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OCTOBER 2022 FE R R I S E T A L . 2325 a,e a b c LAUR FERRIS, DONGLAI GONG, CAROL ANNE CLAYSON, SOPHIA MERRIFIELD, d e e EMILY L. SHROYER, MADISON SMITH, AND LOUIS ST.LAURENT Virginia Institute of Marine Science, William and Mary, Gloucester Point, Virginia Woods Hole Oceanographic Institution, Woods Hole, Massachusetts Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California Office of Naval Research, Washington, D.C. Applied Physics Laboratory, University of Washington, Seattle, Washington (Manuscript received 21 January 2021, in final form 25 May 2022) ABSTRACT: The ocean surface boundary layer is a gateway of energy transfer into the ocean. Wind-driven shear and meteorologically forced convection inject turbulent kinetic energy into the surface boundary layer, mixing the upper ocean and transforming its density structure. In the absence of direct observations or the capability to resolve subgrid-scale 3D turbulence in operational ocean models, the oceanography community relies on surface boundary layer similarity scalings (BLS) of shear and convective turbulence to represent this mixing. Despite their importance, near-surface mixing processes (and ubiquitous BLS representations of these processes) have been undersampled in high-energy forcing regimes such as the Southern Ocean. With the maturing of autonomous sampling platforms, there is now an opportunity to collect high- resolution spatial and temporal measurements in the full range of forcing conditions. Here, we characterize near-surface turbulence under strong wind forcing using the first long-duration glider microstructure survey of the Southern Ocean. We leverage these data to show that the measured turbulence is significantly higher than standard shear-convective BLS in the shallower parts of the surface boundary layer and lower than standard shear-convective BLS in the deeper parts of the sur- face boundary layer; the latter of which is not easily explained by present wave-effect literature. Consistent with the CBLAST (Coupled Boundary Layers and Air Sea Transfer) low winds experiment, this bias has the largest magnitude and spread in the shallowest 10% of the actively mixing layer under low-wind and breaking wave conditions, when relatively low levels of turbulent kinetic energy (TKE) in surface regime are easily biased by wave events. SIGNIFICANCE STATEMENT: Wind blows across the ocean, turbulently mixing the water close to the surface and altering its properties. Without the ability to measure turbulence in remote locations, oceanographers use approxima- tions called boundary layer scalings (BLS) to estimate the amount of turbulence caused by the wind. We compared tur- bulence measured by an underwater robot to turbulence estimated from wind speed to determine how well BLS performs in stormy places. We found that in both calm and stormy conditions, estimates are 10 times too small closest to the surface and 10 times too large deeper within the turbulently mixed surface ocean. KEYWORDS: Turbulence; Wind shear; Boundary layer; Parameterization 1. Introduction transforms North Atlantic Deep Water (NADW) first into Subantarctic Mode Water (SAMW) and eventually into The surface boundary layer is the gateway for heat, mo- Antarctic Intermediate Water (AAIW) (Abernathey et al. mentum, and gas transfer between the atmosphere and inte- 2016). The Scotia Sea east of the Drake Passage is believed to rior ocean. Turbulent kinetic energy (TKE) injected into the be a critical site of SAMW and AAIW modification and sub- upper-ocean boundary layer, together with the surface buoy- duction (Talley 1996; Sallee ´ et al. 2010), but little is known ancy flux, directly affects the depth of mixing, controls water about the formation of these water masses. Despite its impor- mass transformation, and mixes water to increase potential tance, mixing processes in the Southern Ocean have been energy of the upper-ocean structure (at the expense of TKE). undersampled, largely due to its remote location and severe As the only sector of the global ocean that connects all three conditions. major ocean basins through the meridional overturning circu- An autonomous profiling glider program called Autonomous lation (MOC), the Southern Ocean is an especially important Sampling of Southern Ocean Mixing (AUSSOM) was con- site of water mass transformation. Buoyancy forcing through ducted in the Drake Passage region between the end of air–sea exchange and interior mixing driven by internal waves austral winter and the beginning of austral spring in 2017/18. Denotes content that is immediately available upon publica- tion as open access. Publisher's Note: This article was revised on 14 October 2022 to correct typographical errors that occured in the last sentence of the Significance Statement, and in the last sentence of the para- Corresponding author: Laur Ferris, lferris@apl.washington.edu graph in which Eq. (9) appears. DOI: 10.1175/JPO-D-21-0015.1 Ó 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 2326 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG. 1. AUSSOM glider observations (2017/18). (a) Glider track with CCMPv2 winds along glider track, plotted over Operational Mercator currents (blue to yellow) from 5 Dec 2017. (b) CTD and TKE observations with Smith and Sandwell (1997) bathymetry. Vertical lines and crosses correspond to mission events. The Subantarctic Front (SAF), Polar Front (PF), and Southern ACC Front (SACCF) are labeledinwhite. AUSSOM represents the first extended glider deployment in mixing variations in the Polar Front (PF) of the Southern the Drake Passage region of the ACC (Fig. 1) and is the lon- Ocean though a full range of atmospheric forcing conditions. gest continuous glider microstructure record ever collected. The high spatial resolution and temporal extent of this dataset Unlike shipboard methods, gliders remain deployed for is also an opportunity to understand the performance of months at a time sampling though all sea states; thus, it is a boundary layer similarity scaling (BLS) through the full range first opportunity to understand turbulent dissipation rate and of meteorological forcing. OCTOBER 2022 FE R R I S E T A L . 