1. Introduction
Coherent structures in turbulence have been observed in ocean and atmosphere boundary layers. They are mainly large-scale turbulent eddies, which transport energy, momentum, and scalar properties in the ocean mixed layer and play a critical role in ocean circulation, climate variability, biological productivity, and marine pollution. Wind- and convection-driven large-scale turbulent eddies have been studied extensively in the atmospheric boundary layer (Kaimal and Finnigan 1994), when compared to the oceanic counterpart, where surface-wave-induced mechanisms become an important factor at the air–sea interface and below (D’Asaro et al. 2014; Soloviev and Lukas 2014; Thorpe 2005).
In the present study, we focus on large-scale turbulent structures observed over the continental shelf in the northern Gulf of Alaska off Kayak Island when the ocean was forced by strong steady winds, large surface waves, and moderate but persistent surface cooling during late fall and winter months. Observations showed generation of wind- and buoyancy-driven and remotely forced currents (Jarosz et al. 2017), intense surface wave breaking, and generation of bubble clouds, along with high-frequency currents over the northern Alaskan shelf (Wang et al. 2016). These high-frequency motions are likely driven by a combination of different dynamical processes that include convection, shear-driven turbulence, and Langmuir circulation cells generated by the interaction of surface wave effects and background currents. The main objectives of this study are to evaluate turbulent large-eddy structures and their associated eddy momentum fluxes (or turbulent shear stresses), along with turbulent flux divergences in response to local wind stress forcing.
In a convective boundary layer, surface cooling-induced buoyancy forcing dominates in the production of turbulent kinetic energy (TKE; e.g., Brubaker 1987; Shay and Gregg 1986; Lombardo and Gregg 1989), and the buoyancy forcing modifies vertical velocity, which is then transferred by turbulent pressure forces into horizontal velocity components, thus generating coherent flows in ocean and atmospheric boundary layers (see, e.g., Lumley and Panofsky 1964; Thorpe 2005). In the absence of winds, the convective motions are horizontally homogeneous.
When the surface buoyancy flux is small, the production of TKE is dominated by shear production driven by surface wind stress (Dillon et al. 1981; Soloviev et al. 1988). The surface wind stress generates velocity fluctuations in the downwind direction before transferring energy to the crosswind and vertical energy components through turbulent pressure fluctuations. The shear-driven coherent structures can be identified as “ramp-like” structures in temperature and velocity records in the daytime atmospheric boundary layer (Antonia et al. 1979; Phong-Anant et al. 1980), in the nighttime oceanic boundary layer (e.g., Soloviev 1990; Wijesekera et al. 2004), and also in the oceanic bottom boundary layer (Thorpe et al. 1991).
Langmuir (1938) reported the organization of lines of convergence resulting from roll vortices as a response to the wind over the ocean. These roll vortices are referred to as Langmuir circulation cells, with axes roughly parallel to the wind direction. The widely accepted theory of generating “Langmuir cells” is that the surface-wave-induced Stokes drift strains the vertical vorticity associated with wind-driven currents in the horizontal downwind direction, thus generating a vortex force to form counterrotating circulation cells parallel to the wind direction (Craik and Leibovich 1976). Discussions of theory and numerous references are in Leibovich (1983) and Thorpe (2004). The vortex force generates convergence zones and upwelling/downwelling motions in the mixed layer. Although the vortex force has not been measured directly, there are many observations of convergence zones at the surface layer and the associated crosswind and vertical velocities in the deep ocean environment (Weller and Price 1988; Smith et al. 1987; Pollard and Thomas 1989; Zedel and Farmer 1991; Smith 1992, 1998; Plueddemann et al. 1996). A three-dimensional structure in mixed layer velocity was found with narrow regions of downwelling flow coinciding with bands of convergent surface flow (Weller and Price 1988). Weller and Price (1988) reported a jetlike structure in the downwind direction, with downwelling flow in the middle of the mixed layer with speeds up to 0.2 m s−1. Doppler sonar observations showed coherent vortices in the mixed layer, and the generation mechanism appeared to be consistent with vortex forcing (e.g., Zedel and Farmer 1991; Plueddemann et al. 1996; Smith 1992, 1998).
The majority of observations describing oceanic boundary structures, including Langmuir cells, are from deep water environments. There are only a few studies in shallow water environments (e.g., Hunter and Hill 1980; Marmorino et al. 2005; Gargett and Wells 2007; Kukulka et al. 2011; Wijesekera et al. 2013). Unlike in the deep water, Langmuir circulation in the coastal margins plays an important role in sediment transport (e.g., Hunter and Hill 1980). In the coastal environment, physical and geographical setups are different, since top and bottom boundary layers can merge under wind and buoyancy forcing, and thus bottom frictional effects can become a significant factor in mixed layer dynamics. In the shallow water environment, the vertical scale is limited by the water depth, while lateral scales are controlled by the dynamics. Gargett and Wells (2007) report formation of large-scale coherent structures occupying the entire water depth of 15 m and referred to them as Langmuir supercells. These cells were oriented 10°–20° to the right of the wind direction. They reported downwind, bottom-intensified jets near downwelling regions of the circulation. The estimated crosswind spacing of the cells is 3–6 times their vertical scale, which is the water depth. Marmorino et al. (2005) reported banded structures in the remotely sensed temperature records off the Gulf Coast of Florida, and the spacing of the streaks was about 10 times the vertical cell size (approximately water depth), which is significantly larger than the deep ocean aspect ratio of 3 (Smith et al. 1987). Kukulka et al. (2011) suggested, based on observations, scaling arguments, and large-eddy simulation results, that the velocity shear of crosswind currents can deform Langmuir cell structure, thus producing less convergence at the surface and a larger aspect ratio (horizontal to vertical scales). Wijesekera et al. (2013) reported formation of high-frequency currents over an isolated submarine bank (the East Flower Garden Bank) on the shelf off the coast of Texas. They related their current observations to Langmuir cells with high Stokes drifts resulting from surface wave focusing behind the local submarine topography.
In the following, we study formation of high-frequency currents in a water column 73 m in depth, over the continental shelf in the northern Gulf of Alaska during high winds. The paper is organized as follows. Section 2 describes measurements. Section 3 describes observations of surface meteorology, surface wave statistics, background currents, and hydrography. High-frequency variability of currents and estimates of momentum fluxes, eddy diffusivities, and TKE dissipation rates are described in section 4. Forcing mechanisms, vertical profiles of energy, momentum fluxes, and power-spectral and cospectral properties are described in section 5. Discussion is given in section 6. Finally, major findings are summarized in section 7. Detailed estimates of momentum fluxes are provided in the appendixes.
