.

(a) Distributions of backscattering strength between 1 and 1.25 m above AUV as a function of sampling depth. (b) Conditionally averaged dissipation rate based on residual backscattering strength. Solid lines indicate logarithmic regression to data collected at 2 m (blue) and 6 m (red) shown with shaded 95% confidence intervals. Markers show bin-averaged dissipation data.

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Consistent with prior studies that have reported elevated dissipation rates within bubble plumes beneath windrows (Thorpe et al. 2003b; Zippel et al. 2020), these results demonstrate the significant role that downwelling jets play in contributing to elevated TKE dissipation rates often observed beneath breaking waves. The monotonic increase in TKE dissipation rate with backscattering strength is consistent with the conceptual picture that stronger downwelling velocities are effective in transporting larger bubbles downward against their tendency to rise and that local shear and advection associated with energetic downwelling regions act to elevate local dissipation rates.

However, because bubble populations may act to suppress turbulence through buoyancy stratification (Gemmrich 2012) or enhance turbulence via the generation of bubble wakes (Derakhti and Kirby 2014), further work is needed to characterize the complex roles bubbles play in mediating near-surface turbulence.

A number of processes may contribute to the observed enhancement of dissipation in LT downwelling zones including preferential wave breaking in the presence of surface convergences (Zippel et al. 2020) and turbulent advection of boundary-generated turbulence into the interior of the mixed layer by elevated VKE (Thorpe et al. 2003b; Kukulka and Veron 2019). A notable difference between prior studies is the observed vertical decay of TKE dissipation within the wave mixing layer with decay rates consistent with both shear-dominant, downgradient TKE transport (∼z−1; Thorpe et al. 2003b; Sutherland et al. 2014) and a free-shear, diffusive–dissipative balance (∼z−2; Gemmrich 2012; Zippel et al. 2020) being reported. Gemmrich (2012) hypothesized that within LT convergence zones, there is a near-surface layer in which bubble-suppressed dissipation rates follow Eq. (2), below which subducted bubbles are transported downward via TKE advection resulting in enhanced dissipation levels that follow ∼z−1 scaling (e.g., Thorpe et al. 2003b).

Examining the vertical structure of subpopulations of ε corresponding to ambient (S˜υ<3dB) conditions and within downwelling centers (S˜υ>S˜υ75, where S˜υ75 is the 75th percentile of backscattering strength measured at normalized depth z/Hs) indicates that dissipation rates inside and outside of downwelling centers decayed at similar rates proportional to z−1 for |z/Hs| < 5. The close agreement between ambient conditions and surface wall layer scaling is consistent with the observed nondimensional shear profile between 2- and 6-m depth shown in Fig. 6 and suggests that LT acted to modify a background flow that was well described by a classical wind-driven log layer. In downwelling centers, dissipation rates were nearly four times higher than ambient conditions, which is similar to estimates made by Thorpe et al. (2003b) and exhibited a nearly uniform decay rate proportional to ∼z−1 for depths z>h˜, suggesting a regime in which downgradient TKE advection was occurring.

Because direct estimates of TKE advective fluxes were not possible using this dataset, a ratio of LT overturning (Tlc) to dissipation time scales is defined to determine the relative influence of vertical TKE advection in modulating observed dissipation rates. The dissipation time scale is defined as Tε3w*L2/2ε and is calculated using all dissipation rates measured between 2- and 6-m depth during the first six AUV circuits. To permit comparison of asynchronous estimates of Dlc, w*L, and ε, lognormal distributions were fit to observations of Dlc and used in combination with linearly interpolated values of w*L to generate random estimates of Tlc of equal length to Tε. Results indicate that the turbulent vertical advective time scale was nearly two orders of magnitude less than the dissipation time scale, suggesting that downwelling jets were strong enough to rapidly transport surface-generated TKE downward before it dissipated (Fig. 13). A more conservative estimate of Tε calculated using u* instead of w*L yields a distribution of Tlc/Tε with a median value of 0.28; however, as shown in Fig. 8, w*L is a more appropriate scaling for large coherent eddies observed in this study. When calculated using w*L and depth-averaged dissipation rates that included near-surface estimates specified using Eq. (2), rather than individual observations collected at 2- and 6-m depth, a mean ratio of 3.85 indicates that the advective time scale was the same order of magnitude as the dissipative time scale over the vertical extent of Langmuir cells.