2327 TABLE 1. Boundary layer similarity scaling (Lombardo and Gregg 1989). Showing piecewise equation used to estimate TKE dissipation rate () from water friction velocity (u ) and buoyancy flux (J ), with number of microstructure profiles described by each * b regime. Buoyancy flux sign Depth ratio Scaling Profiles of Regime J , 0 ≈ u /kz 700 Wind dominated 0 , J AML/L , 1 ≈ u /kz 218 Wind dominated b MO 1 , AML/L , 10 ≈ 1:76u /kz 1 0:58J 7 Intermediate MO b 10 , AML/L ≈ J 0 Convection dominated MO b No AML identified 7 Much of the energy for turbulent mixing is injected into the production due to Stokes shear, and neither variety of shear is surface mixed layer by a combination of buoyancy flux (con- necessarily aligned with the momentum flux uw. Several vection), wind-driven shear flow, and wind-forced surface past works have explored these additions (Agrawal et al. gravity waves (wave breaking and Langmuir circulation) 1992; Sutherland et al. 2013, 2014, 2016; D’Asaro et al. 2014; (Mackinnon et al. 2013). Due to the inherent challenges of ob- Fox-Kemper et al. 2022). servation and representation of turbulence, the community To develop BLS, the transfer of horizontal momentum in the relies on similarity scaling to estimate surface boundary layer x direction by fluctuations in vertical velocity is assumed to turbulence in a variety of observational, analytical, and be constant (Thorpe 2005) and dominated by fluctuations in ve- modeling pursuits; operational models such as HYCOM and locity rather than density such that Reynolds stress in the loga- ROMS utilize similarity scaling embedded in K-profile pa- rithmic layer is also assumed to be constant, t/r = 2r uw. o o rameterization (KPP) mixing algorithms (Monin and Obukov This shear-dominated simplification of Eq. (1) is 1954; Large et al. 1994). Turbulence parameterizations based (t/r )dU/dz: (2) on law-of-the-wall BLS are common in models (Umlauf et al. 2005), as well as analytical and observational studies. BLS lev- Friction velocity (of the water at the boundary) is given by erages fundamental results for fluid behavior at a boundary to u (t/r ),where t is wind stress and r is water density at o o estimate the turbulent dissipation caused by shear and con- * the surface. When assuming that viscous effects are negligi- vection and is a simplification of the full TKE budget. The ble in the logarithmic layer, dimensional grounds demand TKE budget, assuming the ocean is locally in steady state dU/dz = f(z)u /kz,where k =0.41is von Kar ´ man ´ ’sconstant such that TKE per unit volume is constant, can be described 2 23 (Thorpe 2005). By assuming a perfect logarithmic layer and in horizontally homogenous form (m s )by constant shear, the similarity structure function is taken to be 1 f(z) ≡ 1. Substituting into Eq. (2) gives the principal equation 0 2 wp 1 n k 2 wk r z z z for BLS of shear turbulence dU g 2 uw 2 2 rw, (1) u dz r 2 : (3) kz where (u, y, w) are turbulent velocity components, k =(u 1 In the presence of convection induced by buoyancy flux, 2 2 y 1 w )/2 is the TKE, _ denotes an average, p is the pres- Eq. (3) is adapted to include the effects of buoyancy flux (J ). sure fluctuation, n is kinematic viscosity, dU/dz is vertical shear One such adaptation (Lombardo and Gregg 1989) based on of the mean flow velocity, g is gravity, and r = 2r aT 2 bS similarity scaling of the atmospheric boundary layer is given is the density fluctuation due to temperature and salinity fluc- in Table 1, where buoyancy production is represented as a tuations T and S . The terms on the right-hand side are 1) constant function of surface flux cJ = 2gr w, where c is a pressure-driven divergence of vertical kinetic energy flux, 2) constant between 0 and 1. It is defined using the ratio of the viscous divergence of vertical kinetic energy flux, 3) vertical Monin–Obukhov length scale L = 2u /(kJ ) (the depth at MO * b turbulent transport, 4) shear production, 5) dissipation rate, which the effects of wind-driven shear are equivalent to con- and 6) buoyancy production. Just outside the region closest to vection in turbulent flows) and the actively mixing layer the boundary where viscous effects dominate (the viscous sub- (AML, the vertical extent of active turbulence, given in nega- layer), there exists a logarithmic layer (or inertial sublayer) in tive meters). Here L , which is negative in destabilizing MO which the turbulence budget is typically approximated as a conditions, describes the scale inside of which turbulence first-order balance between shear production, dissipation, and generated by wind-driven shear dominates that generated by buoyancy (terms 4–6). However, there are several issues with this simplification, which neglects wave effects and boundary sources; in the real surface boundary layer, there is addition 2 In the presence of penetrating radiation and Stokes shear pro- duction, similarity structure functions are no longer governed by the same systems of equations as in Monin–Obukhov theory. An In reality, this “logarithmic layer” is logarithmic only when excellent review of this topic is provided by Fox-Kemper et al. shear production exactly balances dissipation. (2022). 2328 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 convection. If the AML is much less than L or L . 