1. Introduction
The oceanic surface layer is controlled by momentum and buoyancy fluxes near the surface and by entrainment fluxes at the base of the mixed layer. These fluxes generate a wide range of physical processes between the air–sea interface and thermocline, and play a vital role in climate variability, biological productivity, and marine pollution. In the highly unstable boundary layer, buoyancy dominates the production of turbulent kinetic energy (TKE) (e.g., Shay and Gregg 1986; Brubaker 1987; Lombardo and Gregg 1989). The production of TKE driven by surface cooling initially modifies the vertical velocity component and is then transferred by turbulent pressure forces into horizontal velocity components, thus generating coherent flows in geophysical boundary layers (see, e.g., Lumley and Panofsky 1964; Thorpe 2005). When the surface buoyancy flux is small and the boundary layer is near neutral, the production of TKE is dominated by shear production driven by surface wind stress (Dillon et al. 1981; Soloviev et al. 1988). Shear production modifies horizontal velocity fluctuations, especially in the downwind direction before transferring energy to the crosswind and vertical energy components via turbulent pressure fluctuations. These ideas have been used in turbulent closure schemes in the oceanic mixed layer (e.g., Mellor and Yamada 1982).
However, transfer of momentum and buoyancy at the air–sea interface is complicated by the presence of surface waves. Surface waves boost the vertical transport of surface fluxes through (i) enhancement of TKE dissipation by breaking and (ii) generation of production-scale coherent structures in the mixed layer via wave–mean flow interactions. Several investigators (Agrawal et al. 1992; Anis and Moum 1995; Drennan et al. 1996; Melville 1996; Terray et al. 1996; Soloviev and Lukas 2003) report that the dissipation rate of TKE in the wave boundary layer is up to an order of magnitude larger than the predictions from wall boundary layer scaling. The enhanced TKE dissipation rate by wave breaking is an important factor for momentum, heat, and gas transfer rates at the air–sea interface.
As a response to the wind over the ocean, roll vortices are formed roughly parallel to the wind direction. These circulation patterns can be recognized by the lines of convergence at the surface, as noted by Langmuir (1938), and they are referred as “Langmuir cells.” The orientation of these Langmuir cells is roughly opposed to the orientation of wind-/shear-driven turbulent eddies in the mixed layer. Craik and Leibovich (1976) describe a plausible theory for the generation of roll vortices. The Craik–Leibovich mechanism requires interaction between surface waves and wind-driven shear flows to generate a forcing function governed by the wave-induced Stokes drift and vertical shear of mean currents. In Langmuir turbulence, the Stokes production term generates TKE in both crosswind and vertical directions. Detailed discussions of theory and relevant references are in Leibovich (1983) and Thorpe (2004).
Several investigators observed convergence zones on the surface layer and the associated crosswind and vertical velocities in surface convergence zones (Weller and Price 1988; Smith et al. 1987; Pollard and Thomas 1989; Zedel and Farmer 1991; Smith 1992, 1998; Plueddemann et al. 1996). Weller and Price (1988) report three-dimensional structure in mixed layer velocity and narrow regions of downwelling flow within the mixed layer, in coincidence with bands of convergent surface flow. They further report that the downwelling flow in the middle of the mixed layer was up to 0.2 m s−1, and that the downwind, downwelling flow had a jetlike structure. Coherent vortices in the mixed layer have been studied using Doppler sonar techniques (e.g., Zedel and Farmer 1991; Plueddemann et al. 1996; Smith 1992, 1998) and these investigators report the consistency of wind/wave forcing of Langmuir circulation. In the existing literature on Langmuir circulation studies, the majority of the observations is from deep water environments and there are only a few references related to shallow-water environments (e.g., Hunter and Hill 1980; Marmorino et al. 2005; Gargett and Wells 2007). In a shallow-water environment, the physical setup is 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. Gargett and Wells (2007) report that Langmuir circulation plays an important role in sediment transport in the shallow-water environment.
There are numerous numerical-modeling studies, mainly large-eddy simulations (LESs), to examine, quantify, and scale Langmuir turbulence in the oceanic mixed layer (Skyllingstad and Denbo 1995; McWilliams et al. 1997; Skyllingstad et al. 1999; Li et al. 2005; Harcourt and D'Asaro, 2008; Grant and Belcher 2009). The papers cited here are just a few references out of many in the literature on this subject. In the majority of these models, Langmuir circulation is simulated by specifying Craik and Leibovich (1976) vortex-force parameters while specifying a Stokes drift corresponding to a monochromatic surface wave field. These studies describe the formation of Langmuir circulation, scaling of Langmuir turbulence, and the distinction among convection, shear-driven turbulence, and Langmuir flows in the upper ocean.