Fig. 13.
Fig. 13.

(a) Detailed view of ε vertical structure in wave mixing layer where mean values for populations drawn from S˜υ<5 (circles) and S˜υ>S˜υ75 (triangles) and all data (squares) are shown with 95% confidence intervals. Terray et al. (1996) scaling shown as thin solid line. Horizontal dashed line indicates h˜. (b) Distribution of the ratio of vertical turbulent advective time scale Tlc to dissipation time scale Tε calculated using w*L (dark gray) and u* (light gray).

Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1

Stokes production and wave breaking may act as dominant generation mechanisms for elevated near-surface TKE, which is then transported downward by turbulent advection. As such, it is informative to compare the relative importance of these two processes through the ratio of surface Stokes production US0u*2 (Skyllingstad and Denbo 1995) to the TKE flux generated by whitecapping Gtu*3: US0/Gtu* (Jones and Monismith 2008). Kukulka and Harcourt (2017) found that as k increases, the relative importance of TKE flux terms decreases until the Stokes decay scale becomes smaller than the surface roughness length, at which point Stokes production only acts to energize a shallow layer comparable to the depth of a wave-breaking layer. Assuming that roughness length scales with wave height (Craig and Banner 1994; Zippel et al. 2018), the Stokes decay scale associated with the wind sea observed during this experiment (1/2 k ∼ 0.8 m) exceeds the surface roughness length (z0 = 0.3 Hs ∼ 0.2 m) indicating that while conditions favored the formation of large coherent LT cells, near-surface Stokes production may have been a relatively weak source of TKE. For conditions during which LT was observed, US0/Gtu* ranged from 0.06 to 0.23 with a mean value of 0.12 indicating that F0 was an order of magnitude larger than the surface TKE flux generated by the interaction of nonbreaking waves and currents via the CL2 vortex force.

Figure 13 shows bin-averaged dissipation profiles that have been calculated for subpopulations corresponding to ambient conditions (S˜υ<5) and downwelling centers (S˜υ>S˜υ75). For depths |z/Hs| < 5, TKE dissipation rates outside of downwelling centers generally follow wall layer scaling, while TKE dissipation rates inside downwelling zones more closely resemble scaling that arises from a diffusive–dissipative balance. This supports the conclusion that whitecapping served as the dominant source for a surface TKE flux, which was then transported downgradient by TKE advection associated with large, coherent LT cells and demonstrates the dominant role that LT plays in redistributing TKE within the wave mixing layer. A similar result was found by Kukulka and Veron (2019), where a Lagrangian analysis of LES simulations was used to show that short-term dispersion rates associated with breaking waves can be substantially enhanced beneath surface-convergent zones due to vertical transport associated with LT. The mean profile of the full dataset exhibits a decay rate similar to z−1 (as also evident in Fig. 10a), with magnitudes that are approximately a factor of 3 larger law-of-the-wall scaling and similar to previous findings by Thorpe et al. (2003b). This suggests that wave breaking in the presence of LT may act as a significant source of TKE to depths that exceed the wave transport layer and that discrepancies in the vertical decay rate of TKE dissipation in prior LT observations may be consistent with the conceptual picture proposed by Gemmrich (2012).

