1. Introduction
Turbulence plays a key role in ocean dynamics at various spatial and temporal scales. It affects exchanges of momentum, buoyancy, and gases across the air–sea interface as well as biological productivity and dispersion of particles in the ocean. Thermal convection, wind-induced shear, and surface waves are major sources of turbulence in the ocean surface boundary layer (e.g., Dillon et al. 1981; Shay and Gregg 1986; Soloviev et al. 1988; Agrawal et al. 1992; Anis and Moum 1995; Steffen and D’Asaro 2002; Soloviev and Lukas 2003; Thorpe 2005). Known forcing mechanisms of turbulence infrequently act in isolation and often occur simultaneously. Within a distance of approximately a wave height below the sea surface, surface waves enhance turbulence by breaking and then creating turbulent patches that increase turbulence by several orders of magnitude (Agrawal et al. 1992; Melville 1996). Surface waves also boost turbulence through generations of Langmuir cells that were first reported by Langmuir (1938). It is generally accepted that Langmuir circulation is generated when the surface-wave-induced Stokes drift strains vertical vorticity associated with wind-driven currents in the horizontal downwind direction creating a vortex force (Langmuir vortex) to form counterrotating cells parallel to the wind direction (Craik and Leibovich 1976).
Langmuir cells (LC), convective cells/plumes, ramp-like structures found in near-surface temperature and velocity, turbulent billows resulting from breaking internal waves at the base of the mixed layer (ML) and in the diurnal warm layer are all examples of turbulent coherent structures in the ocean surface-boundary layer. Spatially coherent organized motions are an inherent part of turbulent boundary layer processes in the atmospheric and oceanic boundary layers (e.g., Kaimal and Finnigan 1994; Thorpe 2004; Soloviev and Lukas 2014), but observations of these structures are still very challenging, especially in the ocean, though they have been detected and described in oceanographic literature. For example, turbulent eddies produced by surface cooling have been reported by Shay and Gregg (1986), Thorpe et al. (1999), and Jonas et al. (2003). For these turbulent motions, buoyancy production dominates over turbulence production due to winds (shear production) and surface waves (Stokes production) as a primary source of TKE. As reported by observational studies (e.g., Kaimal et al. 1976) and by large-eddy simulations (LES) (e.g., Li et al. 2005), vertical velocity variance dominates, while along- and cross-stream variances are comparable in “pure” convective turbulence. Shear-driven ramp-like structures in temperature and velocity have been reported by, for instance, Thorpe and Hall (1982), Soloviev (1990), and Wijesekera et al. (2001). For these turbulent motions, shear production is the dominant source of TKE and along-stream variance > cross-stream variance > vertical variance. Langmuir circulation was observed in deep and shallow oceanic waters (e.g., Weller et al. 1985; Smith 1998; D’Asaro 2001; Marmorino et al. 2005; Gargett and Wells 2007; Wijesekera et al. 2013; Scully et al. 2015; Yoshikawa et al. 2018). For Langmuir turbulence, production of TKE due to surface waves is the dominant production term in the TKE budget and cross-stream variance ≈ vertical variance > along-stream variance.
To improve our understanding of the dynamics of turbulent coherent structures and effects of surface-wind stress, buoyancy flux, and surface waves on turbulence in the upper ocean, the U.S. Naval Research Laboratory (NRL) funded a program entitled “Turbulence in the Ocean Surface Boundary Layer (TGOM).” Two field efforts held on the outer continental shelf in the northern Gulf of Mexico (GOM) were major parts of the TGOM program. The TGOM 2016 field experiment, conducted in July 2016, was focused on summertime diurnal-warm-layer dynamics. The TGOM 2016 observations and their analyses have been discussed by Wijesekera et al. (2020). Fan et al. (2018) have utilized LES and the TGOM 2016 summer observations to show that the large salinity gradients are able to reduce turbulence in the ocean-surface boundary layer. The TGOM 2017 field experiment, conducted in February 2017, targeted winter conditions in the northern GOM, which are characterized by moderate to high winds and large surface waves usually associated with passages of atmospheric cold fronts. This paper is focused on analyses of TGOM 2017 observations to identify and characterize coherent velocity structures, and to quantify turbulent shear stresses and other energetics as well as terms of the TKE budget in the mixed layer under moderate to high winds, large surface waves, and significant destabilizing surface-buoyancy fluxes.
The paper is organized as follows. Section 2 gives an overview of TGOM 2017 instrumentation and measurements. Atmospheric and background oceanographic conditions are discussed in section 3. Basic characteristics of the coherent velocity structures are listed in section 4. Dynamic parameters used to identify plausible forcing mechanisms of turbulent motions are described in section 5. Variabilities of turbulent velocity variances, shear stresses, estimated eddy viscosities, and turbulent dissipation rates are discussed in section 6, while section 7 is focused on the TKE budget. Section 8 presents a summary and concluding remarks.
2. Instrumentation and observations
NRL conducted a 3-week field effort, TGOM 2017, about 10 km northwest of the East Flower Garden Bank, a coral reef, in the northern Gulf of Mexico in February 2017. Locations of the experimental area and four mooring sites are shown in Fig. 1. Water depths varied slightly among the sites, and they were about 81, 91, 100, and 101 m at MS1, MS2, MS3, and MS4, respectively. At all locations, hydrographic and current-velocity observations were collected between 8 and 20 February 2017.
Map showing the locations of mooring sites (MS1–MS4), bathymetry as depicted by thin black contours, and the locations of the East and West Flower Garden Banks (EFGB and WFGB) and NDBC buoy 42047.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Each mooring site consisted of three separate moorings that were about 100–150 m apart. At MS1, MS3, and MS4, a trawl-resistant bottom-mounted Barny (Perkins et al. 2009) and two line moorings were deployed. Each Barny was equipped with a 300-kHz Teledyne RD Instruments Sentinel V100 acoustic Doppler current profiler (ADCP). The ADCP heads were about 0.5 m above the bottom and recorded current profiles at 1-m vertical resolution and at a frequency of 2 Hz. One of the line moorings contained another ADCP instrument deployed at about 15 m below the sea surface. These near-surface ADCPs were 1000-kHz (V20, MS1 and MS3) or 500-kHz (V50, MS4) Teledyne RD Instruments Sentinel V ADCPs. They recorded profiles at 0.25 m (a 1000-kHz V20 ADCP) or 0.5 m (a 500-kHz V50 ADCP) and at a frequency of 2 Hz. All ADCPs were five-beam units with a slant beam angle of 25° and velocity accuracy of 0.3% and 0.5% of the water velocity relative to the instrument for V20/V50 and V100, respectively. Vertical beams were smaller than slant beams in all deployed ADCP units; hence, a single ping radial standard deviation of the vertical beams was larger than that of the slant beams. The Sentinel V100 units, which delivered current velocity data used to characterize turbulence in the paper, have the single ping standard deviation of the vertical beam about 15% larger than that of the slant beams (S. Idle, the Teledyne RDI field service engineer, 2021, personal communication; additional information about the Sentinel V ADCP is available at http://www.teledynemarine.com/sentinel-v-adcp/). Their vertical beam spread angle is 4.2°, while the slant beam angle is 2.7°. The second line mooring (a spar-buoy type) was furnished with sensors for temperature T, conductivity C, and pressure P. There were 33 (MS1) or 38 (MS3 and MS4) units attached to the lines. They were either Sea-Bird Electronics MicroCATs 37 (SBE37; MS1–18, MS3, and MS4–21), Sea-Bird Electronics Temperature Loggers 56 (SBE56; two at each site), or VEMCO Minilog-II-T loggers (VT; MS1–13, MS3, and MS4–15). The sensors were placed from 0.5 to 1 m apart in the upper 19 m, about 2 m apart from 25 m below the sea surface to about 10 m above the bottom. A VT sensor was attached to an acoustic release. Its depth depended on the location and was about 4–5 m above the bottom. The SBE37 and SBE56 collected data every 30 s, while the VT sensors were set to sample every 60 s. At MS2, a 300-kHz Teledyne RD Instruments workhorse ADCP with a 2-Hz ping rate was deployed on a platform (1.3 m × 1.3 m × 1.5 m) on the bottom and recorded current profiles at 2-m vertical resolution and 20-s average ensemble intervals. Near-surface currents at this site were sampled at a 2-Hz ping rate, 0.25-m vertical resolution, and 5-s average ensemble intervals by a 1200-kHz Teledyne RD Instruments workhorse ADCP that was deployed about 15 m below the sea surface. Both workhorses were four-beam units with a slant angle of 20° and velocity accuracy of 0.3% and 0.5% of the water velocity relative to the instrument for the 1200- and 300-kHz ADCPs, respectively. A Sea-Bird Electronics 3, a Sea-Bird Electronics 4, and a Rockland Scientific MicroRider (MR) with two shear probes and a thermistor, which were attached to a Wirewalker (WW) (Rainville and Pinkel 2001), collected profiles of temperature, conductivity, pressure, and microstructure observations at 5–16-min intervals and at depths between approximately 2 and 80 m below the sea surface. The ADCP instruments returned full time series of current velocities except for the near-surface ADCP at MS3 that delivered a partial record ending at 1900 UTC 12 February 2017. The Barny-mounted Sentinel V100 ADCP at MS3 delivered time series, especially from slant beams, that were barely contaminated by returns from swimming large biological life; hence, these slant beam observations and vertical velocities measured by the vertical beam were mainly utilized to present high-frequency signals in the paper. High-quality T, C, and P time series were returned by the sensors at MS1, MS3, and MS4.