However, there are still unresolved issues such as quantitative understanding of the three-dimensional structure of Langmuir circulation and its interaction with convective- and shear-driven mixing and with internal waves in the thermocline, and scaling laws for Langmuir turbulence. The main objectives of this study are to examine surface wave effects on high-frequency flows over the East Flower Garden Bank (EFGB), to quantify spatial and temporal characteristics of these high-frequency flows, and to examine the scaling laws of vertical velocity based on Langmuir circulation theory. In this paper, we describe measurements of high-frequency currents over the EFGB. The bank is located at the edge of the Texas–Louisiana continental shelf and rises from depths of 100–150 m to about 20-m below the surface. When compared with previous observations from shallow (e.g., Gargett and Wells 2007) and deep water (e.g., Smith 1998), our measurements represent both shallow- and deep-water conditions. The vertical velocity fluctuations described here show strong correlations with winds and surface wave properties. We suspect that these velocity fluctuations are a manifestation of Stokes drift–induced wave–current interactions such as Langmuir circulations during wind events. Here, we examine high-frequency velocity fluctuations including temporal, lateral, and vertical distributions, and characteristic vertical length scales for wide ranges of wind speeds and Stokes drifts. The paper is organized as follows. Section 2 describes platforms and measurements. Section 3 describes observations of winds, surface wave statistics, and background currents and hydrography. High-frequency velocity fluctuations and scaling of vertical velocity are described in section 4. A discussion is given in section 5. Finally, major findings are summarized in section 6.
2. Platforms and measurements
Closely spaced observations of velocity (i.e., u, υ, w), temperature T, conductivity C, and pressure P were collected between December 2010 and December 2011 over the EFGB as part of projects sponsored by the Naval Research Laboratory (NRL) [Mixing Over Rough Topography (MORT)] and by the Bureau of Ocean Energy Management (BOEM) [Currents over Banks (COB)]. The year-long observational program consists of two 6-month mooring deployments (from December 2010 to June 2011 and from June to December 2011), and a 2-week intensive experiment from 26 May to 14 June 2011. A detailed discussion of instrumentation, data collection, sampling methods, and data processing is in Teague et al. (2013, hereafter TG) and therefore we just describe a subset of the data, relevant to this study, which is mainly from measurements made during the second half of the experiment (June–December 2011).
Currents and hydrographic fields were collected from five trawl-resistant bottom-mounted ADCP moorings (M1–M5), referred to as “Barnys” because of their barnacle-shaped dome (Perkins et al. 2000), and four subsurface string moorings (S1–S4), equipped with temperature, conductivity, and pressure (TCP) sensors. Bathymetry and locations of moorings at the EFGB are shown in Fig. 1. M1–M4 and S1–S4 were deployed at the four corners of the bank at water depths of 98, 105, 127, and 106 m, respectively, and M5 was deployed at a water of depth of 47 m, about 3-km north of the bank peak (about 20-m depth) (Fig. 1). The separations between Barnys and associated string moorings were about 200 m. The moorings were equipped with Teledyne RD Instruments Workhorse ADCPs operating at 600 (M5) and 300 kHz (M1–M4) with four transducers each with an incidence angle of 20°. ADCPs recorded near-full water column current profiles every 15 min (an ensemble average of 120 realizations). The ADCPs at M1, M2, M4, and M5 had 2-m vertical resolution and at M3 had 4-m vertical resolution. Shallowest ADCP bins at M1, M2, M3, M4, and M5 were 7.5-, 10.4-, 16.4-, 11.5-, and 5.5-m below the mean water line, respectively, while the deepest bins were off the bottom by 6.5, 4.6, 11, 4.5, and 3.5 m, respectively. The standard deviations for 15-min-averaged currents were less than 0.5% of the water velocity at the five mooring sites. Because moorings are bottom mounted, the platform motion is not a factor for velocity measurements. Apart from water column velocities at M5, surface wave parameters such as wave height spectra and directional wave spectra were collected from the ADCP (Strong et al. 2000). The spectral distribution of wave energy E(f, θ) in frequency f and direction θ was provided by a bottom-mounted upward-looking ADCP (600 kHz) based on the Teledyne RD Instrument's Wave Array Technique. It treats the ADCP depth cell bins as an array of independent sensors for acquiring wave orbital velocities. The frequency–direction spectrum E(f, θ) is then derived using an array-processing algorithm for velocities acquired every 2 h for 5 min at a 2-Hz sampling rate. Three Barnys, at M2, M4, and M5, were also equipped with high-resolution pressure sensors (Ppods) developed by Moum and Nash (2008). The other two Barnys (M1, M3) contained SeaBird Electronics wave/tide gauges. The sampling rates of the Ppods were 1 Hz and the resolutions were about 0.14 mm or 1 Pa (1 Pa = 1 N m−2).