5. Conclusions

Observations of large, wave-driven coherent eddies and TKE dissipation rates were collected by an AUV operating off the coast of southern California, which provides evidence that LT plays a dominant role in redistributing wave-breaking turbulence within the OSBL. LT cells were limited to the upper third of the weakly stratified mixed layer in a region where energetic downwelling zones were strong enough to erode stratification (e.g., wave mixing layer) in a manner consistent with previous LES simulations. These downwelling jets, which were twice as strong as upwelling zones and exhibited bubble signatures proportional to void fractions nearly two orders of magnitude higher than the ambient fluid, had near-surface velocities that scaled as w*L and decayed with depth. Conditional averaging of shear probe dissipation estimates using AD2CP backscattering strength indicated that LT downwelling jets were primary drivers of a downgradient turbulent TKE flux, which resulted in lognormally distributed dissipation rates in the wave mixing layer with the majority of estimates falling between wall layer scaling and wave transport layer scaling. A comparison of TKE dissipation rates inside and outside of convergences demonstrates that 1) TKE dissipation rates outside of LT convergence zones were well described by law-of-the-wall scaling consistent with the observed Eulerian shear profile and 2) the observed enhancement of turbulent dissipation in LT downwelling zones, which was a factor of 4 higher than ambient conditions, was likely due to the vertical turbulent advection of wave-breaking turbulence.

This work is motivated by the importance of surface gravity waves to the turbulent exchange of momentum, heat, mechanical energy, and gases within the OSBL. These results highlight the significant role that wave-breaking turbulence and large-coherent LT cells play in structuring mixing in the upper ocean. While the relative influence of downwelling centers and vertical structure of turbulent dissipation rates are well resolved within this dataset, uncertainty in available u* estimates limits confidence in the overall magnitude of dissipation rates relative to surface scalings. Subtle differences in higher-order turbulent statistics across LT cells underscore the need for three-dimensional turbulence sampling to disentangle the relative roles of wave breaking and LT, which may act in concert to enhance mixing, dissolved gas exchange, and heat transfer in the OSBL. Future work is needed to constrain the complex interactions between waves, turbulence, and bubbles near the ocean surface and the specific manner in which coherent wave-driven motions drive spatiotemporal variability in measurements.

Acknowledgments.

Luke Carberry, Jordan Snyder, and Cecily Tye assisted with field data collection. This manuscript benefited greatly from comments by Seth Zippel and two anonymous reviewers. Support for this study was provided by grants from the National Science Foundation (NSF OCE-1829952) and the Office of Naval Research (ONR N00014-20-1-2566).

Data availability statement.

Data used in this study are made publicly available through the California Digital Library Dryad data repository: https://doi.org/10.25349/D9MW50.

REFERENCES

  • Agrawal, Y. C., E. A. Terray, M. A. Donelan, P. A. Hwang, A. J. Williams III, W. M. Drennan, K. K. Kahma, and S. A. Krtaigorodskii, 1992: Enhanced dissipation of kinetic energy beneath surface waves. Nature, 359, 219220, https://doi.org/10.1038/359219a0.

    • Search Google Scholar
    • Export Citation
  • Babanin, A. V., J. McConochie, and D. Chalikov, 2018: Winds near the surface of waves: Observations and modeling. J. Phys. Oceanogr., 48, 10791088, https://doi.org/10.1175/JPO-D-17-0009.1.

    • Search Google Scholar
    • Export Citation
  • Banner, M. L., 1990: Equilibrium spectra of wind waves. J. Phys. Oceanogr., 20, 966984, https://doi.org/10.1175/1520-0485(1990)020<0966:ESOWW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Belcher, S. E., and Coauthors, 2012: A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett., 39, L18605, https://doi.org/10.1029/2012GL052932.

    • Search Google Scholar
    • Export Citation
  • Chawla, A., and J. T. Kirby, 2002: Monochromatic and random wave breaking at blocking points. J. Geophys. Res., 107, 3067, https://doi.org/10.1029/2001JC001042.

    • Search Google Scholar
    • Export Citation
  • Craig, P. D., and M. L. Banner, 1994: Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr., 24, 25462559, https://doi.org/10.1175/1520-0485(1994)024<2546:MWETIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Craik, A. D. D., and S. Leibovich, 1976: A rational model for Langmuir circulations. J. Fluid Mech., 73, 401426, https://doi.org/10.1017/S0022112076001420.