2. Measurements
Hydrographic and velocity fields, profiles of acoustic backscatter, surface wave properties, high-resolution bottom pressure, and surface meteorology were collected in the coastal waters off Kayak Island, Alaska, over a 6-month period (October 2012 to March 2013; Fig. 1). These observations were part of the Naval Research Laboratory’s (NRL) Breaking-Wave Effects under High Winds (BWE) program. Instruments were deployed in a quasi-rectangular (14 km × 9 km) mooring array approximately parallel to the coast between the isobaths of 60 and 90 m. Four 300-kHz Teledyne RD Instruments (RDI) acoustic Doppler current profilers (ADCPs) were deployed in bottom-mounted, trawl-resistant housings, referred to as “Barnys” (Perkins et al. 2000), at stations B1–B4 and recorded nearly full water column current profiles every 15 min. Another 300-kHz RDI ADCP was deployed about 1.5 m off the seafloor on a bottom-mounted platform referred to as the “Lander,” near the center of the array at 73 m water depth (Fig. 1). The Lander ADCP consisted of four transducers, each with a 20° beam angle from the vertical and sampled full water-column profiles of zonal, meridional, and vertical velocity components at 2-m vertical resolution. The Lander rested on a smooth muddy bottom and was remarkably steady throughout the observational period, during which pitch and roll of the ADCP were approximately 1.5°. Good velocity measurements were collected between water depths of 5 and 60 m. The standard error for the ADCP velocities corresponding to 2-min averaging with 48 pings was about 1 cm s−1. The standard error resulting from the aliasing of wave orbital velocity components could be important in the error estimates of the near-surface velocity measurements from the ADCP. The effective standard error due to wave orbital velocity components was estimated by Wang et al. (2016, their Fig. 8 and appendix), and therefore we do not discuss these error estimates in detail here. The wave-induced error decayed exponentially with depth and was about 0.8 cm s−1 at 10 m depth and about 0.3 cm s−1 at 40 m depth. The 2-min averaging of the ADCP data with 48 pings per ensemble basically removed surface-wave-induced particle velocities (Wang et al. 2016). In addition, the Lander housed a BioSonics DT-X echo sounder (BioSonics 2004), also mounted at 1.5 m off the bottom. The echo sounder contains three vertically oriented, upward-looking transducers that operate at 123, 208, and 430 kHz to provide measurements of echo intensity from breaking-wave-induced bubbles within the water column directly above the Lander.
(left) Mooring and meteorological observational sites off Kayak Island in the northern Gulf of Alaska. Moorings B1–B4 are ADCP Barny moorings and S1–S4 are TCP string moorings (filled black circles). The Lander, which housed an upward-looking ADCP and BioSonics echo sounder with three transducer heads, is located at the center of the mooring array at 73 m water depth. Contours represent 50-, 100-, 150-, 200-, 250-, and 300-m bathymetry lines. The solid purple circle near 59.675°N, 143.4°W is the NDBC meteorological buoy, and the brown triangle is the NRL meteorological station on the eastern side of Kayak Island. The X and Y denote along-shelf and cross-shelf coordinates, where the x axis is 28° counterclockwise from the east. The thick purple arrow denotes the approximate wind direction during wind events, and X1 and Y1 denote along-wind (upwind positive) and crosswind coordinates.(right) The Lander during recovery on 8 Mar 2013. The picture shows locations of the ADCP and the echo-sounder transducers, battery packs, and one of the acoustic releases out of two.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(left) Mooring and meteorological observational sites off Kayak Island in the northern Gulf of Alaska. Moorings B1–B4 are ADCP Barny moorings and S1–S4 are TCP string moorings (filled black circles). The Lander, which housed an upward-looking ADCP and BioSonics echo sounder with three transducer heads, is located at the center of the mooring array at 73 m water depth. Contours represent 50-, 100-, 150-, 200-, 250-, and 300-m bathymetry lines. The solid purple circle near 59.675°N, 143.4°W is the NDBC meteorological buoy, and the brown triangle is the NRL meteorological station on the eastern side of Kayak Island. The X and Y denote along-shelf and cross-shelf coordinates, where the x axis is 28° counterclockwise from the east. The thick purple arrow denotes the approximate wind direction during wind events, and X1 and Y1 denote along-wind (upwind positive) and crosswind coordinates.(right) The Lander during recovery on 8 Mar 2013. The picture shows locations of the ADCP and the echo-sounder transducers, battery packs, and one of the acoustic releases out of two.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(left) Mooring and meteorological observational sites off Kayak Island in the northern Gulf of Alaska. Moorings B1–B4 are ADCP Barny moorings and S1–S4 are TCP string moorings (filled black circles). The Lander, which housed an upward-looking ADCP and BioSonics echo sounder with three transducer heads, is located at the center of the mooring array at 73 m water depth. Contours represent 50-, 100-, 150-, 200-, 250-, and 300-m bathymetry lines. The solid purple circle near 59.675°N, 143.4°W is the NDBC meteorological buoy, and the brown triangle is the NRL meteorological station on the eastern side of Kayak Island. The X and Y denote along-shelf and cross-shelf coordinates, where the x axis is 28° counterclockwise from the east. The thick purple arrow denotes the approximate wind direction during wind events, and X1 and Y1 denote along-wind (upwind positive) and crosswind coordinates.(right) The Lander during recovery on 8 Mar 2013. The picture shows locations of the ADCP and the echo-sounder transducers, battery packs, and one of the acoustic releases out of two.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
ADCP velocity data in the upper 10 m were discarded because of side-lobe interference in the ADCP beams. Ping intervals of the ADCPs were 10 s at B1, B2, and B4; 11.25 s at B3; and 2.5 s at the Lander. Current velocity component data are averaged every 15 min at B1–B4 and every 2 min at the Lander. All of the ADCPs returned good quality data except at B4. Barny moorings were also equipped with pressure pods (Ppods; Moum and Nash 2008). Ppods are modified Paroscientific pressure sensors with a precision of about 0.14 mm or 1 Pa (1Pa = 1 N m−2). Additionally, four subsurface string moorings (S1–S4) were deployed close to the B1–B4 moorings. Each string mooring contained 8–12 Sea-Bird SBE-16 temperature–conductivity–pressure (TCP) sensors that were approximately equally spaced between 7 and 12 m below the surface and 3 m above the bottom (Jarosz et al. 2017). Furthermore, each string mooring had one temperature microstructure recorder (chi-pod; Moum and Nash 2009) located about 10 m above the bottom. Fast thermistors and high-resolution pitot tubes in chi-pods produced time series of temperature-variance dissipation rates and high-frequency velocity fluctuations. Sampling rates of TCP sensors were 5 min, and sampling rates of fast thermistors and pitot tubes were 100 Hz. Detailed discussions of instrumentation, data collection, sampling methods, data quality control, and data processing are described in Jarosz et al. (2017) and Wang et al. (2016). Jarosz et al. (2017) described the overall experiment and the low-frequency flow fields including the wintertime variability of the Alaska Coastal Current. Wang et al. (2016) examined near surface bubble distributions and inferred mixing rates from an advection-diffusion model of bubbles (e.g., Thorpe 1984) for a high-wind event observed in late December 2012 by combining ADCP current and BioSonics backscatter profiles.