0, it is a du /dz =(u /t)(t/z )= (u /t)/V.Here n is the molecu- MO MO 26 2 21 wind-dominated regime and convection is neglected. If the AML lar kinematic viscosity of water (∼1 3 10 m s )and u /t is significantly smaller than the L , it is a convection-dominated are velocity fluctuations measured by the shear probes. When MO regime and wind is neglected. Lombardo and Gregg (1989) tested using any package, velocity of the instrument through the water BLS during mild-to-moderate winds, focusing on times with when (V) is required to calculate turbulent dissipation. Glider micro- the ocean steadily lost buoyancy to the atmosphere such that con- structure differs from free-fall microstructure in that the veloc- vection significantly contributed to dissipation. ity of shear probes through the water is not the same as its fall Observations of turbulent dissipation are globally sparse rate. It is possible to calculate vertical glider speed using a flight (Waterhouse et al. 2014). The Southern Ocean has been noted as a model (Merckelbach et al. 2019), but the pressure-derived verti- location believed to exhibit large biases in mixed layer depth in cli- cal velocity W is sufficiently accurate for this application (Fer mate models (e.g., CESM, CCSM; Danabasoglu et al. 2012). Here, et al. 2014). Thevelocity(m s ) of the glider through the water we describe direct observation of boundary layer turbulence from V = W/sin(f 1 a) is calculated using the vertical component AUSSOM using a framework of boundary layer scalings de- of velocity, W, and glide angle, where glide angle is the sum rived from wind and buoyancy forcing. This study focuses on of pitch angle (f) and the angle of attack (a)(St. Laurent and the surface AML and its parameterization across the full range Merrifield 2017). Vertical eddy diffusivity of density K of wind forcing (up 20 m s or ∼40 kt), and it is the first step in C/N is estimated using measured turbulent dissipation rate a larger effort to combine BLS with satellite data products to (), buoyancy frequency (N ) calculated from CTD using adiabatic provide a time-varying estimate of upper-ocean mixing in the leveling, and an assumed efficiency factor of C = 0.2. We explore Southern Ocean. Understanding the physical processes and as- the collected dataset using the framework of shear-convective sociated parameterizations for turbulent mixing in the surface BLS: we implement BLS, compare to glider microstructure, and mixed layer is critical for 1) understanding energy transfer into explore the differences between observed turbulence and BLS es- the mixed layer, 2) improving OSBL flux schemes embedded timates of turbulence in the high-wind Southern Ocean. in circulation models, and 3) expanding turbulence estimations b. Boundary layer similarity scaling to satellite remote sensing platforms. In the absence of direct meteorological measurements, we harness satellite data for records of meteorological forcing, 2. Methods which are required for buoyancy flux calculations. The buoy- a. Glider observations ancy flux is calculated using A Teledyne Webb Research Slocum glider equipped with a J g Q 1 bS (E 2 P) , (5) Rockland Scientific MicroRider was used to collect a 6-week b tot o rc record of upper-ocean turbulence spanning 800 km from the Shackleton Fracture Zone to the Falkland Plateau (Fig. 1). where a and b are the expansion coefficients for heat and salin- This glider-based methodology of measuring turbulence is well ity, c is the specific heatofseawater, Q is the total heat flux p tot documented in published literature (Fer et al. 2014; St Laurent [SeaFlux CDR dataset (Clayson et al. 2016c)], S is sea surface and Merrifield 2017; Zippel et al. 2021). The glider was deployed salinity (Copernicus product Global SSS/SSD L4 Processor at 588S, 648W at the southern edge of the PF on 16 November V1.1), E is the evaporation rate (SeaFlux CDR), and P is pre- 2017 from the R/V Laurence M. Gould, sampled for 60 days cipitation (GPCP V1.3 Daily Rainfall). Friction velocity (u )is until 12 January 2018 when sensing was disabled to preserve computed from surface radiation flux (CERES_SYN1de- the battery, and was recovered near Port Stanley, Falkland g_Ed4A), winds (CCMPv2), near-surface specific humidity(Sea- Islands, on 5 February 2018. The dataset is one of the largest Flux CDR), near-surface temperature (SeaFlux CDR), and SST microstructure datasets ever collected, totaling over 3028 CTD (SeaFlux Ocean CDR) using the COARE Met Flux Algorithm profiles and 932 microstructure profiles from 0 to 350 m (totaling v3.5 (Edson et al. 2013). Wind-sea significant wave height (H )is approximately 300 000 m of microstructure profiles in 60 days). obtained from the Copernicus Global Ocean Waves Reanalysis For context, DIMES (Diapycnal and Isopycnal Mixing Experi- (WAVERYS) multiyear product, which is a global wave reanal- ment in the Southern Ocean) collected 800 000 m of profiles over ysis on a 1/58 grid, at a 3-hourly temporal resolution. Wave steep- 5 years, 8 cruises, and 1 year of ship time. It is likely the most ness (H/L) is calculated from the WAVERYS product (1/58 ever microstructure collected by a single instrument system. grid, at a 3-hourly temporal resolution) using wind wave mean The MicroRider, a glider-based sensor package for making period (T)and significant wave height from wind and swells (H) direct turbulence measurements, was used for AUSSOM. In using L=2pH/gT , and the turbulent Langmuir number is calcu- general, direct measurement of turbulence from a free-fall 1/2 lated La =(u /u ) where u is surface velocity of Stokes drift. t * s0 s0 platform assumes 3D isotropy, which allows viscous dissipa- Direct wave observations are not available. tion () of turbulent kinetic energy to be approximated by The determination of AML depth and mixed layer depth (MLD) are demonstrated by Fig. 2. Whereas the AML is de- n(du /dz ) , (4) fined by elevated turbulent dissipation, the MLD is defined by homogenous density. AML identification is completed for where z is the coordinate aligned with the shear probes, 932 microstructure profiles using a simple algorithm. The u is the water velocity component normal to z ,and steps for each microstructure profile are to 1) find the depth OCTOBER 2022 FE R R I S E T A L . 