Location of the Flower Garden Banks National Marine Sanctuary. Red circles, representing salt domes or banks, are shown with selected bathymetric contours. The black and white inset illustrates bathymetric contours of EGFB and the locations of bottom-mounted ADCP (M1–M5; filled circles) and string (S1–S4; filled stars) moorings. The contour interval is 5 m. The filled triangle denotes NDBC buoy 42047.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Location of the Flower Garden Banks National Marine Sanctuary. Red circles, representing salt domes or banks, are shown with selected bathymetric contours. The black and white inset illustrates bathymetric contours of EGFB and the locations of bottom-mounted ADCP (M1–M5; filled circles) and string (S1–S4; filled stars) moorings. The contour interval is 5 m. The filled triangle denotes NDBC buoy 42047.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Location of the Flower Garden Banks National Marine Sanctuary. Red circles, representing salt domes or banks, are shown with selected bathymetric contours. The black and white inset illustrates bathymetric contours of EGFB and the locations of bottom-mounted ADCP (M1–M5; filled circles) and string (S1–S4; filled stars) moorings. The contour interval is 5 m. The filled triangle denotes NDBC buoy 42047.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Four TCP string moorings were deployed at M1–M4 during the first half of the deployment and three were redeployed at M2–M4 during the second half. Each string mooring contained 8–12 instruments that were approximately equally spaced between 7 and 12 m below the surface and 1-m above the bottom (TG). Some of the instruments recorded only T and C while others recorded T, C, and P. The large majority of the instruments were SeaBird Electronics MicroCats (SBE37). A limited number of Aqua Trolls that recorded T, C, and P were distributed on each of the string moorings. The MicroCats sampled every 6 min with accuracies of ±0.002°C and 3 μS cm−1. The Aqua Trolls sampled every 12 min with lower accuracies of ±0.1°C and ±0.5% of the data magnitude plus 1 μS cm−1. The conductivity sensors sometimes failed toward the ends of the records as a result of biofouling. We do not address processing and data quality issues here, because those topics are discussed in TG.
3. Winds, waves, and background currents
a. Wind field
Time series between 2 Jun (year day 152) and 8 Dec 2011 (year day 342). (a) Wind speed U10 (blue) and direction 
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Time series between 2 Jun (year day 152) and 8 Dec 2011 (year day 342). (a) Wind speed U10 (blue) and direction
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Time series between 2 Jun (year day 152) and 8 Dec 2011 (year day 342). (a) Wind speed U10 (blue) and direction
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
b. Surface waves and Stokes drift
Figure 3 shows the ratio of surface Stokes drift 
Ratio of surface Stokes drift to wind speed, 
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Ratio of surface Stokes drift to wind speed,
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Ratio of surface Stokes drift to wind speed,
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Both wave measurement systems and wave-simulation models impose cutoff frequencies because of observational constraints and computational limitations. Therefore, wave spectral components below this cutoff frequency (i.e., fc) are available for the estimate of Stokes drift [Eq. (2)]. Contributions from high-frequency spectral components can be approximated by assuming a spectral tail shape and directional spreading function for frequencies higher than fc (Webb and Fox-Kemper 2011; Rascle et al. 2008; Belcher et al. 2012). The spectral tail with f−5 contributes 30% to the surface Stokes drift compared to the truncated spectrum with fc = 0.41 Hz (Belcher et al. 2012). Rascle et al. (2008) show that the contribution can be about 0.4% of wind speed for simulated wave spectra with f−5 slope and a constant directional spreading at frequencies beyond fc = 0.41 Hz. The computation of the high-frequency contribution remains uncertain because of the lack of information about the high-frequency directional wave spectrum.
It is noted that Stokes drift resulting from shorter waves penetrate into a very shallow depth near the ocean surface. While short-wave breaking in a shallow layer is important for mixing near the surface (e.g., McWilliams et al. 1997), the contribution of high-frequency (short) wave forcing to Langmuir turbulence is not clear (Belcher et al. 2012). Therefore, in the following analysis, we limit our computation of Stokes drift to the imposed cutoff frequency similar to Kukulka et al. (2011). A detailed discussion of cutoff frequency effects on the Stokes drift estimate is beyond the scope of this study.