Because of mechanical problems, the sensors attached to the Wirewalker delivered incomplete time series of T, C, P, and microstructure observations. Observations from microstructure shear probes were utilized to estimate TKE dissipation rates ε. The TKE dissipation rate from the WW/MR platform are also discussed in the appendix A including comparisons with nearby ε observations from a glider and a vertical microstructure profiler. In the following, we describe briefly a computational procedure used to estimate ε. Ascending profiles of the microstructure shear were only used to calculate the dissipation rates. The good-quality shear data spanned from ~10 to ~75 m. Ascending speeds of the Wirewalker were estimated as Uasc = dP/dt, where P is the pressure; Uasc varied with depth, but it was generally from 0.4 to 0.65 m s−1 with mean profile speeds between 0.55 and 0.61 m s−1. Figure 2 shows examples of the ascending velocity of the Wirewalker/MicroRider package, the raw-velocity shear from the microstructure shear probes, profiles of the estimated TKE dissipation rates, variances of the raw-velocity shear, acceleration components, and clean velocity shears, wavenumber spectra of the clean—that is, despiked and vibrational contamination removed—velocity shear, and fitted wavenumber spectra. The ascending profiles in Figs. 2a and 2b were collected between 1225:03 and 1227:31 UTC 15 February 2017. Variances and spectra in Figs. 2d and 2e were calculated from the observations between depths of 24.6 and 25.5 m. The TKE dissipation rates were estimated by fitting Nasmyth spectra to the turbulent velocity-shear spectra computed from 1024 data points using the nonlinear least squares technique. The raw-velocity shear spectra from Wirewalker platforms contained low- and high-frequency noise mostly associated with cable vibrations. Thus, care must be taken to select a relatively clean spectral band to fit a Nasmyth spectrum. Before the Nasmyth spectra were fitted, the raw-velocity shear data were despiked and vibrational contaminations were removed using software developed by Douglas and Lueck (2015). Narrow spectral bands were selected, and they varied for each data segment, depending on the strength of dissipation rates and noise levels. If an initially estimated dissipation rate εini was less than 10−8 W kg−1, the wavenumber k interval was from 6 to 15 cycles per meter (cpm), while wavenumbers from 7 to 25 cpm were used for εini between 10−8 and 10−7 W kg−1. For εini larger than 10−7 W kg−1, the k interval was from 7 to 30 cpm. The noise level of the TKE dissipation rates was approximately 10−10 W kg−1. Moreover, the TKE dissipation rates discussed in the paper were calculated as averages of the values from both shear probes if they agree to within a factor of 5, or the minimum of the two otherwise.
Examples of (a) the ascending velocity (m s−1) of the Wirewalker/Microrider package, (b) raw velocity shear fluctuations (s−1) from shear probe 1 (blue) and 2 (green), (c) TKE dissipation rates ε (W kg−1) estimated by fitting Nasmyth spectra to clean (despiked and vibrational contamination removed) velocity-shear spectra, (d) variances of raw velocity shear (S1R and S2R), acceleration components (Ax and Ay), and clean velocity shears (S1C and S2C), and (e) wavenumber spectra of the clean velocity shear (S1C and S2C), fitted wavenumber spectra (S1F and S2F), and Nasmyth spectra N. The ascending profiles in (a) and (b) were collected between 1225:03 and 1227:31 UTC 15 Feb 2017; variances and spectra were calculated from observations recorded between 24.6 and 25.5 m.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Atmospheric observations such as air temperature, humidity, wind speed, wind direction, atmospheric pressure, and incoming solar irradiance (limited time series) were recorded by instruments installed on the R/V Pelican. The ship remained inside or just outside the study area throughout the experiment; hence, these observations represented well atmospheric conditions during the February experiment.
3. Atmospheric and oceanographic background conditions
a. Winds, atmospheric pressure, and air temperature
Between October and May, winds over the northern Gulf of Mexico are rather strong and often over 10 m s−1. They are generally southerly, but this southerly wind pattern is frequently disturbed by passages of atmospheric cold fronts that appear in the northern GOM every 3–10 days during this time of the year (e.g., DiMego et al. 1976). In the course of frontal passages, winds rotate rapidly clockwise and become northerly for one or two days before switching again to southerly. Atmospheric front passages are also characterized by a decrease and then an increase in the atmospheric pressure and a drop in the air temperature once winds become northerly. Figures 3a–c show hourly averages of wind speed, wind direction (clockwise from the north), and air temperature during the TGOM 2017 field experiment. Horizontal axes in Fig. 3 as well as in several other figures in the paper display days and hours in the coordinated universal time (UTC) that is 6 h ahead of the time zone of the experiment (the U.S. central time zone). Wind speeds and directions were measured at 5 m (H5) above the sea surface; hence, standard 10-m (H10) wind velocities U10 were estimated by assuming, that the near-surface atmospheric boundary layer was near neutral, from U10 = U5(H10/H5)0.11 (Hsu et al. 1994). The atmospheric observations (strong and rotating winds, decreasing air temperature) indicate that three cold fronts moved over the study area: the first happened on 9 February, the second began on 14 February, and the third front began affecting the area on 20 February. During TGOM 2017, hourly averages of wind speeds (Fig. 3a) were generally above 5 m s−1. The strongest hourly U10 observations (>10 m s−1) with measured wind gusts over 18 m s−1 were observed mainly during the three cold-frontal passages. Figure 3a also shows time series of the wind stress (
Hourly (a) wind speed at 10 m U10 (m s−1; blue line), wind stress τ × 10 (N m−2; green line), and water frictional velocity U* (cm s−1; red line), (b) wind direction
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
b. Surface net heat and buoyancy fluxes
Figures 3d and 3e display the net shortwave solar radiation QSW, net heat flux Qnet (positive downward), and surface buoyancy flux B0 (positive upward); Qnet is the summation of the shortwave, net longwave, latent heat, and sensible heat fluxes. The surface buoyancy flux is defined as B0 = −αgQnet/(ρwCp) (e.g., Shay and Gregg 1986), where α is the coefficient of thermal expansion, g is the gravitational acceleration, and Cp is the specific heat of seawater at constant pressure. Observations of solar irradiance did not cover the entire period of the TGOM 2017 experiment; hence, the surface net heat flux calculated from hourly ERA5 data were also examined. ERA5 is the fifth major European Centre for Medium Range Weather Forecasts (ECMWF) atmospheric reanalysis that combines model data with observations into the global dataset (Hersbach et al. 2020). The net heat fluxes estimated from the ERA5 data and the available TGOM 2017 observations were used to evaluate the surface buoyancy fluxes. As shown in Figs. 3d–f, the ERA5 QSW, Qnet, and B0 compare fairly well to the available shortwave solar radiation observations as well as with Qnet, and B0 estimated from the observations; hence, the ERA5 QSW, Qnet, and B0 should represent well those that prevailed over the region in February 2017 when the observations were not available.