2329 FIG. 2. Mixing sections. Showing (a) turbulent dissipation with actively mixing layer (AML) depth, (b) buoyancy frequency with mixed layer depth (MLD), (c) diffusivity with AML and MLD, and (d) a case of AML identification using log-linear fit. at which a log-linear fit of surface (upper 100 m) falls to an it might be appropriate to just use the simplified version of 28 21 empirically determined background =10 Wkg (Fig. 2d); BLS in wind-dominated situations. However, the rest of our 2) discard obviously wrong fits (∼0.75% of profiles) using auto- paper uses the standard version of BLS. matic checks, and 3) interpolate good AML depths. A critical Individual microstructure and synchronous BLS profiles step in the process is excluding enhanced turbulence at depth were also integrated [Eq. (6)] toobtainthe dissipated that is unrelated to direct surface (wind or buoyancy) forcing; power associated with the observations and scaled esti- restricting polynomial fitting to the upper 100 m}empirically mates (Fig. 4d): selected to focus on surface-forced turbulence}avoids mixing min events that are unrelated to surface boundary layer physics F rdz: (6) (e.g., internal wave and forward cascade). While the polyno- AML mial coefficients are determined from data in the upper Turbulence observations and estimates were temporally 100 m, the resulting fit is allowed to extend below this depth. averaged prior to calculating the observed bias in BLS, The result is a working AML depth dataset that avoids deep log ( /). Because the time scale of mixing events is 10 BLS (e.g., internal wave related) mixing (Fig. 2a). MLD is from shorter than the temporal resolution (6 h) of the CCMPv2 glider CTD using a surface-density difference criterion of wind data, individual microstructure profiles must be aver- Dr =0.03 kg m and DT =0.28C, where the two estimates aged over some time scale (long enough that the wind product of MLD are compared for sensitivity and shallower estimate adequately represents mean turbulent dissipation but short is generally used (Dong et al. 2008). AML depth can change enough to capture changing conditions) to produce useful on a faster (∼20 m h ) time scale than the MLD; turbu- comparison to wind-based BLS profiles. A 14.5-h (inertial pe- lence of the AML works to homogenize the water column, riod) averaging interval is used. Surface boundary layer turbu- producing a mixed layer. lence is normalized by the AML depth and temporally Upon inspection (Fig. 3) it is clear that our study is wind averaged with adjacent profiles using 30 vertical bins. Finally, dominated (with less than 1% of cases invoking buoyancy flux polynomial fits are used to document the structure of the ob- into BLS) such that we can neglect convection. Two versions served bias. of boundary layer similarity scaling (BLS) are implemented (Fig. 4). The standard version (using COARE variables) ap- plies the full wind and buoyancy flux scaling (Table 1) using 3. Results u and J . We also implemented a simplified version of BLS * b a. Comparison to turbulence estimates of standard using solely u interpolated from CCMPv2, the easily accessi- shear-convective BLS ble wind product available from Remote Sensing Systems (http://www.remss.com/). With close agreement relative to the Overall, glider survey revealed interesting subsurface physics, 27 21 biases, the reader may consider for themself (Figs. 4b,d) when observing elevated turbulent dissipation rates ( =10 Wkg ) 2330 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG.3.Monin–Obukhov length scale (L ) in comparison to the actively mixing layer (AML). Note the y axis has been limited from MO 50 to 2250 m to focus on those Monin–Obukhov length scales in proximity to the AML depth. There are 385 additional points above 50 m (representing stabilizing buoyancy forcing) and 141 additional points below 2250 m (representing destabilizing-but-inconsequential buoyancy forcing). for the entire duration for which the glider sampled the core of convection (Ferris et al. 2020). Subsurface phenomena are ex- the Polar Front (Fig. 1b). Glider CTD observed some salt fin- amined in Ferris (2022). Convection forced by buoyancy flux gering and double diffusive staircases north of the PF (consistent played a minimal role in forcing the AML during the study with Merrifield et al. 2016) and sporadic diffusive/oscillatory (Fig. 3), with buoyancy rarely removed from the upper ocean FIG. 4. Boundary layer similarity scaling (BLS) showing (a) observed turbulent dissipation with actively mixing layer (AML) depth, (b) direct meteorological forcing of near-surface turbulence including the full and wind-only estimate of u , (c) turbulent dissipation esti- mated using BLS, and (d) depth-integrated energy levels (units of flux) for each observed (green) and derived (blue and black) profile. Note that estimated turbulent dissipation section derived from COARE (wind and buoyancy flux) and CCMP (wind) are visually identical such that only the latter is shown. OCTOBER 2022 FE R R I S E T A L . 2331 FIG. 5. One centered interval of BLS, (left) time-averaging (over inertial period) turbulent dissipation and (right) bias expressed as ratio of to measured in depth space. Hereafter time averaging is performed in AML-normalized BLS (dimensionless) depth space. Averaged profiles are bold. and energy for near-surface mixing predominately supplied by of near-surface TKE dissipation rates by up to four orders of wind stress. An analysis of time-averaged microstructure and magnitude. The vertical extent of this underprediction varies turbulence profiles estimated using boundary layer scaling in depth, with three strong events lagging 2–3 days after in- (Lombardo and Gregg 1989) demonstrates that the BLS turbu- tense storms; these will be revisited in section 4. Several cases lent dissipation in the shallowest depths is higher than pre- do not have the characteristic bias profile (Fig. 6b, bright red dicted by the BLS paradigm and turbulent dissipation deeper hues at the surface), which are associated with either instances within the AML is lower than predicted by BLS (see Fig. 5 for in which there are fewer than five microstructure profiles available within the 14.5-h interval for averaging (21 and an example profile), consistent with Merrifield’s (2016) bulk analysis of tow-yo VMP transects from DIMES US5. 