As illustrated in Fig. 3, the ratio 
Time series of significant wave height (i.e., Hs), direction (i.e., θp) of dominant waves, and magnitude of Stokes drift at the surface (i.e., 
c. Mixed layer depth and background currents
The stratification was strong and mixed layer depth (hereafter referred as MLD or subscript D) was shallow (~10–15 m) during the summer months (Fig. 4a). The stratification became weak and the mixed layer deepened during the passage of atmospheric fronts in fall of 2011. The MLD was estimated from moored temperature time series at S2–S4, because salinity had a negligible impact here on the vertical structure of density (TG). The MLD was computed as the depth at which temperature has decreased by 0.2°C from the shallowest temperature measurement. Estimates of MLD at M2–M4 are similar, and therefore the MLD at M2 is used for this analysis (Fig. 4a). Note that there was not a TCP string mooring at M5, and therefore MLD is inferred from the temperature records at M2–M4 (Fig. 4a). After 28 October (year day 300), the mixed layer around the bank deepened below 47 m, indicating that the water column over the bank was well mixed. A detailed discussion of MLD and its relationships with longer time scale processes are described by TG. In the present study, we use MLD as a scaling parameter that controls the vertical distribution of high-frequency velocity fluctuations in the mixed layer.
(a) The color shading shows the time–depth temperature (°C) at S2 and thick black line denotes mixed layer depth. Low-pass-filtered (b) east–west U and (c) north–south V velocity components (cm s−1) at M5 where water depth is 47 m. Cutoff frequency of low-frequency currents is 0.08 cph. Black lines indicate MLD at S2.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a) The color shading shows the time–depth temperature (°C) at S2 and thick black line denotes mixed layer depth. Low-pass-filtered (b) east–west U and (c) north–south V velocity components (cm s−1) at M5 where water depth is 47 m. Cutoff frequency of low-frequency currents is 0.08 cph. Black lines indicate MLD at S2.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a) The color shading shows the time–depth temperature (°C) at S2 and thick black line denotes mixed layer depth. Low-pass-filtered (b) east–west U and (c) north–south V velocity components (cm s−1) at M5 where water depth is 47 m. Cutoff frequency of low-frequency currents is 0.08 cph. Black lines indicate MLD at S2.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
TG described low-frequency flows around the bank for 2011. They note that background low-frequency motions were dominated by semidiurnal tides (12.42 h), near-inertial waves (25.58 h), and 60- and 96-h oscillations. In general, barotropic diurnal and semidiurnal tides were weak, and mean surface currents were eastward in the upper 80 m. Mean currents below approximately 20-m above the bottom followed the bathymetry. Figures 4b and 4c show low-frequency horizontal currents at M5. Near-inertial currents were typically stronger and highly baroclinic during summertime when stratification was strong. Once the stratification was broken down during fall and winter seasons, the currents became nearly barotropic with relatively weak shear in the water column.
4. High-frequency velocity fluctuations
a. Three-dimensional velocity structure
To examine strength and distribution of velocity variance at higher frequencies, velocity spectra were computed during several wind events. One example, shown in Fig. 5, is the variance-preserving velocity spectra for event 4. A spectrum for a given depth was computed from 512 data points (or 5.33-day record) centered on the wind event. The spectra were multiplied by the corresponding frequencies to construct the variance-preserving spectra, which were then averaged into 32 frequency bands (Fig. 5). Depth–time series of horizontal and vertical velocities for event 4 are plotted in Fig. 6. Low-frequency currents and high-frequency velocity variances are illustrated separately. Low-frequency currents were constructed by removing velocities at higher than 0.08 cph, while high-frequency velocity currents were constructed by removing velocities at frequencies lower than 0.2 cph. A fourth-order Butterworth filter was used for filtering the velocity fields. Velocity spectra show distinct features: (i) spectral peak in horizontal velocity spectra at near-inertial frequency (0.041 cph), and (ii) elevated velocity variance at higher frequencies between 0.2 cph and the Nyquist frequency of 2 cph (Fig. 5). The high-frequency energy levels were largest near the Nyquist frequency, indicating that the 15-min sampling rate would resolve higher-frequency motions partially.