3. Background winds, waves, surface heat fluxes, and currents
Wind observations were collected hourly from a National Data Buoy Center (NDBC) station (ID 46082) at 59.668°N, 143.392°W, which was about 42 km ESE of the Lander, and at the NRL meteorological station located on the southeastern coast of Kayak Island, approximately 26 km west of the Lander (Fig. 1). Winds at the NDBC station were used, since the NRL/Kayak Island station produced lower wind speeds that were likely due to the impact of land on the flow field. Surface wave data were also available at the NDBC site. The majority of high-wind events, occurring from October 2012 through March 2013, were dominated by southeasterly winds (Figs. 2a,b) associated with the barrier jet that forms in this area (Loescher et al. 2006; Olson and Colle 2009). Wind pulses with magnitudes larger than 10 m s−1 persisted for 1–4 days (Table 1) and can be easily identified from the wind work on the ocean surface E5 (subscript denotes measurement at 5 m height), which is a product of wind stress τ0 and wind speed U5 (Fig. 2c). The Christmas–New Year’s windstorm (23 December 2012 to 2 January 2013) lasted about 10 days and consisted of four separate wind pulses. The ocean surface experienced net cooling (≈10–100 W m−2), but the buoyancy forcing resulting from cooling was significantly smaller than the wind stress forcing (Wang et al. 2016).
(a) Wind speed and (b) direction at 5 m above the sea surface. (c) Wind work at 5 m. The arrows indicate wind events examined here. (d) The estimated net surface heat flux (positive downward). (e) Significant wave height and (f) the period from BioSonics echo-sounder observations. All the meteorological observations were from the NDBC station located at 59.675°N, 143.4°W.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Wind speed and (b) direction at 5 m above the sea surface. (c) Wind work at 5 m. The arrows indicate wind events examined here. (d) The estimated net surface heat flux (positive downward). (e) Significant wave height and (f) the period from BioSonics echo-sounder observations. All the meteorological observations were from the NDBC station located at 59.675°N, 143.4°W.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Wind speed and (b) direction at 5 m above the sea surface. (c) Wind work at 5 m. The arrows indicate wind events examined here. (d) The estimated net surface heat flux (positive downward). (e) Significant wave height and (f) the period from BioSonics echo-sounder observations. All the meteorological observations were from the NDBC station located at 59.675°N, 143.4°W.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Statistics of meteorological and oceanic hydrophysical fields during 16 wind events: Δt is the duration of the event, 
Time series of significant wave height Hs and period Tp of dominant waves were estimated from the surface backscatter strength from BioSonics echo sounder observations (Figs. 2e,f) [for details of this estimate, see Wang et al. (2016)]. During high-wind events wave heights were about 5–9 m, and the dominant wave periods were about 8–14 s (Table 1). The Stokes drift was estimated from ADCP wave information (Wang et al. 2016; Wijesekera et al. 2013). We adapted the following procedure for computing Stokes drift from ADCP wave statistics (Teledyne RDI 2009; Wijesekera et al. 2013). Ocean surface-wave-frequency spectra Sη(ϖ) were measured every 2 h at the Lander by the ADCP, which was equipped with a wave-array system (Teledyne RDI 2009). The wave-frequency spectrum was computed from the time series of surface displacement η extracted from the backscatter databased on the RDI’s surface tracking algorithms. The surface Stokes drift is computed from Sη(ϖ) as 
In the following, we used velocity observations from the Lander-mounted ADCP to examine large-eddy turbulent motions, eddy fluxes, and spectral properties of turbulent fields. ADCP currents and turbulent velocity statistics were examined using two coordinate systems. In the bathymetry-following coordinate system (x, y, z; Fig. 1), x is parallel to the local bathymetry (along shelf), y is perpendicular to the bathymetry (cross shelf), and z is in the vertical direction. In the wind-direction-following coordinate system (x1, y1, z; Fig. 1), x1 is parallel to the local wind direction (along wind) and is positive in the upwind direction and y1 is perpendicular to the local wind direction (crosswind). We adapted these coordinates since mean currents tend to follow the topography over the shelf, while wind- and wave-driven turbulent motions are closely connected with the wind direction. The wind-direction-following coordinates were used when the wind direction was steady and were therefore limited to high-wind events.
In the bathymetry-following coordinate system (x, y, z), we rotated ADCP currents by 28° counterclockwise to match the orientation of the bathymetry (Fig. 1). Then the U component of the current is oriented parallel to isobaths and the V component is oriented perpendicular to isobaths. Time–depth series of U and V, averaged over 2 h, showed a strong along-shelf current (where the flow toward the northeast direction was positive) and a strong cross-shelf current (positive flow toward the coast; Figs. 3b,c). Vertical shears of horizontal currents were small since mean currents were nearly barotropic, especially during high-wind events, except in October 2012 when stratification was strong. The mixed layer depth (hereinafter referred to as MLD or D) was shallow (<25 m) during the early part of October, prior to the beginning of fall storms (Fig. 3). The stratification broke down, and the mixed layer deepened during the passage of multiple storms from December 2012 through March 2013. The MLD was estimated from moored TCP records at S3. The MLD was computed as the depth at which the potential density anomaly σt increased by 0.02 kg m−3 from the shallowest density measurement at 14.3 m. The selected density step captures the mixing layer as typically used in microstructure observations (e.g., Moum et al. 1989; Wijesekera and Gregg 1996; Brainerd and Gregg 1995). Note that there was not a TCP string mooring at the Lander site, and therefore the MLD was inferred from the density records at S3. Low-salinity water moved offshore and the water column became restratified near the surface, which in turn led to shallow MLDs during relaxation of wind events (Jarosz et al. 2017).