30 November), or profiles overlying the continental rise or A section of this bias is shown in Fig. 6c, with blue hues shelf (after 22 December). Few profiles available for averag- (red hues) indicating underprediction (overprediction) of tur- ing is an obvious factor in inconsistent BLS bias due to higher bulence in the surface boundary layer, with underprediction statistical uncertainty [see Moum (2021) for a recent review]. 2332 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG. 6. Bias of BLS showing (a) friction velocity u and wind-sea significant wave height H over glider, (b) availability of microstruc- * s ture and associated BLS profiles for 14.5-h temporal average, (c) BLS bias in the normalized AML, and (d) observed turbulent dissipa- tion rates depth normalized by the AML. Also showing (e) wind direction as a function of time, with 08 and 908 indicating wind toward the north and east, respectively, and total wind speed (m s ) as color axis. OCTOBER 2022 FE R R I S E T A L . 2333 FIG. 7. Histograms for bias in the (a) near-surface (blue) and deeper (red) AML. (b) Full dataset polynomial fit (dotted black) with 95% confidence intervals (dotted magenta). Additionally, polynomial fits for the mean (solid black) and standard deviation (solid magenta) of BLS bias are computed using a moving vertical window. The similarity of observed turbulence to BLS does not de- polynomials (Fig. 7b), z ˆ 0:1, which is the same regardless of pend on whether wind inflection (wind speed increasing or de- whetherbiasisdefined log ( /)orln( /). The near- 10 BLS BLS creasing), nor proximity to Polar Front. surface AML exhibits a larger standard deviation in bias (Fig. 7a) Before documenting the character and magnitude of the than the deeper AML, suggesting wave dynamics at the air–sea bias (Fig. 6c), we place several restrictions on the data. Pro- interface is a significant factor. files are excluded (181 profiles or ∼19.4%) because 1) the pro- b. Controls on bias in two depth regimes file does not have a recognizable AML, 2) the profile is over Next, we examine controls on the normalized bias (Figs. 8–10) the continental rise or shelf and thus likely contaminated by including friction velocity (u ), wind-sea significant wave height elevated bottom boundary layer mixing, or 3) there are no (H ), and turbulent Langmuir number (La ). Parameters u and measurements in an entire vertical bin of a temporal average. s t * H mirror each other such that they are a reasonable proxy Profiles are normalized by AML depth and measurements be- for one another. We separate turbulence estimates into a yond the AML are omitted from analysis. After quality control, near-surface regime and a deeper regime as in Fig. 7a. We ob- bias is quantified in two ways (Fig. 7b): a full dataset polyno- serve that wind speed (Fig. 8) has an inverse effect on the magni- mial fit, and polynomial fitfor themean m(z)= ln( /)and BLS tude of near-surface underestimation (m = 20.574 low wind the standard deviation s(z) of the depth-dependent probability versus m = 0.099 high wind), with larger biases in low-wind condi- distribution function (PDF) fit to individual PDFs computed tions, but a direct effect on the magnitude of deep overestimation from a moving vertical window. Polynomial fits j(z ˆ ) of ln( /) BLS (m = 0.345 low wind versus m = 0.491 high wind). Wave breaking and its standard deviation are given by (Fig. 9) has a direct effect on the magnitude of near-surface un- 5 4 3 2 j(z ˆ) j z ˆ 1 j z ˆ 1 j z ˆ 1 j z ˆ 1 j z ˆ 1 j , (7) derestimation (m = 20.091 nonbreaking versus m = 20.563 5 4 3 2 1 0 breaking waves), with larger biases in breaking wave conditions, where z ˆ z/AML is the magnitude of the distance from the but an inverse effect on the magnitude of deep overestimation surface and coefficients are provided in Table 2. We used a (m = 0.451 nonbreaking versus m = 0.354 breaking waves). Con- fifth-degree polynomial because it best described this particu- ditions conducive to Langmuir circulation (Fig. 10)have a direct lar dataset, but do not suggest there is a physical reason that effect on the magnitude and sign of near-surface underestimation future adaptations to BLS should take this form. Depth re- (m = 0.146 Langmuir inactive versus m = 20.396 Langmuir gimes for Fig. 7a are partitioned by the zero crossing of bias active) and an inverse effect on the deep overestimation 2334 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 TABLE 2. Coefficients for bias polynomials [Eq. (7)] given in Fig. 7. z z z z z z 5 4 3 2 1 0 Curve fit m(z) 65.8318 2195.7996 217.5514 2109.1612 25.0325 21.5199 PDF m(z) 67.0843 2199.1266 220.7982 2110.5756 25.2952 21.5352 PDF s(z) 28.2071 37.8270 267.6796 57.5501 222.4064 3.9510 (m = 0.517 Langmuir inactive versus m = 0.377 Langmuir ac- into the PF on 28 November, marking a sharp reduction in sa- tive). Langmuir circulation is unlikely the principle physical linity (Fig. 1b) and mixed layer depth (Fig. 2b). This is associ- process at work (out of those unrepresented by BLS) because ated with a transition in the relationship between MLD and Langmuir circulation would be expected redistribute turbu- AML (Fig. 11d). Before the PF the AML rarely develops be- lence from the near-surface to the deeper