Prior to arrivals of the atmospheric cold fronts, Qnet was, on average, about −75 W m−2 during nighttime cooling and about 500 W m−2 during daytime heating in the northern GOM (Fig. 3e). When the cold fronts were moving over the region, heat losses were as large as −400 to −600 W m−2 due to rapid air temperature decreases. These large heat losses happened after the winds switched to northerly behind the cold fronts. Large negative heat fluxes usually indicate the presence of convective-driven turbulence in the upper ocean. The large negative net heat and positive surface buoyancy fluxes (2.5 × 10−7–3.5 × 10−7 W kg−1) (Figs. 3e,f) imply that turbulence forced by convection was vigorous during cold air outbreaks. More detailed discussions concerning plausible forcing mechanisms of turbulence and TKE dissipation rates in the mixed layer are in sections 5 and 6d, respectively.
c. Surface waves
(a) Significant wave heights Hs (m), (b) peak periods Tp (s), (c) peak directions
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Between October and May, sea state changes in terms of the significant wave height, peak wave period and direction are generally linked to passages of atmospheric cold fronts in the northern GOM. During the TGOM 2017 experiment, high-sea states with Hs greater than 1.5 m occurred around times when high winds and atmospheric cold fronts impacted the area (Fig. 4a). Prior to a cold-frontal passage, surface waves were generated by long-fetch southerly winds (Fig. 4b). After the arrival of the cold front, the sea surface was dominated by young surface waves generated by fetch-limited northerly winds. Peak periods were mostly from 5 to 7.5 s (Fig. 4b). Based on the deep-water approximation, the corresponding wavelength Lp was between 39 and 88 m, where
d. Background stratification and currents
Hourly averages of potential temperature θp, salinity S, potential density σθ, and buoyancy frequency squared N2 at MS4 are shown in Fig. 5. Temperature spanned between 19.32° and 22.79°C, salinity ranged from 35.65 to 36.52, and density and buoyancy frequency indicated that the major part of the water column was generally either weakly stratified or well mixed in the upper ~50–77 m when the cold fronts were moving over the region. Because of the small vertical salinity variability, density changes followed the θp changes fairly closely. Time series of θp and σθ as well as the net heat and surface buoyancy fluxes (Figs. 3d,e) also indicated that near the sea surface a daily thermocline was able to develop, for instance, on 13 and 14 February 2017. The buoyancy frequency showed some variations with depth, but it was generally less than 0.02 rad s−1. The higher values of N were mainly found in the seasonal thermocline/pycnocline (55–85 m) as well as in the daily thermocline if it developed during the daytime. The mixed layer depth HML also varied over the period of the TGOM experiment as shown in Fig. 5d. The HML was computed as the depth at which density increased by 0.01 kg m−3 from the density at 2 m. When the winds were weak and surface waves subsided the mixed layer depth was as shallow as 3 m during the daytime and then deepened to 10–25 m during the night. The HML deepened significantly, as much as to 77 m, during the atmospheric cold-frontal passages and/or when winds increased considerably over the region.
Hourly averages of (a) potential temperature (°C), (b) salinity, (d) potential density σΘ (kg m−3), and squared-buoyancy frequency log(N2) (rad2 s−2) at MS4. The mixed layer depth (m) is depicted by the black line in (d).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Figures 6a and 6b show hourly averages of the east–west (u) and north–south (υ) current components, respectively, at MS4. u was mainly eastward throughout the water column. A weak westward component was recorded near the bottom between 10 and 16 February and after 20 February. Component υ displayed more variability with depth and time, switching between northward and southward, and it was generally weaker than u. Velocity spectra (not shown) indicated peaks at diurnal/inertial and semidiurnal frequencies implying that the part of the temporal variability was related to tidal and near-inertial currents. Teague et al. (2014) have analyzed year-long current observations collected near the EFGB and reported that barotropic diurnal and semidiurnal tides are weak (<3 cm s−1); however, near-inertial currents are more energetic (≥15 cm s−1), especially in spring and summer, and often account for more than 50% of the total current energy. Our observations indicate that the diurnal/inertial currents were less than 5 cm s−1, whereas the semidiurnal tidal currents were less than 2.5 cm s−1 during the TGOM 2017 experiment.
Hourly averages of (a) east–west (u; cm s−1) and (b) north–south (υ; cm s−1) current velocity components, (c) squared-current shear log(shear2) (s−2) at the MS4 site. East and north components are positive; the mixed layer depth (m) is depicted by the black line in (d). Thin white lines separate observations from the near-surface and bottom-mounted ADCP instruments.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Figure 6c displays time series of the hourly current shear squared estimated from the observations recorded at MS4. Current shear was generally less than 0.04 s−1 and higher values were usually found along the bottom of the expanding mixed layer during nighttime convection and/or when the cold fronts affected the area. On the onset of the high winds and large surface waves, the current shear increased, the Richardson number Ri (not shown) dropped below the critical value of 0.25 near the sea surface, and the ML began to deepen indicating initial development of shear- and wave-induced mixing. As the wind/wave forcing continued larger values of the current shear and low Ri occurred deeper in the water column as the ML expanded farther. At the same time, the current shear became progressively smaller within the ML. The shear estimates also showed that the higher shear values were found in the seasonal thermocline/pycnocline throughout the entire period of the TGOM 2017 experiment.
4. Basic characteristics of observed coherent velocity structures
Subsequent analyses and discussions are focused on concurrent atmospheric and oceanographic observations recorded when the first two cold fronts affected the outer shelf in the northern GOM. During those times, the current observations indicated the development of energetic high-frequency velocity fluctuations implying the presence of enhanced kinetic energy in the mixed layer. High-frequency velocity fluctuations emerged in the ML at all four mooring sites denoting formations of spatially coherent organized motions (coherent velocity structures or CVS) in the area. We refer to periods when CVS were observed in the ML as event 1 and event 2 for the first and second front, respectively. Figure 7 displays the velocity fluctuations recorded at MS3. Figure 7a shows the hourly wind stress, surface Stokes drift, and surface buoyancy fluxes. Figures 7b–d display 2-min averages of along-wind (u′; positive downwind), crosswind (υ′; positive 90° counterclockwise from the downwind direction), and vertical (w′; positive upward) current velocity components, and the last plot depicts layer-averaged magnitudes of the vertical velocity fluctuations (a layer between 5 and 60 m; ⟨w′⟩5–60m). Figure 7e also shows time spans for events 1 and 2. The 2-min averages were calculated from processed current observations, i.e., surface-wave orbital velocities were removed by filtering fluctuations with periods less than 2 min from the raw 2-Hz current observations, and then a linear least squares fit was removed from 2-h subsets of the filtered data to eliminate low-frequency variability following an approach proposed by Gargett and Wells (2007).
