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
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.
(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
(a) Sample bubble plume detection in Signature 1000 echogram collected during 10-m circuit leg. Horizontal black lines indicate the average depth of plumes
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
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.
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
(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
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
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
(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
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
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
Summary of surface mixed layer length scales observed during C1–C6 shown in meters.
Conditionally averaged vertical velocities as a function of transverse distance from the downwelling center. (a) Depth-averaged vertical velocity for
Citation: Journal of Physical Oceanography 54, 9; 10.1175/JPO-D-23-0136.1
Analysis of cell aspect ratios, defined as
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
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
(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
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
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
(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 (
Because direct estimates of TKE advective fluxes were not possible using this dataset, a ratio of LT overturning (
(a) Detailed view of ε vertical structure in wave mixing layer where mean values for populations drawn from
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
Figure 13 shows bin-averaged dissipation profiles that have been calculated for subpopulations corresponding to ambient conditions (
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
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
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.
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