AML, causing a yond the mixed layer; TKE erodes the base of MLD, mixing tendency toward overestimation in the near-surface and under- away this interface. But beyond the PF in the cold, fresh estimation at depth (the opposite of what we observed). Southern Ocean waters, the AML routinely develops beyond the MLD; there is with little compliance from the mixed layer c. Relationship of mixed layer development and the itself (Fig. 2). This could be due to greater stratification resist- Polar Front ing mixed layer deepening (despite churning by TKE), or in- We observe an interesting relationship between frontal hy- tense lateral density gradients within the PF core creating drography and shallow mixing (Fig. 11). The glider crossed stability and preventing convection. The relationship between FIG. 8. Histograms for BLS separated by water friction velocity (u ) and position within the AML. (a)–(c) A bias section, near-surface histogram, and deeper AML histogram for low-wind conditions. (d)–(f) As in (a)–(c), but for high-wind conditions. Near-surface and deeper regimes are separated by z ˆ 0:1as in Fig. 7a. OCTOBER 2022 FE R R I S E T A L . 2335 FIG. 9. Histograms for BLS separated by wave steepness (H/L) and position within the AML. (a)–(c) A bias sec- tion, near-surface histogram, and deeper AML histogram for low-wind conditions. (d)–(f) As in (a)–(c), but for high- steepness conditions. Near-surface and deeper regimes are separated by z ˆ 0:1as in Fig. 7a. water masses and the AML:MLD ratio is complicated by sea- production, BLS likely underpredicts energy input into the sonal transition from winter to summer, increasing stratifica- near-surface ocean because it does include surface gravity tion of the upper Southern Ocean, similar to that observed by wave breaking and/or TKE from alternative sources in the ob- du Plessis et al. (2019). A deepening of isopycnals occurs served Southern Ocean environment. Our observations sug- gest BLS (Lombardo and Gregg 1989) of shear turbulence in during the 6 and 12 December storm events (Fig. 11), as well the Southern Ocean exhibit a systematic bias, underestimat- as following Langmuir-circulation-favorable conditions on ing (overestimating) turbulent dissipation rates in the shal- 17 December. The influence of both the Polar Front and sea- lower (deeper) parts of the surface boundary layer. The sonal transition on mixing dynamics are worthy of future magnitude of the near-surface underestimate is greatest when investigation. wind is mild (Fig. 8) and waves are breaking (Fig. 9). This is not surprising; the Lombardo and Gregg (1989) form of BLS 4. Discussion is a rigid-boundary theory and assumes a TKE budget domi- nated by shear production, buoyancy production, and dissipa- a. Influence of waves tion [Eq. (1)]. Contrary to the rigid-boundary paradigm, Throughout AUSSOM buoyancy flux played a minimal surface gravity waves are known to alter boundary layer struc- role in deepening the AML in the Drake Passage and Scotia ture within several significant wave heights of the surface Sea region (usually extracting energy and reducing its devel- (Agrawal et al. 1992), and our observations are not the first opment), with energy for near-surface mixing supplied almost for which waves cause a departure from BLS theory. Gerbi solely by wind stress. Focusing our discussion on shear et al. (2009) used a model and observations from the Coupled 2336 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG. 10. Histograms for BLS separated by whether conditions are conducive or not conducive to Langmuir circula- tion, as well as position within the AML. (a)–(c) A bias section, near-surface histogram, and deeper AML histogram for low-wind conditions. (d)–(f) As in (a)–(c), but for Langmuir-stable conditions. Near-surface and deeper regimes are separated by z ˆ 0:1in Fig. 7a. Boundary Layers and Air–Sea Transfer (CBLAST) low-winds (McWilliams et al. 1997; Belcher et al. 2012) and shear is experiment to find production alone was unable to balance dis- not necessarily aligned with the momentum flux uw sipation [as in Eq. (1)] in the wave-affected surface layer, which (McWilliams et al. 2014) such that more updated represen- lies above the logarithmic layer (Terray et al. 1996). tation of Eq. (1) with terms 1–3 neglected is We have reproduced the Gerbi et al. (2009) finding in dU Fig. 12 using our measurements, which should produce 0 2uw F(U )F(z/L )cos A S MO dz identical statistics to those computed using an Eulerian plat- dU g form (Derakhti et al. 2020). The inclusion of a transport term 2 uw cos B 2 2 r w 1 WBP, (8) (representing wave breaking, nonlinear wave–turbulence in- dz r teractions, and Langmuir turbulence) improved the model, though contributions of Langmuir turbulence were found un- where angles A and B are the wind direction relative to the important relative to wave breaking (like our results, Figs. 9 shear terms. In conditions where is strongly driven by the wave and 10). Fox-Kemper et al. (2022) note that systematic incon- field and Stokes drift, surface gravity waves reduce the shear by sistencies arise when wind waves deviate in direction from the a function of the Stokes drift F(U )(Large, et al. 2019)and there wind stress itself or propagate from a nonlocal generation site, is wave breaking production (WBP) such that Reynolds stress is which is worth mentioning given that our dataset contains a realistically a decaying function of depth F(z). The angles A and prominent wave presence. In the real ocean surface boundary B are rarely both near zero, and A can exceed 908 in some real layer, there is addition production due to Stokes drift (U ) ocean conditions due to varying wind direction, such that energy s OCTOBER 2022 FE R R I S E T A L . 