(a) Along-shelf (τ0x) and cross-shelf (τ0y) wind stresses. Time–depth sections (m s−1) of 2-h averaged (b) along-shelf velocity U and (c) cross-shelf velocity V observed from the ADCP mounted on the Lander. (d) Log10 values of total shear squared of U and V based on 4-m vertical resolution. (e) Log10 values of buoyancy frequency squared. (f) MLDs are marked in dots, where the MLD (or D) is the depth at which the 14.3-m density changes by 0.02 kg m−3.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Along-shelf (τ0x) and cross-shelf (τ0y) wind stresses. Time–depth sections (m s−1) of 2-h averaged (b) along-shelf velocity U and (c) cross-shelf velocity V observed from the ADCP mounted on the Lander. (d) Log10 values of total shear squared of U and V based on 4-m vertical resolution. (e) Log10 values of buoyancy frequency squared. (f) MLDs are marked in dots, where the MLD (or D) is the depth at which the 14.3-m density changes by 0.02 kg m−3.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Along-shelf (τ0x) and cross-shelf (τ0y) wind stresses. Time–depth sections (m s−1) of 2-h averaged (b) along-shelf velocity U and (c) cross-shelf velocity V observed from the ADCP mounted on the Lander. (d) Log10 values of total shear squared of U and V based on 4-m vertical resolution. (e) Log10 values of buoyancy frequency squared. (f) MLDs are marked in dots, where the MLD (or D) is the depth at which the 14.3-m density changes by 0.02 kg m−3.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
4. High-frequency variability
As discussed above, the coastal ocean in the northern Gulf of Alaska in fall and winter was forced by strong winds, net surface cooling, and large wind waves and swells. These conditions can generate both shear-convection-driven eddies and wave-driven Langmuir cells in the mixed layer. Wang et al. (2016) showed that most of the high-frequency energy was found between the frequencies of 0.5 cycles per hour (cph) and the Nyquist frequency of 15 cph. By applying a 2-h high-pass filter to the velocity components, high-frequency velocity components of along-shelf (u), cross-shelf (υ), and vertical (w), and TKE were computed, where TKE = (u2 + υ2 + w2)/2. Velocity fluctuations at frequencies higher than the 15 cph were not included in the high-frequency velocity components because of the averaging scheme used in the ADCP sampling, and therefore we may underestimate true strength of turbulent velocity components.
Large turbulent eddies were likely to dominate the 2-h high-pass-filtered velocities in the mixed layer. A 256-min segment of u, υ, and w starting at 1109:48 UTC 1 January 2013 (Fig. 4) shows the magnitude and temporal scales of large-scale turbulent motions. The surface was forced by southwesterly winds of ~17 m s−1 and by surface cooling at a rate of ~12 W m−2. The wind speed and direction were fairly steady during wind events. Anemometers at the NDBC buoy sampled for 8 min hourly. The standard deviation of wind speed for a 4-h interval was about 5% of the mean wind speeds used in the analysis. The dominant wave height and period were 8 m and 12 s, respectively. The water column was well mixed, and the background currents were nearly uniform with a time–depth averaged speed of 0.4 m s−1 (Figs. 4a,b). Vertical velocity fluctuations extended from near-surface to bottom, with dominant periods varying from 10 to 20 min. Magnitudes of u and υ fluctuations were smaller than the mean, but u and υ were significantly larger than w. Frequency spectra for the time–depth series of u, υ, and w (Figs. 4c–e) display bands of energy containing motions ranging from 2 × 10−3 Hz (period ~5 min) to 5.5 × 10−4 Hz (period ~30 min) (Fig. A1 in appendix A). A similar energy-containing band can be seen in the spectra computed from the acoustic backscatter intensity (Fig. A2). The spatial scales of these motions for periods of 10–30 min can be approximated from “Taylor’s frozen hypothesis” (Tennekes and Lumley 1972) and are 250–800 m for a mean speed of 0.4 m s−1 (see also section 5). The assumption of Taylor’s frozen hypothesis is valid if turbulent velocity fluctuations (u, υ) are much smaller than the background mean velocities (U, V), that is, (u, υ)/(U, V) ≪ 1. Our observations showed 2-h-averaged background velocities of ~0.3–0.7 m s−1 and turbulent velocity fluctuations of ~0.02–0.2 m s−1. The ratio [〈u2〉 + 〈υ2〉]1/2/[〈U2〉 + 〈V2〉]1/2 averaged over 16 wind events (Table 1) is about 0.2. Note that the orientations of these turbulent motions were not clearly known, and therefore, spatial scales could be overestimated.
A 256-min time–depth record of ADCP currents (m s−1) from 1009:48 to 1425:48 UTC 1 Jan 2013. (a) Along-shelf current U; (b) cross-shelf current V; and 2-h, high-pass-filtered velocity components (c) u, (d) υ, and (e) w. The sampling was 2 min. The wind speed and direction during this period were 17 m s−1 and 112°, respectively.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
A 256-min time–depth record of ADCP currents (m s−1) from 1009:48 to 1425:48 UTC 1 Jan 2013. (a) Along-shelf current U; (b) cross-shelf current V; and 2-h, high-pass-filtered velocity components (c) u, (d) υ, and (e) w. The sampling was 2 min. The wind speed and direction during this period were 17 m s−1 and 112°, respectively.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
A 256-min time–depth record of ADCP currents (m s−1) from 1009:48 to 1425:48 UTC 1 Jan 2013. (a) Along-shelf current U; (b) cross-shelf current V; and 2-h, high-pass-filtered velocity components (c) u, (d) υ, and (e) w. The sampling was 2 min. The wind speed and direction during this period were 17 m s−1 and 112°, respectively.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
The time–depth sections of high-pass-filtered velocity variances representing large-eddy TKE for the entire observational period are shown in Fig. 5. In general, magnitudes of along-shelf and cross-shelf components of TKE were similar. However, during high-wind events, υ2 was slightly larger than u2; we further examine these differences in detail in section 5. The vertical component w2 was about a factor of 10 smaller than υ2. TKE was strongest and penetrated deep into the water column during high-wind events. Wang et al. (2016) reported that TKE decayed exponentially with depth during a multiple wind event that occurred between 23 December 2012 and 2 January 2013. Here we found similar profiles of TKE for the rest of data record.
High-frequency velocity variances (cm2 s−2) of (top) along-shelf u2, (middle) cross shelf υ2, and (bottom) vertical w2 components. Velocity variances were computed by 2-h, high-pass filtering ADCP data of 2-min time resolution and 2-m vertical resolution at the Lander.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
High-frequency velocity variances (cm2 s−2) of (top) along-shelf u2, (middle) cross shelf υ2, and (bottom) vertical w2 components. Velocity variances were computed by 2-h, high-pass filtering ADCP data of 2-min time resolution and 2-m vertical resolution at the Lander.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
High-frequency velocity variances (cm2 s−2) of (top) along-shelf u2, (middle) cross shelf υ2, and (bottom) vertical w2 components. Velocity variances were computed by 2-h, high-pass filtering ADCP data of 2-min time resolution and 2-m vertical resolution at the Lander.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
a. Turbulent large-eddy momentum fluxes
We noted that turbulent velocity fluctuations and TKE were large during wind events and penetrated deep when the MLD was large. In the following, we further examine turbulent velocity fluctuations and their role in transporting momentum imparted by the wind stress. Turbulent large-eddy momentum fluxes such as uw, υw, and uυ correlations are typically evaluated by computing either a covariance or a cospectrum or by a combination of both methods. To evaluate the covariance or the cospectrum of fluxes accurately, velocity components u, υ, and w must be measured within a specified volume of water such that the sampling scales are sufficiently smaller than the spatial scales of energy containing eddies. For example, the four-beam estimate of ADCPs, with a 20° beam separation from the vertical, samples within a 2 × 2 × 2 m3 volume of water at 5 m above the bottom and samples within a 40 × 40 × 2 m3 volume of water at 65 m above the bottom. For eddies (size ≫ 40 m), the four-beam estimate of ADCP velocities can be used to examine the cospectral properties of energy-containing turbulent motions. However, the four-beam ADCP estimate is not the best method to obtain vertical velocities accurately, as pointed out by Gargett et al. (2008). Nevertheless, during high-wind events, vertical velocities for large-scale eddies with sizes 200–800 m were as large as 5 cm s−1, indicating that the four-beam estimate can be used to compute turbulent fluxes.