Variance-preserving frequency spectra: (a) u, (b) υ, and (c) vertical w velocity components computed at 5.5-, 11.5-, 17.5-, and 23.5-m water depths for the wind event 4. The inertial frequency is 0.041 cph.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Variance-preserving frequency spectra: (a) u, (b) υ, and (c) vertical w velocity components computed at 5.5-, 11.5-, 17.5-, and 23.5-m water depths for the wind event 4. The inertial frequency is 0.041 cph.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Variance-preserving frequency spectra: (a) u, (b) υ, and (c) vertical w velocity components computed at 5.5-, 11.5-, 17.5-, and 23.5-m water depths for the wind event 4. The inertial frequency is 0.041 cph.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Depth–time sections of currents at M5 during wind event 4. (left) Low-pass filtered currents (a) U, (c) V, and (e) W (m s−1). East, north, and upward directions are positive. (right) Log10 values of squared high-frequency (denoted by angle brackets) currents (m s−1) (b) 
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Depth–time sections of currents at M5 during wind event 4. (left) Low-pass filtered currents (a) U, (c) V, and (e) W (m s−1). East, north, and upward directions are positive. (right) Log10 values of squared high-frequency (denoted by angle brackets) currents (m s−1) (b)
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Depth–time sections of currents at M5 during wind event 4. (left) Low-pass filtered currents (a) U, (c) V, and (e) W (m s−1). East, north, and upward directions are positive. (right) Log10 values of squared high-frequency (denoted by angle brackets) currents (m s−1) (b)
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
During event 4, winds increased from 4 to 15 m s−1; the southerly winds rotated counter clockwise to form westerly winds in the middle part of event (days 246–247) before veering toward the south during the latter part of the event (Fig. 2). The mixed layer deepened from 20 to 40 m; and low-frequency currents (such as near-inertial waves) as large as 0.5 m s−1 were formed. Here, 
We further examined other wind events to understand the three-dimensional velocity structure in the mixed layer. Figure 7 illustrates two examples of depth–time variability of 
(a),(b) The magnitude of 
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a),(b) The magnitude of
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a),(b) The magnitude of
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
b. Probability distribution
As discussed above, high-frequency flows observed during wind events were strongest near the surface and decayed rapidly with depth. We also noted that magnitudes of upward and downward motions were comparable. Skewness of w for the 12 events between 5.5 and 15.5 m is −0.34 with a standard deviation 0.36, and the corresponding kurtosis (or flatness) is 4.67 with a standard deviation 0.23. These statistics show that the probability distribution of w differs from the Gaussian distribution (in which skewness is 0 and kurtosis is 3). Figure 8 shows cumulative probability distributions of normalized u, υ, and w and the corresponding cumulative normal Gaussian distributions at 5.5-m depth for two wind events (2 and 12), where the normalized variable 
Cumulative probability distribution function Cpdf of high-frequency velocity at 5.5-m depth is plotted against the normalized velocity φ for (a) summer event 2, (b) fall–winter event 12. The black triangles, blue open circles, and red dots denote u, υ, and w velocity components, respectively. The red dashed line represents the Gaussian distribution function.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Cumulative probability distribution function Cpdf of high-frequency velocity at 5.5-m depth is plotted against the normalized velocity φ for (a) summer event 2, (b) fall–winter event 12. The black triangles, blue open circles, and red dots denote u, υ, and w velocity components, respectively. The red dashed line represents the Gaussian distribution function.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Cumulative probability distribution function Cpdf of high-frequency velocity at 5.5-m depth is plotted against the normalized velocity φ for (a) summer event 2, (b) fall–winter event 12. The black triangles, blue open circles, and red dots denote u, υ, and w velocity components, respectively. The red dashed line represents the Gaussian distribution function.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
c. Spatial variability
Figure 9 illustrates high-frequency kinetic energy at M1–M5 for three wind events (2, 4, and 12). Vertical profiles of horizontal kinetic energy (HKE) and vertical kinetic energy (VKE) were computed from high-pass-filtered ADCP velocity profiles. Kinetic energy profiles for these selected events were constructed by time averaging of squared high-pass-filtered velocities (u, υ, w), where VKE = 0.5«w2» and HKE = 0.5(«u2» + «υ2») and «» denotes a time average over wind events. Here, the cutoff frequency was set to 0.2 cph. As we mentioned earlier, these events (Fig. 9) represent different background stratification and wind/wave patterns (Figs. 2 and 4). In event 2, the MLD was shallow (~20 m) and winds were from the south-southeast at an average speed of about 8 m s−1. During event 4, the MLD deepened from 20 to 40 m and winds accelerated from 4 to 15 m s−1 while wind and waves rotated clockwise from north to south. During event 12, there was a frontal passage and the water column was well mixed. The high-frequency kinetic energy at M5 was the largest of all mooring observations. The differences in energy were more pronounced in the vertical kinetic energy profiles than in the horizontal kinetic energy profiles. A significantly high energy level at M5 could be caused by the intensification of surface waves over the bank. M5 is located at 47-m water depth and 3-km north of the peak, which is about 20-m below the sea surface. The region north of the peak is a plausible wave-focusing region for waves propagating from the south. We will discuss these wave-focusing effects and their impacts on Stokes drift and vertical velocity in section 5.