    • Search Google Scholar
    • Export Citation
  • Crosby, S. C., N. Kumar, W. C. O’Reilly, and R. T. Guza, 2019: Regional swell transformation by backward ray tracing and swan. J. Atmos. Oceanic Technol., 36, 217229, https://doi.org/10.1175/JTECH-D-18-0123.1.

    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., 2001: Turbulent vertical kinetic energy in the ocean mixed layer. J. Phys. Oceanogr., 31, 35303537, https://doi.org/10.1175/1520-0485(2002)031<3530:TVKEIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., J. Thomson, A. Y. Shcherbina, R. R. Harcourt, M. F. Cronin, M. A. Hemer, and B. Fox-Kemper, 2014: Quantifying upper ocean turbulence driven by surface waves. Geophys. Res. Lett., 41, 102107, https://doi.org/10.1002/2013GL058193.

    • Search Google Scholar
    • Export Citation
  • Derakhti, M., and J. T. Kirby, 2014: Bubble entrainment and liquid–bubble interaction under unsteady breaking waves. J. Fluid Mech., 761, 464506, https://doi.org/10.1017/jfm.2014.637.

    • Search Google Scholar
    • Export Citation
  • Derakhti, M., J. Thomson, C. Bassett, M. Malila, and J. T. Kirby, 2024: Statistics of bubble plumes generated by breaking surface waves. J. Geophys. Res. Oceans, 129, e2023JC019753, https://doi.org/10.1029/2023JC019753.

    • Search Google Scholar
    • Export Citation
  • Donelan, M. A., 1990: Air-sea interaction. Ocean Engineering Science, B. LéMehauté and D. Hanes, Eds., Vol. 9, The Sea, Wiley, 239–292.

  • Drazen, D. A., W. K. Melville, and L. Lenain, 2008: Inertial scaling of dissipation in unsteady breaking waves. J. Fluid Mech., 611, 307332, https://doi.org/10.1017/S0022112008002826.

    • Search Google Scholar
    • Export Citation
  • Drennan, W. M., M. A. Donelan, E. A. Terray, and K. B. Katsaros, 1996: Oceanic turbulence dissipation measurements during SWADE. J. Phys. Oceanogr., 26, 808815, https://doi.org/10.1175/1520-0485(1996)026<0808:OTDMIS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Edson, J. B., and Coauthors, 2013: On the exchange of momentum over the open ocean. J. Phys. Oceanogr., 43, 15891610, https://doi.org/10.1175/JPO-D-12-0173.1.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, 2003: Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm. J. Climate, 16, 571591, https://doi.org/10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Farmer, D., and M. Li, 1995: Patterns of bubble clouds organized by Langmuir circulation. J. Phys. Oceanogr., 25, 14261440, https://doi.org/10.1175/1520-0485(1995)025<1426:POBCOB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fer, I., T. M. Baumann, Z. Koenig, M. Muilwijk, and S. Tippenhauer, 2022: Upper-ocean turbulence structure and ocean-ice drag coefficient estimates using an ascending microstructure profiler during the MOSAiC drift. J. Geophys. Res. Oceans, 127, e2022JC018751, https://doi.org/10.1029/2022JC018751.

    • Search Google Scholar
    • Export Citation
  • Filipot, J.-F., F. Ardhuin, and A. V. Babanin, 2010: A unified deep-to-shallow water wave-breaking probability parameterization. J. Geophys. Res., 115, C04022, https://doi.org/10.1029/2009JC005448.

    • Search Google Scholar
    • Export Citation
  • Fisher, A. W., L. P. Sanford, M. E. Scully, and S. E. Suttles, 2017: Surface wave effects on the translation of wind stress across the air–sea interface in a fetch-limited, coastal embayment. J. Phys. Oceanogr., 47, 19211939, https://doi.org/10.1175/JPO-D-16-0146.1.