Along-shelf and cross-shelf turbulent momentum fluxes were computed for the entire record (Fig. 6) by using the cospectral method as discussed in appendix B. Turbulent stresses were strong and penetrated deeply when the wind stress was large and the MLD was deep (Figs. 6b,c). Furthermore, turbulent stress components computed during wind events were nearly in the directions of the wind stress, indicating that these large eddies carry horizontal momentum vertically. During low-wind conditions, vertical velocity fluctuations were negligible or close to the noise level, and the estimated momentum fluxes during low-wind conditions were also close to the noise level.
(a) Wind stress magnitudes (cm2 s−2) for along-shelf τ0x (red) and cross-shelf τ0y (black) directions. Time–depth sections (cm2 s−2) of (b) along-shelf momentum flux (uw) and (c) cross-shelf momentum flux (υw). Turbulent momentum fluxes were computed from the cospectral method. (d) The estimated eddy viscosity (KM; m2 s−1) plotted in log10(KM) and (e) log10 values of shear production of TKE (P; W kg−1).
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Wind stress magnitudes (cm2 s−2) for along-shelf τ0x (red) and cross-shelf τ0y (black) directions. Time–depth sections (cm2 s−2) of (b) along-shelf momentum flux (uw) and (c) cross-shelf momentum flux (υw). Turbulent momentum fluxes were computed from the cospectral method. (d) The estimated eddy viscosity (KM; m2 s−1) plotted in log10(KM) and (e) log10 values of shear production of TKE (P; W kg−1).
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Wind stress magnitudes (cm2 s−2) for along-shelf τ0x (red) and cross-shelf τ0y (black) directions. Time–depth sections (cm2 s−2) of (b) along-shelf momentum flux (uw) and (c) cross-shelf momentum flux (υw). Turbulent momentum fluxes were computed from the cospectral method. (d) The estimated eddy viscosity (KM; m2 s−1) plotted in log10(KM) and (e) log10 values of shear production of TKE (P; W kg−1).
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
b. Eddy viscosity and shear production of TKE
Eddy viscosity profile averaged over 16 wind events with wind speed ≥7 m s−1. Horizontal bars denote the 95% confidence limits. The dashed line is the KM averaged between 23 Dec 2012 and 2 Jan 2013.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Eddy viscosity profile averaged over 16 wind events with wind speed ≥7 m s−1. Horizontal bars denote the 95% confidence limits. The dashed line is the KM averaged between 23 Dec 2012 and 2 Jan 2013.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Eddy viscosity profile averaged over 16 wind events with wind speed ≥7 m s−1. Horizontal bars denote the 95% confidence limits. The dashed line is the KM averaged between 23 Dec 2012 and 2 Jan 2013.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
TKE dissipation rates estimated approximately 9 m and 11 m above the bottom at S1 (blue) and S3 (black), respectively. Shear production of TKE [P, (3)] at 10 m above the bottom at the Lander (red). Water depths at S1, S3, and the Lander are 65, 99, and 73 m, respectively. The moorings were separated by approximately 9 km. Dissipation rates at S1 and S3 were estimated from high-frequency velocities from pitot tubes and at the Lander from turbulent flux estimates given in Fig. 6.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
TKE dissipation rates estimated approximately 9 m and 11 m above the bottom at S1 (blue) and S3 (black), respectively. Shear production of TKE [P, (3)] at 10 m above the bottom at the Lander (red). Water depths at S1, S3, and the Lander are 65, 99, and 73 m, respectively. The moorings were separated by approximately 9 km. Dissipation rates at S1 and S3 were estimated from high-frequency velocities from pitot tubes and at the Lander from turbulent flux estimates given in Fig. 6.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
TKE dissipation rates estimated approximately 9 m and 11 m above the bottom at S1 (blue) and S3 (black), respectively. Shear production of TKE [P, (3)] at 10 m above the bottom at the Lander (red). Water depths at S1, S3, and the Lander are 65, 99, and 73 m, respectively. The moorings were separated by approximately 9 km. Dissipation rates at S1 and S3 were estimated from high-frequency velocities from pitot tubes and at the Lander from turbulent flux estimates given in Fig. 6.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
5. Energy and momentum flux profiles and spectra
a. Dominant forcing mechanisms
Shear-driven turbulent eddies generated by wind-driven currents are more intense near the surface and their axes are perpendicular to the wind direction, whereas Langmuir circulation cells, whose axes are parallel to the wind direction, are formed by the interaction between Stokes drift currents and background shear (Soloviev and Lukas 2014; Thorpe 2004). Pure convective motions in the mixed layer resulting from surface cooling are horizontally homogeneous (e.g., Shay and Gregg 1986). A combination of these forcing factors can generate complex turbulent motions in the mixed layer, and their relative influences are identified from a set of nondimensional parameters such as turbulent Langmuir number (La), Raleigh number (Ra), Reynolds number (Re), and the ratio between mixed layer depth and Monin–Obukhov length (LMO) (e.g., Li et al. 2005; Gargett and Grosch 2014; Walker et al. 2016) , where 
Relationships between (a) La and D/LOM and (b) Ra and D/LOM based on 2-h averaged products. A total of 365 segments from 16 wind events with wind speeds greater than 7 m s−1 were found (Table 1, Fig. 2). Colors represent Ra − D/LOM groups (A–E) belonging to different surface-forcing scenarios (wind speeds, surface waves, and surface heat fluxes). The circles show 2-h averaged mixed layer depths greater than 65 m.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Relationships between (a) La and D/LOM and (b) Ra and D/LOM based on 2-h averaged products. A total of 365 segments from 16 wind events with wind speeds greater than 7 m s−1 were found (Table 1, Fig. 2). Colors represent Ra − D/LOM groups (A–E) belonging to different surface-forcing scenarios (wind speeds, surface waves, and surface heat fluxes). The circles show 2-h averaged mixed layer depths greater than 65 m.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Relationships between (a) La and D/LOM and (b) Ra and D/LOM based on 2-h averaged products. A total of 365 segments from 16 wind events with wind speeds greater than 7 m s−1 were found (Table 1, Fig. 2). Colors represent Ra − D/LOM groups (A–E) belonging to different surface-forcing scenarios (wind speeds, surface waves, and surface heat fluxes). The circles show 2-h averaged mixed layer depths greater than 65 m.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
b. Vertical profiles of TKE
In the following we examine vertical profiles of energy and momentum flux for five different groups, whose properties were selected by considering strengths of wind forcing and vortex forcing. Here we adopted the wind-direction-following coordinates, since mixed layer turbulence is closely related with the magnitude and direction of the wind, but depends on the forcing scenario, such as shear-driven, Langmuir vortex forcing, and surface buoyancy forcing. We divided La − D/LOM space into five different groups (A–E) representing different forcing regimes (Fig. 9). Groups A and B (in which 0.01 < D/LOM < 0.1 and La ≈ 0.25–0.4) represent regimes of high winds and strong Langmuir vortex forcing. Groups C and D belong to regimes of moderate to strong winds with strong Langmuir vortex forcing. The group E (1 > D/LOM > 0.5 and 107 > Ra > 105) represents moderate convection, but wind forcing was not negligible, since wind speeds were greater 7 m s−1. Profiles of TKE components (