(a) Hourly τ (N m−2; black line), US0 (m s−1; blue line), and B0 × 106 (W kg−1; red line), and 2-min means of (b) along-wind (u′; cm s−1), (c) crosswind (υ′; cm s−1), and (d) vertical (w′; cm s−1) current velocity components and (e) layer-averaged magnitudes of w′ (w′ averaged between 5 and 60 m) at MS3. The mixed layer depth (m) is depicted by the black lines in (b)–(d); timings for events 1–2 and subsets 1–2 are marked by black and magenta vertical lines in (e).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Velocity observations from the ADCPs indicated that the CVS developed rapidly in the ML when the first front was affecting the region. As shown in Figs. 7b–e, the CVS were detected around 1100 UTC 9 February and lasted for about 7 h. They weakened/disappeared around 1800 UTC 9 February, perhaps due to a combination of the following: 1) inadequate resolution of ADCPs to detect weak fluctuations, 2) rotating winds that switched from northerly to southerly and modified the surface-wave field, and 3) stabilizing surface buoyancy fluxes that are able to build near surface stratification, which tends to inhibit vertical penetration of Langmuir circulation (e.g., Min and Noh 2004; Walker et al. 2016). The CVS redeveloped again after 0200 UTC 10 February when the southerly winds and destabilizing surface buoyancy fluxes were established over the area and vanished by 1700 UTC 10 February. The background flow in the ML was rather uniform with depth but showed some time variability. Depth-averaged speeds of the background flow were between 0.17 and 0.24 m s−1, and turbulent-velocity fluctuations were less than 0.10 m s−1; that is, magnitudes of u′, υ′, and w′ were typically less than 0.07, 0.08, and 0.05 m s−1, respectively. The second front began affecting the area on 14 February. The winds (Fig. 7a) and surface waves (Fig. 4a) increased quickly; however, the CVS (Figs. 7b–e) developed around 0000 UTC 15 February when winds blew consistently from the north (Figs. 3a,b), surface waves were larger than 2 m (Fig. 4a), and buoyancy fluxes became destabilizing (Fig. 7a). The CVS disappeared by 1200 UTC 16 February when the winds and waves subsided, and the surface buoyancy flux switched from destabilizing to stabilizing. The background flow in the ML was nearly uniform with a time-depth averaged speed of 0.15 m s−1, whereas turbulent velocity fluctuations were generally less than 0.10 m s−1, i.e., magnitudes of u′, υ′, and w′ were mostly less than 0.10, 0.10, and 0.06 m s−1, respectively. The CVS spanned from the sea surface to the HML for both examined events.
Figures 8a–c display the 6-h subset of u′, υ′, and w′ between 1430 and 2030 UTC 15 February, whereas Fig. 8d depicts time series of the layer-averaged crosswind (a layer between 72 and 76 m; ⟨υ′⟩72–76m) and mixed layer averaged vertical (⟨w′⟩ML) velocity components. These plots show clearly positive and negative fluctuations of the along-wind, crosswind, and vertical current components for this period. Figure 8c displays regions of downwelling (negative w′) separated by upwelling zones (positive w′) similar to those of LCs reported by previous studies (e.g., Smith et al. 1987; Weller and Price 1988; Gargett and Wells 2007; Scully et al. 2015; Wijesekera et al. 2017). The downwelling regions were usually narrower than the upwelling regions. The w′ extrema were asymmetric with larger downwelling speeds than upwelling speeds. w′ magnitudes in the downwelling regions were often 1.5–3 times as large as neighboring magnitudes of the upwelling w′. The asymmetry is well measured by w′ skewness (γ = ⟨w′3⟩/⟨w′2⟩3/2). Vertical-velocity skewness has been utilized to indicate the presence of both Langmuir and convective cells (e.g., McWilliams et al. 2012; Moeng and Rotunno 1990), and it is one of the qualitative features that Langmuir and convective cells share. Negative values of γ are indicative of strong short-lived downwelling episodes alternating with weaker and longer upwelling episodes. Figure 9 displays mean profiles and 2-h averages of the w′ skewness at MS3 for both events. The mean profiles are negative as expected for cells with stronger and narrower downwelling and weaker and wider upwelling. During event 1, the 2-h averages of γ was generally negative, often less than −0.4; however, during event 2, the 2-h averages of γ at depths larger than 0.3HML were negative, but at depths less than 0.3HML, they were intermediate, i.e., positive and negative. The Hs was above 1.5 m (Fig. 4a), the winds were from 7 to 14.6 m s−1 (Fig. 3a), and the buoyancy flux was destabilizing (Fig. 3e); hence, the positive values of skewness are difficult to explain because they are usually associated with low winds and small surface waves as well as with the stabilizing surface buoyancy flux (Scully et al. 2015).
Zoom-ins of high-frequency (a) u′ (cm s−1), (b) υ′ (cm s−1), and (c) w′ (cm s−1) current velocity components. Shown are 2-min means of the velocity components at MS3, and the mixed layer depth (m) is depicted by the black lines. Also depicted are (d) layer-averaged υ′ averaged between 72 and 76 m (⟨υ′⟩72–76m; black line) and mixed layer—averaged ⟨w′⟩ML (magenta line), along with (e) wavelet power spectrum log2Φ (cm−2 s−2) of the ⟨w′⟩ML shown in (d), with a 95% significance level (thin black line).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Profiles of vertical-velocity skewness γ for events (a) 1 and (b) 2; γ was calculated from observations recorded at MS3. Mean profiles and their 95% confidence intervals are depicted by thick and thin horizontal black lines, respectively, and 2-h averages are shown by thin colored lines.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
For a fixed-point observer of drifting LCs, the downwelling regions coincide with convergence and divergence zones of υ′ at the sea surface and the base of the ML, respectively. For the data subset in Fig. 8, the mean flow in the ML was eastward and also positive and aligned with the crosswind direction when rotated onto the wind direction. This configuration of the mean flow indicates that υ′ should switch from positive to negative at the downwelling regions near the base of the ML if there is a correct phasing of the crosswind velocity relative to the vertical velocity. This change of the direction was fairly often observed in the crosswind velocities shown in Figs. 8b and 8d; however, the direction changes often did not occur exactly in the center of the downwelling regions as reported by Gargett and Wells (2007). The horizontal velocity observations spanned between 11 and 97 m; hence, LC convergence zones of the crosswind velocity at the sea surface, which were expected to appear at the same time as divergence zones near the base of the ML, were not sampled by the ADCP instruments. Lack of the near-surface observations also prevented us from verifying possible near-surface intensifications of the crosswind flow. There were, however, very infrequent times when υ′ exhibited higher shear at depths less than 20 m that might indicate the existence of the near-surface intensification. The limited near-surface current observations showed very rarely a subsurface maximum of the downwind flow that coincided with the downwelling zones as reported by Weller and Price (1988). The vertical velocity observations covered the water column between 5 and 97 m and spanned nearly throughout the entire ML, that is, from ~0.07HML to the base of the ML. These observations showed that depth maxima of the downwelling velocities varied and were located between 0.1HML and 0.5HML, which is in the depth range reported by previous studies (e.g., Smith et al. 1987; Weller and Price 1988; D’Asaro 2001; Tseng and D’Asaro 2004; Gargett and Wells 2007; Scully et al. 2015).