    • Search Google Scholar
    • Export Citation
  • Fisher, A. W., N. J. Nidzieko, M. E. Scully, R. J. Chant, E. J. Hunter, and P. L. F. Mazzini, 2018a: Turbulent mixing in a far-field plume during the transition to upwelling conditions: Microstructure observations from an AUV. Geophys. Res. Lett., 45, 97659773, https://doi.org/10.1029/2018GL078543.

    • Search Google Scholar
    • Export Citation
  • Fisher, A. W., L. P. Sanford, and M. E. Scully, 2018b: Wind-wave effects on estuarine turbulence: A comparison of observations and second-moment closure predictions. J. Phys. Oceanogr., 48, 905923, https://doi.org/10.1175/JPO-D-17-0133.1.

    • Search Google Scholar
    • Export Citation
  • Gargett, A., J. Wells, A. E. Tejada-Martínez, and C. E. Grosch, 2004: Langmuir supercells: A mechanism for sediment resuspension and transport in shallow seas. Science, 306, 19251928, https://doi.org/10.1126/science.1100849.

    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and J. R. Wells, 2007: Langmuir turbulence in shallow water. Part 1. Observations. J. Fluid Mech., 576, 2761, https://doi.org/10.1017/S0022112006004575.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J., 2010: Strong turbulence in the wave crest region. J. Phys. Oceanogr., 40, 583595, https://doi.org/10.1175/2009JPO4179.1.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J., 2012: Bubble-induced turbulence suppression in Langmuir circulation. Geophys. Res. Lett., 39, L10604, https://doi.org/10.1029/2012GL051691.

    • Search Google Scholar
    • Export Citation
  • Gerbi, G. P., J. H. Trowbridge, J. B. Edson, A. J. Plueddemann, E. A. Terray, and J. J. Fredericks, 2008: Measurements of momentum and heat transfer across the air–sea interface. J. Phys. Oceanogr., 38, 10541072, https://doi.org/10.1175/2007JPO3739.1.

    • Search Google Scholar
    • Export Citation
  • Gerbi, G. P., J. H. Trowbridge, E. A. Terray, A. J. Plueddemann, and T. Kukulka, 2009: Observations of turbulence in the ocean surface boundary layer: Energetics and transport. J. Phys. Oceanogr., 39, 10771096, https://doi.org/10.1175/2008JPO4044.1.

    • Search Google Scholar
    • Export Citation
  • Goodman, L., E. R. Levine, and R. G. Lueck, 2006: On measuring the terms of the turbulent kinetic energy budget from an AUV. J. Atmos. Oceanic Technol., 23, 977990, https://doi.org/10.1175/JTECH1889.1.

    • Search Google Scholar
    • Export Citation
  • Grant, A. L. M., and S. E. Belcher, 2009: Characteristics of Langmuir turbulence in the ocean mixed layer. J. Phys. Oceanogr., 39, 18711887, https://doi.org/10.1175/2009JPO4119.1.

    • Search Google Scholar
    • Export Citation
  • Harcourt, R. R., and E. A. D’Asaro, 2008: Large-eddy simulation of Langmuir turbulence in pure wind seas. J. Phys. Oceanogr., 38, 15421562, https://doi.org/10.1175/2007JPO3842.1.

    • Search Google Scholar
    • Export Citation
  • Herbers, T. H. C., P. F. Jessen, T. T. Janssen, D. B. Colbert, and J. H. MacMahan, 2012: Observing ocean surface waves with GPS tracked buoys. J. Atmos. Oceanic Technol., 29, 944959, https://doi.org/10.1175/JTECH-D-11-00128.1.

    • Search Google Scholar
    • Export Citation
  • Hristov, T., and J. Ruiz-Plancarte, 2014: Dynamic balances in a wavy boundary layer. J. Phys. Oceanogr., 44, 31853194, https://doi.org/10.1175/JPO-D-13-0209.1.

    • Search Google Scholar
    • Export Citation
  • Husain, N. T., T. Hara, and P. P. Sullivan, 2022: Wind turbulence over misaligned surface waves and air–sea momentum flux. Part II: Waves in oblique wind. J. Phys. Oceanogr., 52, 141159, https://doi.org/10.1175/JPO-D-21-0044.1.