Vertical profiles of velocity variances representing large-scale turbulent motions show horizontal anisotropy of TKE components in the water column. The TKE in the crosswind direction (
(a)–(e) Vertical profiles of 
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a)–(e) Vertical profiles of
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a)–(e) Vertical profiles of
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
c. Vertical profiles of turbulent momentum fluxes
Profiles of turbulent momentum fluxes were estimated from the cospectral method discussed in section 4 and in appendix B. The normalized momentum fluxes 
(a)–(e) Group-averaged vertical flux profiles of u1w1 (red), υ1w1 (blue), and u1υ1/5 (black) normalized by 
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a)–(e) Group-averaged vertical flux profiles of u1w1 (red), υ1w1 (blue), and u1υ1/5 (black) normalized by
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a)–(e) Group-averaged vertical flux profiles of u1w1 (red), υ1w1 (blue), and u1υ1/5 (black) normalized by
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
For vertical transports of horizontal momentum, 
d. Spectral characteristics of energy and momentum flux
Parameter dependence on spectral properties was examined by averaging normalized power and cospectra of 16 wind events into five groups (A, B, C, D, E; Fig. 9). The frequency-weighted power spectra (Fig. 12) were nearly flat up to about 5 × 10−4 Hz and peaked at higher frequencies. Typically, the frequency-weighted velocity spectrum in the atmospheric boundary layer has a spectral peak before rolling off at smaller scales by following the inertial subrange spectral slope (Kaimal et al. 1972; Peltier et al. 1996). Similar spectral shapes in the temperature spectrum were found in the near-surface ocean boundary layer during surface cooling and moderate wind forcing (e.g., Wijesekera et al. 2001, 2004). Here, the ADCP measurements captured low-frequency, production-scale motions, but sampling every 2 min was not sufficient to resolve inertial subrange turbulence. Gargett and Wells (2007) examined high-resolution velocities from a bottom-mounted ADCP at 15 m water depth and reported broader low-frequency peaks associated with Langmuir supercells for frequencies from 10−3 to 10−2 Hz and a surface wave peak near 0.1 Hz.
Normalized area-preserving cospectra of 
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Normalized area-preserving cospectra of
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Normalized area-preserving cospectra of
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
In general, Φυ1υ1 contained slightly more energy than Φu1u1 (Fig. 12), similar to the vertical profiles of 
The group-averaged Φu1w1 was significantly larger than the group-averaged Φυ1w1 (Fig. 13) and is consistent with the flux profiles shown in Fig. 11, where most of the momentum flux was in the downwind direction. For high winds with D/LOM ≤ 0.1 (groups A and B), the spectral levels of Φu1υ1 and Φu1w1 were comparable, but for moderate to high winds with 0.1 < D/LOM < 0.5 (groups C and D), the spectral level of Φu1υ1 was one order magnitude larger than that of Φu1w1.
Normalized area-preserving cospectra of 
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Normalized area-preserving cospectra of
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Normalized area-preserving cospectra of
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
6. Discussion
a. Coherent structures and turbulent shear stress
Momentum fluxes associated with large-scale turbulent motions under high-wind conditions were estimated with 2-min averaged currents from a bottom-mounted 300-kHz ADCP with 2-m vertical resolution. Here, wind stress and Stokes-drift forcing were the dominant forcing mechanisms for driving turbulence in the water column. The observations showed that these large-eddy motions had temporal scales ranging from 10 to 30 min, and on average, lateral scales ranging from 100 to 600 m, which are 1.4–8 times the water depth (73 m). For the present observations, the horizontal length to vertical length ratio is consistent with the observations reported by Gargett and Wells 2007, but larger than for deep open-ocean observations (Smith et al. 1987).
The analyses showed more high-frequency kinetic energy in the crosswind direction than in the downwind direction. On average, the ratio 
The averaged velocity variances 
The major part of the turbulent stress is in the downwind direction (
The turbulent stress component 
b. Turbulent flux divergence and the acceleration of the flow
As discussed above, large turbulent eddies carried horizontal momentum downward, and the wind stress and turbulent fluxes were highly correlated. At the early stages of wind forcing, the vertical divergence of turbulent stresses can play a major role in transferring the wind-induced momentum through turbulent mixing processes. In the following, we discuss these processes by evaluating the along-wind momentum balance. Note that a detailed analysis of momentum balance at weekly to monthly time scales was discussed in Jarosz et al. (2017).
During early stages of wind forcing, the vertical divergence of turbulent stress and the acceleration of the flow for a layer (ΔH) were likely to be the major terms in the downwind momentum balance, that is, 
(left) Momentum balance in the along-wind direction for the wind events observed during 23–30 Dec 2012 and (right) cumulative plots of wind stress and momentum balance: (a),(d) wind stress at 5 m above the surface; (b),(e) time derivative of along-wind current, based on 26-h low-pass-filtered velocity fields (blue) and vertical stress divergence (red); and (c),(f) Coriolis acceleration in the direction of wind (black) and bottom-pressure gradient in the crosswind direction (magenta).
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(left) Momentum balance in the along-wind direction for the wind events observed during 23–30 Dec 2012 and (right) cumulative plots of wind stress and momentum balance: (a),(d) wind stress at 5 m above the surface; (b),(e) time derivative of along-wind current, based on 26-h low-pass-filtered velocity fields (blue) and vertical stress divergence (red); and (c),(f) Coriolis acceleration in the direction of wind (black) and bottom-pressure gradient in the crosswind direction (magenta).
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(left) Momentum balance in the along-wind direction for the wind events observed during 23–30 Dec 2012 and (right) cumulative plots of wind stress and momentum balance: (a),(d) wind stress at 5 m above the surface; (b),(e) time derivative of along-wind current, based on 26-h low-pass-filtered velocity fields (blue) and vertical stress divergence (red); and (c),(f) Coriolis acceleration in the direction of wind (black) and bottom-pressure gradient in the crosswind direction (magenta).