Visual inspections of the fluctuations indicated that dominant periods were from 10 to 30 min. Wavelet power spectra of the ⟨w′⟩ML subset in Fig. 8e indicate that higher energy was generally found for motions with periods from 10 to 40 min. In fact, the enhanced energy at this period range was found for the entire event 2. For event 1, the higher energy was limited to motions with periods approximately from 10 to 30 min. Corresponding crosswind spatial scales of the CVS were between 100 and 430 m based on “Taylor’s frozen hypothesis” and the background flow between 0.17 and 0.24 m s−1 for event 1, whereas for event 2 with the background flow of 0.15 m s−1, they were approximately from 90 to 360 m. These horizontal scales of the CVS were roughly 1.5–6 times as large as their vertical scale, which was limited by the mixed layer depth.
5. Nondimensional numbers and scaling metrics
Turbulence in the ML is generated primarily by wind-driven currents, surface waves, and surface cooling. These forcing mechanisms rarely occur in isolation, instead a combination of these mechanisms drives turbulence in the upper ocean. Their relative importance is often identified by nondimensional numbers. The overall strength of the Langmuir vortex is measured by the turbulent Langmuir number Lat (e.g., McWilliams et al. 1997) given as Lat = (U*/US0)1/2; Lat ≪ 1 implies the dominance of the Langmuir vortex force relative to the inertial force. It is typically 0.2–0.5 in the open ocean; however, higher values have been found in shallow waters (e.g., Gargett and Wells 2007; Scully et al. 2015; Wijesekera et al. 2017; Yoshikawa et al. 2018). In the original theory, Leibovich (1977) introduced the Langmuir number La to measure the dominance of the vortex force. La expresses a balance between the rates of diffusion of downwind vorticity and its production by vortex tilting and stretching by the effect of Stokes drift. It is defined as La = (Kνδ/U*)3/2(0.5US0/U*)−1/2 (Li and Garrett 1995), where Kν is the eddy viscosity and δ is the e-folding depth of the Stokes-drift penetration. Leibovich and Paolucci (1981) have reported that La has to be less than a critical value of 0.66, and Thorpe (2005) has indicated that La has to be less than 0.5 for downwind vortices to develop. The Rayleigh number Ra describes the significance of the destabilizing buoyancy forcing to the inertial forcing and is defined as (e.g., Gargett et al. 2014)
Parameter Lat was less than 0.7 during both events (Fig. 10a). The higher values were found at the beginning of event 1 and at the end of event 2. In general, Lat did not vary much and was between 0.32 and 0.4 during the remaining times. As reported by previous studies (e.g., Gargett and Grosch 2014), this lack of the Lat variability is contributed to the high linear relationship between U* and US0. There was high linear correlation between these two variables during the TGOM 2017 experiment as indicated by the correlation coefficient r of 0.92 (the 95% confidence interval of r: 0.89–0.94). Clarke and Van Gorder (2018) have also reported that U* and US0 are highly correlated in the GOM, indicating that U*/US0 is nearly constant. The La was below the critical value and was between 0.01 and 0.38 during event 1 (Fig. 10a). It varied from 0.03 to 2.5 during event 2, with values above the critical La value found after 0200 UTC 16 February. When the CVS developed in the water column, the estimated Ra was less than 105 (Fig. 10b). The Ho was larger than 1 during the latter part of event 2, that is, after 0300 UTC 16 February 2017, indicating the dominance of convection at that time (Fig. 10b). The estimated values of −HML/LMO were larger than 5, also suggesting that the observed turbulent motion was forced at least partly by the destabilizing buoyancy forcing after 0300 UTC 16 February 2017 (Fig. 10b). A range of the nondimensional numbers, mainly La, Ho, and −HML/LMO, suggested that the observations had to be divided further for forthcoming analyses and discussions, that is, event 1 and two subsets for event 2: 1) 0000 UTC 15 February–0300 UTC 16 February 2017 when high winds, large surface waves, and destabilizing surface buoyancy fluxes were present and fairly constant (subset 1) and 2) 0300–1200 UTC 16 February 2017 when the winds and waves diminished but the surface buoyancy flux was still negative and large (subset 2). The nondimensional numbers for event 1 and both subsets of event 2 are listed in Table 1. Time spans for event 1 and both subsets of event 2 are marked in Figs. 7e and 10. Note also that, if available, Qnet and B0 estimated from the TGOM 2017 observations were used to calculate Ra, Ho, and LMO; otherwise, Qnet and B0 evaluated from the ERA5 data were utilized to compute the nondimensional numbers.
(a) The turbulent Langmuir number Lat (blue line) and the Langmuir number La (shown only for U10 > 3 m s−1; black line); (b) the Rayleigh number Ra (ERA5: green line; observations: black line), the Hoenikker number Ho (ERA5: cyan line; observations: blue line), and the −HML/LMO ratio (ERA5: magenta line; observations: red line); and (c) U* (black line), the magnitude of w* (green line: B0 < 0; blue line: B0 > 0), u*LC (red line), and US0 (magenta line). All numbers in (b) are shown only for B0 > 0; horizontal lines in (b) mark 105 (dotted black line), 5 (dotted red line), and 1 (dotted blue line). Timings for events 1 and 2 are marked by thin vertical black lines in (a)–(c).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
The turbulent Langmuir number Lat, the Langmuir number La, the Rayleigh number Ra, the Hoenikker number Ho, and the ratio of the mixed layer depth to the Monin–Obukhov length scale −HML/LMO for event 1 and subsets 1 and 2 of event 2.
The U* is commonly used as the velocity scale for turbulent motions in the ML; however, given the importance of the Stokes drift to Langmuir circulation, it has been suggested that the better scaling for Langmuir turbulence is
6. Energetics
a. Turbulent kinetic energy and velocity variances
Figure 11 displays 2-h averages of the TKE [q2 = 0.5(⟨u′2⟩ + ⟨υ′2⟩ + ⟨w′2⟩)] and velocity fluctuation variances, while Figs. 12a–c show mean velocity variance profiles for event 1 and subsets 1 and 2 of event 2 estimated from the MS3 data. As suggested by Gargett et al. (2009), turbulent horizontal velocity variances are first-order horizontal-velocity variance estimates. Additionally, we investigate how well turbulent first-order horizontal-velocity variances can be determined from observations collected by Sentinel V100 ADCPs in appendix B. The largest values of TKE and variances were generally found in the ML (Fig. 11) when the CVS were present. LES modeling studies (e.g., Li et al. 2005; Polton and Belcher 2007) have shown that the vertical velocity variance (⟨w′2⟩) dominates, whereas along-wind (⟨u′2⟩) and crosswind (⟨υ′2⟩) velocity variances are comparable when turbulence is forced by convection. In shear-driven turbulence, along-wind variance > crosswind variance > vertical variance. When turbulence is driven by the Langmuir vortex force: crosswind variance ≈ vertical variance > along-wind variance. During event 1, none of the forcing mechanisms occurred in isolation; hence, we expected deviations in the TGOM 2017 observations from findings of LES models with idealized forcing conditions. The crosswind velocity variance was, on average, larger than the along-wind velocity variance and both were larger than the vertical velocity variance in the ML (Figs. 12a–c). This was also the case during the latter part of event 2 (subset 2) when the destabilizing surface buoyancy flux was still substantial, and the winds and surface waves diminished significantly. However, when all three mechanisms, i.e., high winds, large surface waves, and destabilizing surface buoyancy flux were present during the first part (subset 1) of event 2, ⟨υ′2⟩ and ⟨u′2⟩ were comparable (Figs. 12a,b), and they both were larger than the vertical velocity variance in the ML (Figs. 12a–c). The velocity variances also indicate that the turbulent motion was anisotropic (Figs. 12a–c). Moreover, all mean ⟨u′2⟩ profiles (Fig. 12a) show a decreasing trend in the ML. The mean ⟨υ′2⟩ profiles (Fig. 12b) are fairly constant for depths less than 0.5HML, and then decrease in the lower half of the ML for event 1 and subset 2 of event 2, while the ⟨υ′2⟩ profile of subset 1 declines gradually in the ML. For event 1 and subset 1 of event 2, the mean vertical-velocity variance profiles show a gradual decrease toward the top and bottom of the ML from their subsurface maxima, especially evident for the profile of subset 1, located approximately at 0.15HML. The mean ⟨w′2⟩ profile of subset 2 was nearly constant at depths less than 0.5HML and then decreased gradually toward the base of the ML (Fig. 12c). Lack of an expected subsurface maximum, especially, a rapid decrease toward the sea surface for this profile, is possibly due to lack of near-surface observations. Results from LES reported, for instance, by Skyllingstad and Denbo (1995) and Li et al. (2005) have shown that as opposed to a surface-intensified shape in the shear turbulence, the vertical velocity variance profile has a parabolic-shape with a broad middepth maximum in the convective turbulence; hence, the barely changing values of ⟨w′2⟩ might be indicative of the expected parabolic shape with a broad peak.