    • Search Google Scholar
    • Export Citation
  • Janssen, P. A. E. M., 1989: Wave-induced stress and the drag of air flow over sea waves. J. Phys. Oceanogr., 19, 745754, https://doi.org/10.1175/1520-0485(1989)019<0745:WISATD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Janssen, P. A. E. M., 1991: Quasi-linear theory of wind-wave generation applied to wave forecasting. J. Phys. Oceanogr., 21, 16311642, https://doi.org/10.1175/1520-0485(1991)021<1631:QLTOWW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Janssen, P. A. E. M., 1999: On the effect of ocean waves on the kinetic energy balance and consequences for the inertial dissipation technique. J. Phys. Oceanogr., 29, 530534, https://doi.org/10.1175/1520-0485(1999)029<0530:OTEOOW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Jones, N. L., and S. G. Monismith, 2008: The influence of whitecapping waves on the vertical structure of turbulence in a shallow estuarine embayment. J. Phys. Oceanogr., 38, 15631580, https://doi.org/10.1175/2007JPO3766.1.

    • Search Google Scholar
    • Export Citation
  • Juszko, B.-A., R. F. Marsden, and S. R. Waddell, 1995: Wind stress from wave slopes using Phillips equilibrium theory. J. Phys. Oceanogr., 25, 185203, https://doi.org/10.1175/1520-0485(1995)025<0185:WSFWSU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kenyon, K. E., 1969: Stokes drift for random gravity waves. J. Geophys. Res., 74, 69916994, https://doi.org/10.1029/JC074i028p06991.

  • Kitaigorodskii, S. A., 1983: On the theory of the equilibrium range in the spectrum of wind-generated gravity waves. J. Phys. Oceanogr., 13, 816827, https://doi.org/10.1175/1520-0485(1983)013<0816:OTTOTE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., and K. Brunner, 2015: Passive buoyant tracers in the ocean surface boundary layer: 1. Influence of equilibrium wind-waves on vertical distributions. J. Geophys. Res. Oceans, 120, 38373858, https://doi.org/10.1002/2014JC010487.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., and R. R. Harcourt, 2017: Influence of stokes drift decay scale on Langmuir turbulence. J. Phys. Oceanogr., 47, 16371656, https://doi.org/10.1175/JPO-D-16-0244.1.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., and F. Veron, 2019: Lagrangian investigation of wave-driven turbulence in the ocean surface boundary layer. J. Phys. Oceanogr., 49, 409429, https://doi.org/10.1175/JPO-D-18-0081.1.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., A. J. Plueddemann, J. H. Trowbridge, and P. P. Sullivan, 2009: Significance of Langmuir circulation in upper ocean mixing: Comparison of observations and simulations. Geophys. Res. Lett., 36, L10603, https://doi.org/10.1029/2009GL037620.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., A. J. Plueddemann, J. H. Trowbridge, and P. P. Sullivan, 2010: Rapid mixed layer deepening by the combination of Langmuir and shear instabilities: A case study. J. Phys. Oceanogr., 40, 23812400, https://doi.org/10.1175/2010JPO4403.1.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., A. J. Plueddemann, J. H. Trowbridge, and P. P. Sullivan, 2011: The influence of crosswind tidal currents on Langmuir circulation in a shallow ocean. J. Geophys. Res., 116, C08005, https://doi.org/10.1029/2011JC006971.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., A. J. Plueddemann, and P. P. Sullivan, 2012: Nonlocal transport due to Langmuir circulation in a coastal ocean. J. Geophys. Res., 117, C12007, https://doi.org/10.1029/2012JC008340.

    • Search Google Scholar
    • Export Citation
  • Langmuir, I., 1938: Surface motion of water induced by wind. Science, 87, 119123, https://doi.org/10.1126/science.87.2250.119.