2337 FIG. 11. Near-surface hydrography showing (a) friction velocity and significant wind wave height, (b) turbulent Langmuir number and wave steepness (H/L), (c) shallow density with isopycnal contours at 0.07 kg m intervals, and (d) stratification with AML and MLD depth normalized by MLD. is extracted. In the absence of background velocity shear, positive bias were made to accommodate uw decreasing we cannot evaluate the leftmost term of Eq. (8) but evaluate from the surface as in Eq. (8). 2uw(dU /dz)cosB to demonstrate the importance of Stokes Numerical modeling literature has aimed to understand the shear production, with dU /dz estimated from Craik (1988) using implications of breaking surface waves and Langmuir turbu- lence, which are not included in wall-bounded (standard 2 2 4p a 4pz/k shear-convective BLS) turbulence parameterizations and sub- U (z)≈ e , (9) kT grid mixing schemes unless explicitly added (e.g., Kantha and Clayson 2004). Belcher et al. (2012) concluded surface wave- where c = gT/(2p), T is the wave period of the spectral peak, forced Langmuir turbulence should be a dominant TKE and a is the amplitude of the primary swell. Near-surface under- source in the Southern Ocean, and several observational stud- estimation (bias in the shallowest 10% of the AML) reduces ies (D’Asaro et al. 2014; Sutherland et al. 2014) corroborate from m = 20.554 to m = 20.450 overall (as in Fig. 7a), the importance of Langmuir circulation in turbulence genera- m = 20.574 to m = 20.517 in low-wind conditions and m = 0.099 tion. While the inclusion of Langmuir turbulence parameteri- to m = 0.133 in high wind conditions (as in Fig. 8), m = 20.091 to zation schemes in ocean general circulation models (OGCMs) m = 20.048 in nonbreaking and m = 20.563 and m = 20.510 produces mixed layers of 2%–25% deeper in extratropical, in breaking wave conditions (as in Fig. 9), and m = 20.396 to weak-convection regions such as the austral summer Southern m = 20.344 in Langmuir active and m =0.146 to m =0.177 in Ocean (Li et al. 2019), it is unclear to what extent Langmuir Langmuir active conditions (as in Fig. 10); representing an im- turbulence is mechanistically responsible for deeper mixed provement in all cases except high wind and Langmuir inactive layers in the real ocean (D’Asaro 2014). Sullivan et al. (2007) conditions, when bias is positive to begin with. The deep over- used large eddy simulation to find that the wave age c /u estimation worsens from m = 0.960 to m = 1.111 overall and in p *a (where c is phase speed of the spectral peak and u is air fric- all cases, but this is unsurprising because we did not account p *a for vertical decay due to F(U ). Notably, however, this repre- tion velocity) impacted the near-surface mixing, with younger sentation does not explain the bias in our dataset. Deep wave groups and higher wind speeds exhibiting a larger positive understimation events (Fig. 6c) would worsen if overall feedback with Langmuir turbulence and increasing near-surface 2338 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG. 12. Boundary layer structure. (a) Cartoon schematic from Gerbi et al. (2009) and (b) the same figure constructed using AUSSOM glider microstructure dissipation measurements, wind-sea significant wave height H , and wind forcing F 2u G ,where G is an empiri- s 1 t t cal function of approximate wave age. Scatter (blue) includes 1 in 5 profiles for clarity. dissipation. To explore scalings leveraging these wave char- Surface gravity wave breaking in the high-wind Southern acteristics, we tested two alternative scalings in comparison Ocean environment violates a key assumption of BLS (that to depth-integrated TKE (Fig. 13) including ones based on shear stress in the logarithmic layer is constant function of wave age (F G u , Craig and Banner 1994) and wave- wind-imparted stress). However, this physical explanation 1 t rangeeffectivespeed (F c u , Gemmrich et al. 1994). alone is insufficient because near-surface bias is more severe 2 e Thomson et al. (2016) tested these scalings (albeit without during the mildest winds. While presence of nonlocally gener- consideration of buoyancy flux) and found that F marginally ated swell could be a factor, it is also possible that contribu- had the best agreement with observations. Our data (Fig. 13) tions from surface gravity waves are persistent but only are inconsistent with their result; we find both scalings pro- noticeable in low-wind cases due to lower levels of TKE dissi- duce inflated energy levels relative to Eq. (3).Even with pation. The near-surface underestimation and deeper-AML bias, BLS performs one to two orders of magnitude better overestimation is inherently coupled; energy lost in the near- than alternative scalings based on wave age or wave-range surface will not reach the deeper AML, resulting in lower effective speed. levels of turbulent dissipation than predicted. Near-surface FIG. 13. Depth-integrated TKE in comparison to inputs of TKE from wind estimated by alternative scalings; G is an empirical function of wave age (Terray et al. 1996) which ranges from 37 to 182 for our dataset. Wave age is calculated using an approximation of data published in Edson et al. (2013),given by u /c ≈ 0.004U 2 0.003 (J. B. Edson 2020, personal communication). Effective energy transfer *a p 10 velocity c ≈ 0.148U 1 1.11 is calculated after Hwang (2009) and is generally 1.5–3m s in the ocean. e 10 OCTOBER 2022 FE R R I S E T A L . 