(a)–(c) Vertical profiles of VKE and (d)–(f) HKE averaged over three wind events [(top) 2, (middle) 4, and (bottom) 12]. Thick solid lines represent energy levels at M5 and dashed lines show 95% confidence limits. Energy levels at M1, M2, M3, and M4 are marked in crosses, open circles, open diamonds, and open triangles, respectively. Confidence limits of energy levels at M1–M4 are not plotted.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a)–(c) Vertical profiles of VKE and (d)–(f) HKE averaged over three wind events [(top) 2, (middle) 4, and (bottom) 12]. Thick solid lines represent energy levels at M5 and dashed lines show 95% confidence limits. Energy levels at M1, M2, M3, and M4 are marked in crosses, open circles, open diamonds, and open triangles, respectively. Confidence limits of energy levels at M1–M4 are not plotted.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a)–(c) Vertical profiles of VKE and (d)–(f) HKE averaged over three wind events [(top) 2, (middle) 4, and (bottom) 12]. Thick solid lines represent energy levels at M5 and dashed lines show 95% confidence limits. Energy levels at M1, M2, M3, and M4 are marked in crosses, open circles, open diamonds, and open triangles, respectively. Confidence limits of energy levels at M1–M4 are not plotted.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
d. The e-folding scales
The entrainment depth of vertical velocity can be examined from the e-folding length of w2, because the e-folding length compares individual profiles independently of their magnitudes. The e-folding length ζ of w2 was estimated by fitting the exponential profile between the shallowest depth (5.5 m) and 30.5 m, provided that w at the shallowest depth was greater than 3 cm s−1. This minimizes uncertainties of ζ by maintaining well-resolved vertical profiles for the computation. For the Craik and Leibovich (1976) theory, the Langmuir circulation is governed by the vortex force [Eq. (3)], where the magnitude and vertical structure of w2 depend strongly on Stokes drift 
Figure 10 illustrates time series of e-folding lengths ζ and η along with the mixed layer depth at S2. The e-folding length of w2 varied between 3.5 and 45 m (Fig. 10b) with an average and a standard deviation of 8.3 and 3.9 m, respectively for the 12 events. Large values of ζ were found with deep MLD (Figs. 10a,b). Because the vertical scale of turbulent eddies depends strongly on the depth of the mixed layer, we can expect large values of ζ for deep mixed layers. The e-folding length of 
(a) Time series of MLD at S2. Black dashed line denotes water depth (47 m) at M5. (b) The e-folding length (i.e., ζ) of w2 at M5 for individual profiles. (c) The e-folding length of Stokes drift (i.e., η) (black lines) and the vertical scale of the peak wave [1/(2kp); red lines] at M5. Numbers 1–12 are the wind events marked in Fig. 2.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a) Time series of MLD at S2. Black dashed line denotes water depth (47 m) at M5. (b) The e-folding length (i.e., ζ) of w2 at M5 for individual profiles. (c) The e-folding length of Stokes drift (i.e., η) (black lines) and the vertical scale of the peak wave [1/(2kp); red lines] at M5. Numbers 1–12 are the wind events marked in Fig. 2.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a) Time series of MLD at S2. Black dashed line denotes water depth (47 m) at M5. (b) The e-folding length (i.e., ζ) of w2 at M5 for individual profiles. (c) The e-folding length of Stokes drift (i.e., η) (black lines) and the vertical scale of the peak wave [1/(2kp); red lines] at M5. Numbers 1–12 are the wind events marked in Fig. 2.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
e. Scaling vertical velocity
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Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Another important scaling parameter is the Hoenikker number (Li et al. 2005), which describes the relative importance of convection (unstable buoyancy forcing) and vortex force driving Langmuir circulation. However, we do not have the net surface buoyancy flux to evaluate the Hoenikker number. We examined day and night variability of 
The vertical velocity is examined within the framework of the wind/wave mechanism such as Langmuir circulation (Craik and Leibovich 1976). This framework is often used to describe the surface velocity variance observed from Doppler sonar systems (e.g., Plueddemann et al. 1996; Smith 1998) and the large-eddy simulation of the oceanic mixed layer, where the vortex forcing is added to mimic Langmuir circulation (Skyllingstad and Denbo 1995; McWilliams et al. 1997; Harcourt and D'Asaro 2008; Grant and Belcher 2009). D'Asaro and Dairiki (1997) and Tseng and D'Asaro (2004) compared MLD averaged and squared vertical velocity with squared friction velocity, and found that on average, 
We will apply some of the existing scaling methods to the observed vertical velocity in the mixed layer over the bank. We limit our analysis to 12 wind events shown in Fig. 2f where a significant number of good vertical velocity profiles can be found. These wind events occupied a total of about 41 days between June and December 2011. We used 3928, 15-min-averaged w profiles for the analysis. We note that the magnitude and vertical structure of w2 and the magnitudes and directions of Stokes drifts and winds varied significantly within a wind event. Therefore, the scaling of vertical profiles should be conducted by identifying profiles that have similar dynamical regimes or belong to similar parameter regimes defined by the underlying physical process. Figure 12 shows spreading of 
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Scaled 
Scaled squared vertical velocity plotted as a function of scaled water depth (z/D) (a)–(c) 