  • Leibovich, S., 1983: The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech., 15, 391427, https://doi.org/10.1146/annurev.fl.15.010183.002135.

    • Search Google Scholar
    • Export Citation
  • Li, M., and C. Garrett, 1997: Mixed layer deepening due to Langmuir circulation. J. Phys. Oceanogr., 27, 121132, https://doi.org/10.1175/1520-0485(1997)027<0121:MLDDTL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Li, M., C. Garrett, and E. Skyllingstad, 2005: A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I, 52, 259278, https://doi.org/10.1016/j.dsr.2004.09.004.

    • Search Google Scholar
    • Export Citation
  • Li, M., S. Vagle, and D. M. Farmer, 2009: Large eddy simulations of upper-ocean response to a midlatitude storm and comparison with observations. J. Phys. Oceanogr., 39, 22952309, https://doi.org/10.1175/2009JPO4165.1.

    • Search Google Scholar
    • Export Citation
  • Lueck, R., 2016: Calculating the rate of dissipation of turbulent kinetic energy. RSI Tech. Note 028, 19 pp.

  • Macoun, P., and R. Lueck, 2004: Modeling the spatial response of the airfoil shear probe using different sized probes. J. Atmos. Oceanic Technol., 21, 284297, https://doi.org/10.1175/1520-0426(2004)021<0284:MTSROT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., P. P. Sullivan, and C.-H. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mech., 334, 130, https://doi.org/10.1017/S0022112096004375.

    • Search Google Scholar
    • Export Citation
  • Miles, J. W., 1957: On the generation of surface waves by shear flows. J. Fluid Mech., 3, 185204, https://doi.org/10.1017/S0022112057000567.

    • Search Google Scholar
    • Export Citation
  • Min, H. S., and Y. Noh, 2004: Influence of the surface heating on Langmuir circulation. J. Phys. Oceanogr., 34, 26302641, https://doi.org/10.1175/JPOJPO-2654.1.

    • Search Google Scholar
    • Export Citation
  • Oakey, N. S., 1982: Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr., 12, 256271, https://doi.org/10.1175/1520-0485(1982)012<0256:DOTROD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • O’Reilly, W., R. Guza, and R. Seymour, 2000: Wave prediction in the Santa Barbara channel. Proc. Fifth California Islands Symp., Camarillo, CA, Minerals Management Service, 76–80, https://sbbotanicgarden.org/wp-content/uploads/2022/08/OReilly_et-al-2002-Wave_prediction_SB_Channel.pdf.

  • Osborn, T., D. M. Farmer, S. Vagle, S. A. Thorpe, and M. Cure, 1992: Measurements of bubble plumes and turbulence from a submarine. Atmos.–Ocean, 30, 419440, https://doi.org/10.1080/07055900.1992.9649447.

    • Search Google Scholar
    • Export Citation
  • Phillips, O. M., 1985: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech., 156, 505531, https://doi.org/10.1017/S0022112085002221.

    • Search Google Scholar
    • Export Citation
  • Plant, B., 1982: A relationship between wind stress and wave slope. J. Geophys. Res., 87, 19611967, https://doi.org/10.1029/JC087iC03p01961.

    • Search Google Scholar
    • Export Citation
  • Plueddemann, A. J., J. A. Smith, D. M. Farmer, R. A. Weller, W. R. Crawford, R. Pinkel, S. Vagle, and A. Gnanadesikan, 1996: Structure and variability of Langmuir circulation during the surface waves processes program. J. Geophys. Res., 101, 35253543, https://doi.org/10.1029/95JC03282.

    • Search Google Scholar
    • Export Citation
  • Rogers, W. E., J. M. Kaihatu, L. Hsu, R. E. Jensen, J. D. Dykes, and K. T. Holland, 2007: Forecasting and hindcasting waves with the SWAN model in the Southern California bight. Coastal Eng., 54, 115, https://doi.org/10.1016/j.coastaleng.2006.06.011.