2339 underestimation by BLS is worse when there are breaking direction of inertial rotation (Fig. 6e) during storm events. wave conditions and low wind-driven shear (Figs. 8 and 9), An important question is why the TKE contribution shear instability in inertial currents would appear in BLS bias but the opposite effect is not seen in the deeper histograms log ( /)asa delayed underestimation event and not im- suggesting there must be other physical processes at work. 10 BLS mediately. During the storm itself, the calculation of bias b. Influence of sources other than breaking waves would be heavily buffered by the wind-forced shear turbu- lence, such that the secondary component would perhaps not A second physical explanation is that sources of turbulent ki- become noticeable until the wind relented and only the cur- netic energy (TKE) other than wind-driven shear significantly rent shear remained. As wind subsides, the contribution of contribute to observed turbulent dissipation. Lombardo and mixing due to current shear would subside, both and Gregg (1989) assume energy injection into the dissipative scale BLS become smaller, and this additional contribution becomes is accomplished by direct meteorological forcing (wind-driven more noticeable. We speculate that this mechanism could shear and convection) in the surface boundary layer, but other similarly create a delayed TKE contribution from the storms, processes such as Langmuir driven turbulence (discussed in though this cannot be confirmed with the available data. section 4a), shear instabilities, and submesoscale instabilities could be active in an intense wind-sheared frontal zone. As 5. Conclusions stated in section 4a, our dataset does not support a dominant role of Langmuir-driven turbulence; generation and redistribu- We tested boundary layer scalings (BLS) from satellite data tion of TKE by Langmuir circulation cannot be the only addi- against direct measurements of TKE dissipation rate from a tional source of TKE because the presence or absence of this glider. We found that BLS underestimates turbulent dissipation mechanism does not explain deep underestimation events. in the near-surface and overestimates turbulent dissipation be- Rather, it favors alternative (other than wind-driven) mecha- low the near-surface, consistent with Merrifield (2016).The nisms such in Sutherland et al. (2016), who observed a wind- structure of this bias is consistent across wind speeds in the driven jet in the subtropical Atlantic during the SPURS lower 90% of the AML, but strongly contingent on wind speed (Salinity Processes in the Upper Ocean Regional Study) to in the upper 10% of the AML. In the near-surface AML, un- find that diurnal increase in stratification restricts vertical dif- derestimation by BLS is larger in low-wind conditions, breaking fusion of wind stress and depth of momentum flux, increasing wave conditions, or when Langmuir circulation is active; how- near-surface shear instability (an additional source of near- ever, in the deep AML, differences across-wind and wave con- surface TKE). Mixing in the Antarctic Circumpolar Current ditions are much less statistically significant. Explanations for (ACC) might be further complicated by the numerous other this systematic bias are that 1) the rigid-boundary paradigm processes turbulently transforming the upper ocean, such as does not account for surface gravity wave breaking and momen- internal wave driven mixing (St. Laurent et al. 2012) and dou- tum loss in the high-wind Southern Ocean environment; ble diffusion (Merrifield et al. 2016). It should be emphasized 2) sources of TKE other than wind-driven shear and buoy- that this second explanation is not a complete explanation by ancy flux are contributing to dissipation, and furthermore, itself because it does not account for the lack of observed tur- Langmuir circulation alone cannot explain deep underesti- bulence at depth in Figs. 7–10. mation events; and 3) deep underestimation events are due to additional shear caused by storm-forced inertial currents c. Impact of storms (see Dohan and Davis 2011). Despite these shortcomings, We revisit the cause of the deeper underestimation events we found that BLS still outperforms alternative scalings (Fig. 6c); restated, patches of elevated observed turbulence (Craig and Banner 1994; Gemmrich et al. 1994) based on (blue hues) extending deeper into the AML which were not wave age or wave-range effective speed, motivating its fur- captured by BLS. There is some second-order dynamical ef- ther development. We built on the observational work of fect; the time scale of this effect is much longer than the iner- Lombardo and Gregg (1989) by showing a wind-dominated tial period (∼14.5 h), and time scale for a storm system to pass regime is characterized by significant momentum loss, alter- the glider is less than one day. Glider depth-averaged current native TKE sources, and significantly greater turbulent dissipa- is comparable to ACC velocity (from Operational Mercator, tion in the near-surface than predicted by BLS. Representing Fig. 1) extracted along the track of the glider such that the the physical processes responsible for this near-surface TKE dis- platform is effectively Lagrangian; it is not the case that ACC sipation is critical for understanding mixed layer dynamics and velocity is advecting/distorting patches of turbulence (associ- water mass transformation when wind-driven shear dominates convection in the global ocean. AUSSOM tested boundary ated with wave breaking) faster than the glider such that they layer scaling in high-wind, nonconvective conditions, but appear lagged in the turbulence record. A plausible physical future investigations covering the full wind and buoyancy mechanism explaining these deeper underestimation events is forcing parameter space are needed; especially involving described in Dohan and Davis (2011); who observed a storm cases where both wind-driven shear and buoyancy loss are to excite near-inertial oscillations and currents (with their significant. own additional shear), causing elevated mixing for 3 days after the storm itself. Wind direction turned with the direc- tion of inertial rotation such that it resonantly excited the Acknowledgments. 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Journal of Physical Oceanography – American Meteorological Society
Published: Oct 19, 2022
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