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Scaled squared vertical velocity plotted as a function of scaled water depth (z/D) (a)–(c)
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Scaled squared vertical velocity plotted as a function of scaled water depth (z/D) (a)–(c)
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Wind events generate near-inertial currents (e.g., Fig. 5), and the relative direction between winds and surface currents can make a difference in the vertical shear of horizontal currents which in turn can alter turbulence production in the mixed layer. This scenario could be a plausible explanation why our parameterizations were significantly different from previous publications. We examined the impact of low-frequency (near inertial) currents on high-frequency vertical velocity by examining correlations between vertical velocity and directional difference between winds and near-surface currents. Relations among wind and surface current directions, wind speed, and variability of high-frequency flows for 12 events (Fig. 2) were examined. We did not find a clear relation between the angular difference of the mixed layer current and wind speed, and 
5. Discussion
a. Vertical scaling
(a) 
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a)
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
(a)
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
b. Wave focusing over the bank
We noted that high-frequency kinetic energy over the bank at M5 is significantly larger than the kinetic energy around the bank, and these differences can be clearly seen in the vertical kinetic energy, especially when winds were from the south-southeast (Fig. 8). We suspect that these higher velocity fluctuations are generated by wave–current interaction mechanisms defined by the vortex force [Eq. (3)]. The amplitude of the vertical component of the vortex force is 
Squared vertical shear (i.e., Sh2) of low-frequency horizontal currents at M1–M5 for three different wind events: (a) 2, (b) 4, and (c) 12. Bullets, open circles, diamonds, triangles, and thick solid line denote M1, M2, M3, M4, and M5, respectively. Thick dashed lines denote mean MLD at M2 mooring and thin dashed lines denote one std dev from the mean.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Squared vertical shear (i.e., Sh2) of low-frequency horizontal currents at M1–M5 for three different wind events: (a) 2, (b) 4, and (c) 12. Bullets, open circles, diamonds, triangles, and thick solid line denote M1, M2, M3, M4, and M5, respectively. Thick dashed lines denote mean MLD at M2 mooring and thin dashed lines denote one std dev from the mean.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Squared vertical shear (i.e., Sh2) of low-frequency horizontal currents at M1–M5 for three different wind events: (a) 2, (b) 4, and (c) 12. Bullets, open circles, diamonds, triangles, and thick solid line denote M1, M2, M3, M4, and M5, respectively. Thick dashed lines denote mean MLD at M2 mooring and thin dashed lines denote one std dev from the mean.
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
The propagation of surface waves over complex bottom bathymetric features may be associated with many processes including shoaling, refraction, energy dissipation, and diffraction. We suspect that waves coming from the south (from southwest to southeast) generate a focusing region behind the peak of the bank, while enhancing surface wave amplitudes and Stokes drift. To examine the plausibility of wave focusing, we apply a refraction and diffraction numerical wave model (REF/DIF1) developed by Kirby and Dalrymple (1994). REF/DIF1 is a phase-resolving parabolic refraction–diffraction model for ocean surface wave propagation.
We apply REF/DIF1 to a domain of 14 km (north–south) by 10 km (east–west) encompassing the EFGB (Fig. 1) with the x axis as the offshore boundary for incoming waves. The surface Stokes drift for a monochromatic wave can be estimated as 
Figure 16 shows simulation results of wave height and Stokes drift for a representative monochromatic wave of 1-m amplitude (or 2-m wave height) and 8-s wave period, propagating from the southern boundary into the model domain. The selected wave statistics are similar to the waves statistics observed during event 2 (Fig. 2). The model results display the spatial variation of wave height and Stokes drift induced by the depth changes from the presence of the bank. The northward-propagating wave focuses over a narrow area behind the peak of the bank while generating a much higher wave height and Stokes drift. The wave height in the focusing area reaches 3 m which is a 50% increase over the incoming wave. The surface Stokes drift increases to 12 cm s−1, which is approximately a factor of 2.5 higher than that of the incoming wave. Several sensitivity REF/DIF1 simulations were also conducted by changing the incoming wave direction by ±15°. Similar narrow band wave-focusing zones were found. Out of five moorings, only one mooring (M5) is in the vicinity of the focusing zone. Our simulation is limited to a monochromatic wave train with a single direction and no background currents. Nevertheless this simulation demonstrates the underlining physical process. It is likely that the observations of high energy levels of kinetic energy at M5 would be a result of enhancement of Stokes drift caused by wave focusing induced by the bathymetric variation of the EFGB.
Color shading shows spatial variations of (left) wave height and (right) Stokes drift from REF/DIF1 simulations. Thin dashed black contours show the bathymetry of EFGB. Black squares are the locations of Barny moorings (M1–M5) and M5 is located over the bank (see also Fig. 1).