    • Search Google Scholar
    • Export Citation
  • Romero, L., D. Hypolite, and J. C. McWilliams, 2020: Submesoscale current effects on surface waves. Ocean Modell., 153, 101662, https://doi.org/10.1016/j.ocemod.2020.101662.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., A. W. Fisher, S. E. Suttles, L. P. Sanford, and W. C. Boicourt, 2015: Characterization and modulation of Langmuir circulation in Chesapeake Bay. J. Phys. Oceanogr., 45, 26212639, https://doi.org/10.1175/JPO-D-14-0239.1.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., J. H. Trowbridge, and A. W. Fisher, 2016: Observations of the transfer of energy and momentum to the oceanic surface boundary layer beneath breaking waves. J. Phys. Oceanogr., 46, 18231837, https://doi.org/10.1175/JPO-D-15-0165.1.

    • Search Google Scholar
    • Export Citation
  • Shay, T. J., and M. C. Gregg, 1986: Convectively driven turbulent mixing in the upper ocean. J. Phys. Oceanogr., 16, 17771798, https://doi.org/10.1175/1520-0485(1986)016<1777:CDTMIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Skyllingstad, E. D., and D. W. Denbo, 1995: An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer. J. Geophys. Res., 100, 85018522, https://doi.org/10.1029/94JC03202.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., 1992: Observed growth of Langmuir circulation. J. Geophys. Res., 97, 56515664, https://doi.org/10.1029/91JC03118.

  • Smith, J. A., 1996: Observations of Langmuir circulation, waves, and the mixed layer. The Air Sea Interface: Radio and Acoustic Sensing, Turbulence, and Wave Dynamics, M. A. Donelan, W. H. Hui, and W. J. Plant, Ed., University of Toronto Press, 613–622.

  • Smith, J. A., 1998: Evolution of Langmuir circulation during a storm. J. Geophys. Res., 103, 12 64912 668, https://doi.org/10.1029/97JC03611.

    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., J. C. McWilliams, and W. K. Melville, 2007: Surface gravity wave effects in the oceanic boundary layer: Large-eddy simulation with vortex force and stochastic breakers. J. Fluid Mech., 593, 405452, https://doi.org/10.1017/S002211200700897X.

    • Search Google Scholar
    • Export Citation
  • Sutherland, G., K. H. Christensen, and B. Ward, 2014: Evaluating Langmuir turbulence parameterizations in the ocean surface boundary layer. J. Geophys. Res. Oceans, 119, 18991910, https://doi.org/10.1002/2013JC009537.

    • Search Google Scholar
    • Export Citation
  • Sutherland, P., and W. K. Melville, 2013: Field measurements and scaling of ocean surface wave-breaking statistics. Geophys. Res. Lett., 40, 30473079, https://doi.org/10.1002/grl.50584.

    • Search Google Scholar
    • Export Citation
  • Sutherland, P., and W. K. Melville, 2015: Field measurements of surface and near-surface turbulence in the presence of breaking waves. J. Phys. Oceanogr., 45, 943965, https://doi.org/10.1175/JPO-D-14-0133.1.

    • Search Google Scholar
    • Export Citation
  • Tejada-Martínez, A., and C. E. Grosch, 2007: Langmuir turbulence in shallow water. Part 2. Large-eddy simulation. J. Fluid Mech., 576, 63108, https://doi.org/10.1017/S0022112006004587.

    • Search Google Scholar
    • Export Citation
  • Terray, E. A., M. A. Donelan, Y. C. Agrawal, W. M. Drennan, K. K. Kahma, A. J. Williams, P. A. Hwang, and S. A. Kitaigorodskii, 1996: Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr., 26, 792807, https://doi.org/10.1175/1520-0485(1996)026<0792:EOKEDU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thomson, J., E. A. D’Asaro, M. F. Cronin, W. E. Rogers, R. R. Harcourt, and A. Schcerbina, 2013: Waves and the equilibrium range at Ocean Weather Station P. J. Geophys. Res. Oceans, 118, 59515962, https://doi.org/10.1002/2013JC008837.