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
At the early stage of the wind event during 24–25 December 2012, 
The maximum downwind current lagged the maximum of acceleration and turbulent stress divergence by a half day, or close to one inertial period. However, separating the role of turbulent stress divergence during multiple wind events lasting several days became problematic because of large fluctuations of 
The bottom stress was not used in the analysis discussed above, since the momentum balance was computed between 10- and 67-m depths. However, the mixed layer penetrated to the bottom at about 73 m, and therefore the bottom stress could be important in the mixed layer dynamics. We note that the bottom floor over the northern Alaskan shelf consists of a smooth muddy bottom and that the bottom roughness scale can be as small as 0.02 mm. The estimated bottom drag coefficient was about 10−3 and the resulting bottom stress was too small to play a significant role in the along-wind momentum balance (Jarosz et al. 2017). Therefore, it is unlikely that the bottom stress would play a significant role on the mixed layer dynamics.
However, 
(a) Wind stress (N m−2) at 5 m above the surface, (b) D (m), and (c) turbulent stress divergence (red) and current acceleration (blue) in the along-wind direction for the wind event observed during 9–12 Nov 2012. The divergence and tendency terms were computed between 10 and 40 m.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Wind stress (N m−2) at 5 m above the surface, (b) D (m), and (c) turbulent stress divergence (red) and current acceleration (blue) in the along-wind direction for the wind event observed during 9–12 Nov 2012. The divergence and tendency terms were computed between 10 and 40 m.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Wind stress (N m−2) at 5 m above the surface, (b) D (m), and (c) turbulent stress divergence (red) and current acceleration (blue) in the along-wind direction for the wind event observed during 9–12 Nov 2012. The divergence and tendency terms were computed between 10 and 40 m.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
The tendency and the divergence of turbulent stress during the early stage of wind forcing were not balanced for all of the wind events examined here. As mentioned earlier, this is not surprising because of remotely forced currents over the shelf (Jarosz et al. 2017). The observed velocity contained both remotely forced and local wind-driven motions, and therefore isolating purely wind-driven events and the associated tendency terms were not trivial.
7. Summary and conclusions
Momentum transport by energy-containing turbulent eddies in the oceanic mixed layer were investigated from five months of velocity, hydrographic, and meteorological measurements collected off Kayak Island in the northern Gulf of Alaska. Sixteen high-wind events, lasting from one to several days, were examined. Winds were from the southeast with magnitudes ranging from 7 to 22 m s−1, while the ocean surface cooled, and significant wave heights varied between 5 and 9 m. The water column was well mixed to the bottom (73 m) during the majority of high-wind events. Langmuir numbers were 0.2–0.4 and the Monin–Obukhov length was significantly larger than the mixed layer depth (where D/LOM ≈ 0.01–0.5). The following are the major findings of this study.
Large-scale turbulent motions extending to the bottom were observed, which had temporal scales ranging from 10 to 30 min, corresponding to estimated lateral scales (150–600 m), of approximately 2–8 times the water depth. The acoustic backscatter intensity of bubble clouds, created by breaking waves, showed large-scale turbulent structures whose temporal scales were consistent with the ADCP measurements. Dynamical parameters such as La and D/LOM indicate that both shear-driven turbulence and Langmuir circulation were plausible mechanisms for generating large turbulent structures over the northern Alaskan shelf.
The turbulent large-eddy momentum flux was computed from both cospectral and covariance methods. The turbulent stress in the downwind direction at 10–20 m below the surface was approximately 40% of the averaged wind stress at the NDBC buoy and about 5%–10% of the wind stress near the bottom. Although almost all of the turbulent stress was in the downwind direction, the TKE components were found in both downwind and crosswind directions. The crosswind component of the TKE was 30% larger than the downwind component, indicating generation of significant turbulence in the crosswind direction. The vertical component of the TKE was about 10% of the downwind component. Scaling associated with continuity suggests that the horizontal length scale was at least a factor of 3 larger than the vertical length scale.
Averaged over 16 wind events (or a total of nearly 31 days of observations), the large-eddy turbulent momentum fluxes in the mixed layer were found to be asymmetric (u1w1 > 0, υ1w1 > 0, and u1υ1 > 0). Negative values of −u1w1 and −u1υ1 indicate that the downwind momentum was transported downward and in the crosswind direction 90° counterclockwise to the wind direction, respectively. Vertical and horizontal divergences of turbulent shear stress components can be equally important, where −u1υ1/L ≈ −u1w1/H.
The estimated eddy viscosity at depths between 10 and 30 m was about 0.1 m2 s−1 and is consistent with the turbulent diffusion coefficients inferred from bubble distribution studies by Wang et al. (2016). Below 40 m, the eddy viscosity decayed exponentially with depth to about 5 × 10−3 m2 s−1 at a depth of 68 m.
By examining momentum balances of several wind events, we found that the local acceleration in the downwind direction during the early stage of development, within one inertial period, was largely controlled by the vertical divergence of turbulent stress. However, after a couple of inertial periods of wind forcing, when mean currents became large, pressure gradient, Coriolis acceleration, and nonlinear advection (estimated as a residual) were the dominant terms in the downwind momentum balance.
During these high-wind events, generation of Langmuir cells and their extension to the bottom can intensify sediment resuspension, as also observed in shallow water observations (e.g., Gargett and Wells 2007), and such processes will have major impacts on physical as well as biological activities on shelves as deep as 73 m. We examined large-scale turbulent structures, but our study did not separate Langmuir cells and shear-induced turbulence motions. We found that momentum fluxes in the mixed layer were asymmetric. Vertical mixing derived from flux estimates and from the vertical distribution of bubble concentrations using a simple advection–diffusion model (Wang et al. 2016) were comparable. However, the role of Langmuir cells in transporting momentum is yet to be understood.
Acknowledgments
This work was sponsored by the Office of Naval Research (ONR) in a Naval Research Laboratory (NRL) project referred to as Breaking-Wave Effects under High Winds (BWE). We are thankful for the assistance provided by U. S. Coast Guard. We thank Mark Hulbert, Steve Sova, Andrew Quaid, and Justin Brodersen for their technical support. We also thank the captain, crew, and marine technicians of the R/V Oceanus and the crew of Sound Pacer for their assistance. The authors thank Dr. Wesson for helpful comments. Dr. Moum was funded by the ONR. Dr. Pegau was supported by the Prince William Sound Oil Spill Recovery Institute.