Two-hour averages of (a) turbulent kinetic energy ⟨q2⟩ and (b) along-wind ⟨u′2⟩, (c) crosswind ⟨υ′2⟩, and (d) vertical ⟨w′2⟩ variances (cm2 s−2) at MS3. The mixed layer depth (m) is depicted by the black lines.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Mean variance profiles of the (a) along-wind ⟨u′2⟩ (cm2 s−2), (b) crosswind ⟨υ′2⟩ (cm2 s−2), and (c) vertical ⟨w′2⟩ (cm2 s−2) velocity components, along with profiles of the normalized vertical-velocity variance by (d) the frictional velocity
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
The mean ⟨w′2⟩ profiles of event 1 and subset 1 of event 2 normalized by the frictional velocity are displayed in Fig. 12d. When they are compared with those reported by other observational and LES modeling studies (e.g., Skyllingstad and Denbo 1995; McWilliams et al. 1997; D’Asaro 2001; Tseng and D’Asaro 2004; Li et al. 2005; Polton and Belcher 2007; McWilliams et al. 2012) the profiles have similar shapes with subsurface maxima located at comparable depths; however, values of
The vertical-velocity variance is often used as a metric to classify turbulence in the ocean and to appraise turbulence strength. The 2-h mixed layer averaged vertical-velocity variance (⟨w′2⟩MLD) was utilized to evaluate and classify turbulence in the ML. Figure 13 shows ⟨w′2⟩MLD from MS3. A color scale indicates a magnitude of the vertical-velocity variance for each record. The variance spans generally between 0.5 × 10−4 m2 s−2 and 4 × 10−4 m2 s−2 indicating enhanced turbulence in the ML. This variance range is similar to those found by past observational studies (e.g., Tseng and D’Asaro 2004; D’Asaro et al. 2014; Gargett and Grosch 2014; Scully et al. 2015; Yoshikawa et al. 2018). In Fig. 13, ⟨w′2⟩MLD is displayed in the turbulent Langmuir number–versus–Hoenikker number and Langmuir number–versus–Hoenikker number spaces. Figure 13a also shows the separation diagram of the wave-, convection-, and wind-forcing-dominated regimes reported by Li et al. (2005), while Fig. 13b displays the separation of the wave-forcing-dominated regime from convection-dominated regime presented by Li and Garrett (1995). The Lat, La, Ho, and estimated mixed layer vertical velocity variances indicate that surface waves were the dominate forcing mechanism during event 1, while both surface waves and convection played a part during event 2 with surface waves being a more important forcing during subset 1 and convection dominating during subset 2.
The mixed layer averaged vertical-velocity variance ⟨w′2⟩MLD (cm2 s−2; 2-h averages) at MS3 as a function of (a) Lat and Ho and (b) La and Ho (event 1: circles; event 2 subset 1:, triangles; event 2 subset 2: diamonds). Black lines mark the separation of the wave-forcing-dominated regime from the convection-dominated regime and wind-dominated regime as reported by Li et al. (2005) in (a) and the separation of the wave-forcing-dominated regime from the convection-dominated regime as reported by Li and Garrett (1995) in (b).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Figures 12d–f display the profiles of the mean vertical-velocity variance normalized by
b. Turbulent shear stresses
To further examine velocity fluctuations and their role in transporting momentum, time series and mean profiles of turbulent shear stresses were evaluated and are displayed in Figs. 14 and 15a–c, respectively. The shear stresses (⟨−u′υ′⟩, ⟨−u′w′⟩, and ⟨−υ′w′⟩) were estimated from the data recorded at MS3 and are displayed in the wind-coordinate system. The mean profiles in Figs. 15a–c were estimated for the same data subsets as the mean variance profiles shown in Fig. 12. Figure 15 also displays normalized stresses. For event 1 and subset 1 of event 2, all three stresses were normalized by the frictional velocity, while they were normalized by the convective velocity for subset 2 of event 2. The approach for a five-beam ADCP configuration proposed by R. Dewey and S. Stringer (2007, unpublished manuscript), which has been also described in Guerra and Thomson (2017), was followed to calculate the turbulent shear stresses. The method employs the variance technique (e.g., Lu and Lueck 1999), and also includes approximations for a small-nonzero pitch and roll. The mean pitch and roll at MS3 were reasonably small and were −1.47° ± 0.02° and −2.40° ± 0.01°, respectively.
Time series of turbulent shear stress components (2-h averages) (a) ⟨−u′υ′⟩, (b) ⟨−u′w′⟩, and (c) ⟨−υ′w′⟩ (cm2 s−2) at MS3. The mixed layer depth (m) is depicted by the black lines.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Mean turbulent shear-stress profiles of (a) ⟨−u′υ′⟩, (b) ⟨−u′w′⟩, and (c) ⟨−υ′w′⟩ (cm2 s−2), and mean normalized shear-stress profiles (e) ⟨−u′υ′⟩/vel2, (f) ⟨−u′w′⟩/vel2, and (g) ⟨−υ′w′⟩/vel2, where vel2 denotes
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Consistently larger values of the turbulent stresses were found for the periods when the CVS occupied the ML; however, they were also briefly significantly larger at other times, for example, below 50 m on 9 and 13 February 2017. When the structures were present the ⟨−u′w′⟩ stress was at maximum and positive (Figs. 14b and 15b) during event 1 and subset 1 of event 2 in the upper part of the ML, and it was also positive but showed a decreasing trend in the lower part of the ML. Time series of the ⟨−u′w′⟩ at 11 m were used to evaluate the downwind stress (τw = ρo⟨−u′w′⟩) measured in the water column. For subset 1 of event 2, τw (not shown) varied and was about 13% of the surface wind stress at the beginning, and it was up to 83% of the surface wind stress when the structures were fully developed in the ML. On average, this stress was about 26% at 0.2 HML and 52% at 0.15 HML of the surface wind stress for event 1 and subset 1 of event 2, and it decreased to about 1% of the surface wind stress near the bottom of the ML for both (Fig. 15e). During the latter part of event 2 (subset 2) the ⟨−u′w′⟩ stress was also positive and fairly constant in the ML. Concurrently, the ⟨−υ′w′⟩ stress (Figs. 14c and 15c) was the smallest among the shear stresses and more variable, i.e., positive and negative in the ML for event 1 and subset 1 of event 2. It was also positive and negative but, on average, had similar magnitude as the ⟨−u′w′⟩ stress in the ML during subset 2 of event 2. The ⟨−u′υ′⟩ stress (Figs. 14a and 15a) also changed sign within the ML. It was often smaller than the ⟨−u′w′⟩ stress in the upper part of the ML and usually larger than the other two stresses in the lower part of the ML. The ⟨−u′υ′⟩ also did not show any consistent mean patterns in the ML for the same set of forcing mechanisms.