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Color shading shows spatial variations of (left) wave height and (right) Stokes drift from REF/DIF1 simulations. Thin dashed black contours show the bathymetry of EFGB. Black squares are the locations of Barny moorings (M1–M5) and M5 is located over the bank (see also Fig. 1).
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
Color shading shows spatial variations of (left) wave height and (right) Stokes drift from REF/DIF1 simulations. Thin dashed black contours show the bathymetry of EFGB. Black squares are the locations of Barny moorings (M1–M5) and M5 is located over the bank (see also Fig. 1).
Citation: Journal of Physical Oceanography 43, 8; 10.1175/JPO-D-12-0197.1
c. Impact of vertical motion on corals
The EFGB marine sanctuary is a biologically diverse environment and supports a large number of species including corals. Coral reefs are complex, dynamic, and sensitive ecosystems. Therefore understanding of the hydrodynamics, turbulence characteristics, mixing of water masses over banks, and transport of suspended sediment are important for the coral reef system. Wave–current interactions and generation of deeply penetrating vertical motions can play an important role in mixing, rapid deepening of the mixed layer, and vertical transports of near-surface water toward coral habitats on the bottom. Vertical velocities intensify during wind events, while wave focusing can further enhance wave-driven Stokes drift thus providing an efficient mixing and transport mechanism over the bank.
6. Conclusions
The main objectives of this study are as follows: (i) to examine surface wave effects on high-frequency flows over the EFGB, (ii) to quantify spatial and temporal characteristic of these high-frequency flows, and (iii) to examine the scaling laws of vertical velocity based on the Langmuir circulation theory. The major observational findings and inferences of this study are the following.
High-frequency, three-dimensional flows with frequencies ranging from 0.2 to 2 cph (Nyquist frequency) were found in the mixed layer when wind speed and Stokes drift were large. It is suggested that Stokes drift and mean flow interactions such as Langmuir circulation are responsible for generating the observed velocity fluctuations.
Stokes drift over the bank was estimated from two-dimensional directional wave spectra from a 600-kHz ADCP. The estimated Stokes drift at the surface (i.e.,
Vertical velocity fluctuations showed upward and downward motions with similar magnitudes. The probability distribution of velocity fluctuations (u, υ, w) departs from the Gaussian distribution especially at the tail ends of the distribution.
Squared vertical velocity w2 was strongest near the surface and decayed exponentially with depth, and the associated e-folding length is a factor of 2 larger than the e-folding length associated with Stokes drift.
The 2-h and mixed layer–averaged
Scaling of squared vertical velocity profiles was examined as functions of
Largest velocity variances were found over the bank at M5, located nearly 3 km north of the peak of the bank. It is suggested based on a wave refraction–diffraction model (REF/DIF1) that the increase in kinetic energy over the bank is due to enhancement of Stokes drift by topography-induced waves focusing.
The lack of agreement with open-ocean parameterizations of vertical kinetic energy over the bank is likely due to the enhancement of kinetic energy resulting from localized focusing of surface waves.
Wave-driven velocity fluctuations play an important role in mixing and vertical transports and, in addition, can strongly impact coral habitats over the EFGB. Our study reveals that such velocity fluctuations over the bank are closely related to surface wave conditions that can have strong localized variability as a result of wave focusing over the bank. Our findings indicate that the scaling of wave-induced mixed layer currents over a shelf edge bank differs from the open ocean. Recently, Belcher et al. (2012) examined the global perspective of Langmuir turbulence in the ocean surface boundary layer using LES and diagnostic analysis techniques. However, the lack of understanding of detailed physical process suggests that further studies are needed for the generalization of wave-driven mixing processes in the coastal environment.
Acknowledgments
This work was sponsored by the Office of Naval Research in a Naval Research Laboratory (NRL) project referred to as “Mixing Over Rough Topography (MORT)” and by the Bureau of Ocean Energy Management (BOEM; formerly Minerals Management Service) in the project referred to as “Currents Over Banks (COB)” through the Interagency Agreement M10PG0003. Support for James Moum was provided through ONR Grant N00014-09-1-0280. The measurements were made in cooperation with the Flower Garden Banks National Marine Sanctuary, administered by the National Oceanic and Atmospheric Administration (NOAA). Support provided by Alexis Lugo Fernandez of BOEM and Emma Hickerson of NOAA were greatly appreciated. We thank Mark Hulbert, Steve Sova, Andrew Quaid, and Justin Brodersen for their technical support in mooring preparations and successful deployments. We also thank the captain, crew, and marine technician of the R/V Pelican and crew of R/V Manta for their assistance. We thank the two anonymous reviewers for their thorough and careful review of the manuscript, and useful comments.
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