APPENDIX A
Large-Scale Turbulent Structures
To demonstrate plausibility of estimating turbulent momentum fluxes associated with energy containing turbulent motions, we computed cospectra of uw (Φuw), υw (Φυw), and uυ (Φuυ) for the time series shown in Figs. 4c–e. Here, wind speed was about 17 m s−1, the wind direction was approximately westward, and the water column was well mixed to the bottom. Figure A1 shows power spectra Φuu, Φυυ, and Φww and cospectra (Φuw and Φυw as a function of time and depth. Note that Φuυ is not shown in Fig. A1. For this velocity record, strong coherences between along-shelf and vertical velocity fluctuations were found, especially at 800- and 1600-s periods (or at the corresponding length scales of 300 and 600 m for a mean velocity of 0.4 m s−1).
Along-shelf and cross-shelf spectra for the data record shown in Fig. 4. Power spectra of (a) u, (b) υ, and (c) w and cospectra of (d) uw and (e) υw. Log10 spectral estimates are plotted in (a), (b), and (c). The contour lines in (d) and (e) denote Φuw = 0 and Φυw = 0, respectively. The depth-averaged (f) power spectra and (g) cospectra are also shown.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Along-shelf and cross-shelf spectra for the data record shown in Fig. 4. Power spectra of (a) u, (b) υ, and (c) w and cospectra of (d) uw and (e) υw. Log10 spectral estimates are plotted in (a), (b), and (c). The contour lines in (d) and (e) denote Φuw = 0 and Φυw = 0, respectively. The depth-averaged (f) power spectra and (g) cospectra are also shown.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Along-shelf and cross-shelf spectra for the data record shown in Fig. 4. Power spectra of (a) u, (b) υ, and (c) w and cospectra of (d) uw and (e) υw. Log10 spectral estimates are plotted in (a), (b), and (c). The contour lines in (d) and (e) denote Φuw = 0 and Φυw = 0, respectively. The depth-averaged (f) power spectra and (g) cospectra are also shown.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
Similar flow patterns of eddy motions can be inferred from backscattering layers observed by the BioSonics echo sounder (e.g., Wang et al. 2016). A 4000-s record of 208-kHz echo intensity, Sv (Fig. A2), from the BioSonics echo sounder shows vertical penetrations of bubble clouds at multiple time scales. The vertical and time resolutions of Sv were 1.8 cm and 2 Hz, respectively. The frequency–depth spectra, computed at 1.8-cm vertical intervals, and the depth-averaged spectrum of Sv show spectral peaks at 1.25 × 10−3 Hz, similar to what was found in velocity spectra. This suggests that bubbles, generated by breaking waves, were advected by large-eddy turbulence in the mixed layer. Turbulent motions penetrated deep, but bubble clouds were limited to the upper 30 m due to pressure effects. Here, turbulent eddies were partially resolved from echo-sounder data since the record length of Sv was limited to 4000-s segments.
(a) Time–depth record of backscatter echo intensity Sv (dB) measured from the 208-kHz Biosonic echo sounder. The starting time is 11:09:48 UTC 1 Jan 2013. The sampling rate is 2 Hz and vertical resolution is 1.5 cm. (b) Power spectrum of Sv [ΦSv(ω, z)] as a function of depth. The black contour lines represent log10[ΦSv] = 4. (c) Depth-averaged power spectrum of Sv for 10–20-m depth range.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Time–depth record of backscatter echo intensity Sv (dB) measured from the 208-kHz Biosonic echo sounder. The starting time is 11:09:48 UTC 1 Jan 2013. The sampling rate is 2 Hz and vertical resolution is 1.5 cm. (b) Power spectrum of Sv [ΦSv(ω, z)] as a function of depth. The black contour lines represent log10[ΦSv] = 4. (c) Depth-averaged power spectrum of Sv for 10–20-m depth range.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(a) Time–depth record of backscatter echo intensity Sv (dB) measured from the 208-kHz Biosonic echo sounder. The starting time is 11:09:48 UTC 1 Jan 2013. The sampling rate is 2 Hz and vertical resolution is 1.5 cm. (b) Power spectrum of Sv [ΦSv(ω, z)] as a function of depth. The black contour lines represent log10[ΦSv] = 4. (c) Depth-averaged power spectrum of Sv for 10–20-m depth range.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
APPENDIX B
Turbulent Flux Estimates
The cospectrum in the along-shelf direction Φuw was positive for the entire high-frequency band, indicating that the turbulent stress (−uw) was southwestward. The cospectrum in the cross-shelf direction Φυw was negative indicating that the turbulent stress −υw was northwestward. Turbulent fluxes were estimated by integrating cospectral estimates using (1) for the spectral band between ω1 = 3 × 10−4 Hz and ω2 = 4 × 10−3 Hz and are plotted in Fig. B1. We also computed uw and υw using the direct covariance method for 128-min segments of data, and both methods produced similar estimates (Fig. B1). The estimated turbulent stress is oriented toward the direction of the wind (Fig. B1), with a sight veering to the right of the wind, but these differences are likely to be within measurement uncertainties. Furthermore, winds from the NDBC buoy were measured 43 km away from the Lander (Fig. 1), and therefore differences in wind direction can be expected, as also found between the Kayak Island station and the NDBC buoy.
(left) Along-shelf (uw) and cross-shelf (υw) turbulent momentum flux profiles for the velocity record given in Fig. 4. The corresponding cospectral estimates of uw and υw are given in Figs. A1d,e. The cospectral method is marked in blue and the covariance method is marked in magenta. Surface wind stress components −τx0/ρ and −τy0/ρ are marked by black squares. (right) Relative angle between turbulent stress (Θτ) and wind (ΘU5). The dashed red lines denote the difference in wind stress direction between the land station located near the coast on Kayak Island and the NDBC buoy (Fig. 1). Averaged wind speed (U5) and direction (ΘU5) were 17 m s−1 and 112°, respectively.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(left) Along-shelf (uw) and cross-shelf (υw) turbulent momentum flux profiles for the velocity record given in Fig. 4. The corresponding cospectral estimates of uw and υw are given in Figs. A1d,e. The cospectral method is marked in blue and the covariance method is marked in magenta. Surface wind stress components −τx0/ρ and −τy0/ρ are marked by black squares. (right) Relative angle between turbulent stress (Θτ) and wind (ΘU5). The dashed red lines denote the difference in wind stress direction between the land station located near the coast on Kayak Island and the NDBC buoy (Fig. 1). Averaged wind speed (U5) and direction (ΘU5) were 17 m s−1 and 112°, respectively.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
(left) Along-shelf (uw) and cross-shelf (υw) turbulent momentum flux profiles for the velocity record given in Fig. 4. The corresponding cospectral estimates of uw and υw are given in Figs. A1d,e. The cospectral method is marked in blue and the covariance method is marked in magenta. Surface wind stress components −τx0/ρ and −τy0/ρ are marked by black squares. (right) Relative angle between turbulent stress (Θτ) and wind (ΘU5). The dashed red lines denote the difference in wind stress direction between the land station located near the coast on Kayak Island and the NDBC buoy (Fig. 1). Averaged wind speed (U5) and direction (ΘU5) were 17 m s−1 and 112°, respectively.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0286.1
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