For the Langmuir vortex-driven turbulence, the estimated mean profiles of the
c. Eddy viscosity
(a) Time series of eddy-viscosity coefficients ⟨Kν⟩ (m2 s−1; 2-h averages), and mean eddy viscosity Kν profiles (b) estimated from the turbulent shear stresses and normalized by U*HML for event 1 and subset 1 of event 2 and by w*HML for subset 2 of event 2 and (c) calculated from the simplified TKE budget and normalized by U*HML only for event 1 and subset 1 of event 2. (d) Mean TKE dissipation rates εobs (W kg−1) estimated from microstructure velocity-shear observations. Shown are mean profiles for event 1 (blue lines), subset 1 of event 2 (black lines), and subset 2 of event 2 (magenta line). Thin horizontal lines in (b)–(d) denote 95% confidence intervals.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
If the TKE budget equation is reduced to a balance between the shear production {Pshear = Kν[(∂U/∂z)2 + (∂V/∂z)2]} and the TKE dissipation rate εobs then the eddy viscosity can be also estimated from εobs ≡ Pshear and results are shown in Fig. 16c. The blue and black lines depict the mean profiles only for event 1 and subset 1 of event 2, respectively. Figure 16d shows the TKE dissipation rate profiles obtained from the microstructure observations for the same periods. There were no microstructure data to estimate dissipation rates for subset 2. TKE dissipation rates computed from the TGOM 2017 data are discussed in detail in section 6d. The mean profile of Kν estimated for subset 1 of event 2 (Fig. 16c) show a similar concave shape as that estimated from the turbulent stresses. Estimated values, however, are slightly larger for depths from 0.2HML to 0.4HML, and smaller at depths less than 0.2HML and at depths larger than 0.4HML. The mean profile of event 1 (Fig. 16c), however, is different. It decreases gradually from 0.1HML to the base of the ML. Differences might have resulted from the fact that 1) the simple TKE balance did not hold when the coherent velocity structures were observed in the ML, and/or 2) the observations, especially the microstructure observations, were very limited in the upper part of the ML (0.15HML–0.3HML).
d. TKE dissipation rates
Time series of the estimated TKE dissipation rates for events 1 and 2 are shown in Figs. 17a and 17b, respectively. Due to technical problems with both the Wirewalker and MicroRider, the microstructure shear data captured nearly the entirety of event 1 but only part of event 2 was covered. The higher ε was found throughout in the ML with values mainly between 10−8 and 2 × 10−6 W kg−1 when the CVS were observed in the water column during event 1 (Fig. 17a, the first part of event 1: 1100–1800 UTC 9 February 2017). The rates were also above 10−7 W kg−1 in the upper part of the ML but they were less 10−7 W kg−1 after 0200 UTC 10 February 2017 during the latter part of event 1. In fact, the dissipation rates began decreasing in the entire ML (Fig. 17a) after 1200 UTC 10 February 2017 when the buoyancy forcing started weakening, i.e., the destabilizing surface buoyancy flux began decreasing and switched to the stabilizing buoyancy flux at the end of event 1. The TKE dissipation rates were primarily from 10−7 to 2 × 10−6 W kg−1 in the upper part of the ML and showed some variability in the ML during event 2 (Fig. 17b). Note that the high dissipation rates were also found when our current observations indicated lack of coherent velocity structures in the ML, that is, between 1800 UTC 9 February 2017 and 0200 UTC 10 February 2017 and prior to 0000 UTC 15 February 2017 (Figs. 7b–e). A potential explanation might be inability of our ADCPs to detect weakened turbulent eddies. These higher dissipation rates might be also attributed to the other ML processes. For example, the background current shear was still high during these two periods (Fig. 6c); hence, higher rates might be indicative of the shear-driven turbulence.
TKE dissipation rates ε (W kg−1) during (a) event 1 and (b) event 2, and (c) layer-averaged (10–15 m) TKE dissipation rates (W kg−1) estimated from observations (red dots), predicted by law-of-the-wall scaling εW (blue line), calculated from the scaling proposed by Terray et al. (1996) εT (magenta line), and convection scaling εc (ERA5: black line; observations: green line).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
The mean profiles of the TKE dissipation rates for event 1 and subset 1 of event 2 are plotted in Fig. 16d. These profiles are very similar, and both display a gradual decrease from about (5–6) × 10−7 W kg−1 at 0.1HML to (6–8) × 10−8 W kg−1 at the bottom of the ML. Moreover, Fig. 17c displays near-surface layer-averaged (10–15 m) TKE rates estimated from the microstructure shear observations, predicted by the law-of-the-wall scaling
7. Turbulent kinetic energy budget
(a)–(c) Terms of the TKE budget (terms × 107; m2 s−3) and (d)–(f) vertical transport components of the TKE flux (transport × 107; m2 s−3) estimated from the data collected during (left) event 1 and (center) subset 1 of event 2 and (right) the data recorded during event 1 and subset 1 of event 2 at MS3. The rate of change of the TKE ∂q2/∂t; shear PSH, Stokes PST, and buoyancy PB production terms; dissipation ε; and vertical transport of the TKE flux T1 are depicted by green, red, black, light-blue, magenta, and cyan lines, respectively. Dotted blue lines depict residuals (RES) in (a)–(c). Horizontal (T1H) and vertical (T1V) components of the vertical transport are depicted by blue and black lines in (d)–(f). Thin horizontal lines denote 95% confidence intervals.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Figures 18a–c also display residuals. These residuals partially represent errors associated with the estimated TKE budget terms and partly T2. Scully et al. (2016) have reported that energy from breaking surface waves is primarily transmitted via pressure work into the water column. In the atmospheric surface layer, Wyngaard and Coté (1971) have reported imbalance in the TKE budget under unstable conditions and suggested that this imbalance was a part of the pressure transport. Here we speculate that the pressure work part of the transport is also important for the closure of the local TKE budget and is represented by the residuals since their mixed layer average for both periods is 0.21 × 10−7 m2 s−3 and is fairly comparable to the mixed layer means of PST (0.61 × 10−7 m2 s−3), PSH (1.36 × 10−7 m2 s−3), and T1 (−0.15 × 10−7 m2 s−3).
8. Summary and conclusions
Turbulent coherent velocity structures in the mixed layer were investigated utilizing atmospheric, hydrographic, current, and microstructure observations collected on the outer shelf in the northern Gulf of Mexico in February 2017. Two periods characterized by moderate–high winds (U10 ~ 6–14.6 m s−1), large surface waves (Hs ~ 1.5–2.7 m), and large surface buoyancy fluxes (B0 ~ 2.5 × 10−7–3.5 × 10−7 W kg−1) were examined. During these two events, the mixed layer deepened significantly due to initially shear- and wave-driven mixing but never extended to the bottom. On the onset of high winds and large surface waves, turbulent coherent velocity structures reaching the base of the mixed layer developed a few hours after the initial deepening of the ML during the first period and a day later during the second period. The structures had temporal scales from 10 to 40 min and estimated lateral scales ranging from 90 to 430 m that were 1.5–6 times as large as their vertical scales limited by the mixed layer depth. These scales are in a range reported by past observational studies (e.g., Smith et al. 1987; Weller and Price 1988; Wijesekera et al. 2017).
The coherent velocity structures exhibited several qualitative features that previous studies have attributed as characteristics of Langmuir and convective cells (e.g., Smith et al. 1987; Weller and Price 1988; Gargett and Wells 2007; Gargett and Grosch 2014). Large amplitudes of along-wind, crosswind, and vertical velocity fluctuations, narrower downwelling regions than upwelling regions, elevated vertical-velocity variance, vertical-velocity maxima in the upper part of the ML (0.1HML and 0.5HML), and phasing of the crosswind velocities relative to the vertical velocities near the base of the mixed layer were commonly observed in the data discussed here. Because of the lack of near-surface velocity data, some of the characteristics such as near-surface intensification and convergence zones of the crosswind velocity or subsurface maxima of the downwind velocity in downwelling regions were largely not captured by the observations. During atmospheric cold-frontal passages in the northern Gulf of Mexico, strong winds and resulting high surface-wave energy and large Stokes drift as well as large surface-heat losses are common and occur simultaneously (e.g., Wijesekera et al. 2013); hence, the separation of shear, Langmuir, and convective-driven turbulence was not really possible here. Instead, dynamical parameters such as the Langmuir, turbulent Langmuir, Hoenikker, and Rayleigh numbers and the ratio of the mixed layer depth to the Monin–Obukhov length scale were employed, and they indicate that Langmuir vortex and convection were plausible mechanisms for generating the coherent velocity structures in the ML.
When the CVS were present the TKE, turbulent shear stresses, eddy diffusivities calculated from the turbulent stresses, and measured TKE dissipation rates were also consistently large in the ML. The velocity variances did not show expected relationships for turbulence driven only either by the Langmuir vortex or the buoyancy forcing. The vertical-velocity variance was always smaller than the horizontal variances regardless of the forcing mechanisms, whereas the crosswind variance was either larger or comparable to the along-wind variance. When turbulence was primarily generated by the Langmuir vortex the vertical-velocity variance was scaled relatively well by both
Our observations allowed evaluations of almost all terms of the TKE budget when the ocean was experiencing moderate to high winds, large surface waves, and significant surface cooling. The time rate of change of the TKE was the smallest (~10−9 m2 s−3) among the estimated TKE budget terms indicating stationary conditions. The TKE production was dominated by the Stokes and shear production in the upper part of the ML and by the shear production in the lower part of the ML, whereas the buoyancy production was an order of magnitude smaller at depths larger than 0.1HML. The TKE production did not balance dissipation in the ML indicating that the vertical-transport term was not negligible for the local balance of the TKE budget. The TGOM 2017 observations only allowed an estimation of a part of the vertical transport, that is, the TKE-flux transport term that was negative and on the order of 10−7 m2 s−3, similar to the Stokes and shear productions in the upper part of the ML. Residuals, which were also on the order of 10−7 m2 s−3, suggested further that the pressure-work term of the vertical transport was also significant and had to be included to close the local TKE budget.
Acknowledgments
This work was sponsored by the Office of Naval Research in a Naval Research Laboratory project referred to as “Turbulence in the Ocean Boundary Layer (TGOM)” (Grant N0001420WX00410). We thank Dr. Joel Wesson for his help with the TGOM 2017 field experiment and Andrew Quaid and Ian Martens for their technical support. We also thank the captain, crew, and marine technicians of the R/V Pelican for their assistance. We thank the anonymous reviewers for their constructive comments.
APPENDIX A
Comparisons of TKE Dissipation Rates from Vertical Microstructure Profiler, Glider, and Wirewalker Platforms
Near the end of the TGOM 2017 experiment, microstructure velocity-shear observations were concurrently collected by a vertical microstructure profiler (VMP; Rockland Scientific International), a 200-m Slocum glider (GG; Teledyne Webb Research) equipped with a MicroRider-1000LP (MR; Rockland Scientific International), and a Wirewalker (WW; Del Mer Oceanographic) also with a mounted MR. A more detailed description of the glider, its dives, instrumentation, and sampling is found in Wijesekera et al. (2020). The VMP and both MRs had two air-foil velocity-shear probes. Past studies have proved that shear probes mounted on VMP profilers and gliders are able to deliver reliable microstructure velocity-shear observations (e.g., Lueck et al. 2002; Wolk et al. 2009; Fer et al. 2014; Wijesekera et al. 2020). We evaluate here velocity-shear measurements and estimated TKE dissipation rates from the WW platform through comparisons with TKE dissipation rates from the VMP profiler and the Slocum glider.
Concurrent velocity-shear measurements from all three platforms were available between 0217 and 0417 UTC 19 February 2017 (s1 survey) as well as between 1525 and 1800 UTC 19 February 2017 (s2 survey). During these two periods, 21 and 27 VMP casts, 17 and 24 WW profiles, and 6 and 8 GG dives were respectively collected and later processed. Distances between the WW and the VMP and GG locations varied approximately from 0.8 to 2.6 km and from 4 to 7.3 km, respectively. Additionally, the glider and the Wirewalker profiled simultaneously within the experimental area between 0415 UTC 18 February 2017 and 1530 UTC 21 February 2017 (s3 survey). There were 268 glider dives and 728 WW profiles recorded during the s3 survey. The distance between the GG and WW platforms varied between 2.8 and 7.3 km. Locations of the VMP, GG, and WW surveys are shown in Fig. A1.
Locations of the TGOM 2017 mooring sites (MS1–MS4; black asterisks), VMP casts (the first survey period VMP s1: blue dots; the second survey period VMP s2: red dots), WW profiles (blue asterisk), and GG dives (the first survey period GG s1: blue line; the second survey period GG s2: red line; the third survey period GG s3: cyan line).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
The 512-Hz microstructure velocity-shear data from the three platforms were used to estimate TKE dissipation rates. Shear observations from GG and WW ascending profiles were only utilized in these calculations. The good-quality shear data spanned from ~6 to ~75 m for s1 and s2 and from ~10 to ~75 m for s3. The TKE dissipation rates were estimated by fitting Nasmyth spectra to the turbulent velocity-shear spectra computed from 1024 data points using the nonlinear least squares technique as discussed in section 2. The noise level of the TKE dissipation rates was approximately 10−10 W kg−1 for the GG (e.g., Wijesekera et al. 2020) and approximately 10−11 W kg−1 for the VMP. Because of depth differences of the ε estimates among three platforms, the rates were binned on a common vertical grid with 3-m resolution.
Because of the inherent variability of oceanic waters, the intermittent nature of turbulence, and the separation among the WW, VMP, and glider locations, ε comparisons are challenging. Under these conditions meaningful comparisons can be made with sufficient averaging of the TKE dissipation rates, say, for example, temporal averages of the rates over a period of the dominant flow field such as an inertial period in the GOM. In the following, we compare microstructure observations averaged over s1, s2, s3 surveys and also over a 30-min averaging interval. For s1 and s2, the VMP and WW platforms have similar number of profiles; hence, the comparison of the averages is meaningful. Table A1 lists survey-long means for each platform. The survey means from the VMP and WW are within a factor of 2, which is considered to be a good comparison of the ε estimates from different platforms (e.g., Fer et al. 2014), while the GG means are the smallest. The VMP means are 1.6 and 2.7 times the survey-long averages obtained from the GG data for the s1 and s2 surveys, respectively. The WW means are about 3 times the GG means for s1 and s2 surveys. In summary, all three platforms produce comparable TKE dissipation rate estimates when averaged over survey-long periods.
Survey-long means and standard errors of TKE dissipation rates (W kg−1) estimated from the microstructure velocity-shear observations collected by the vertical microstructure profiler (VMP), Wirewalker (WW), and glider (GG) platforms.
We also compare the TKE dissipation rates, averaged over 30-min intervals along the survey paths, where we can expect a lot of spatial/temporal variability and intermittency. Figure A2 displays survey-averaged TKE dissipation rate profiles and 30-min averages of ε profiles for s1 and s2 surveys. The 30-min-averaged VMP-measured rates show generally less temporal and depth variability than those from the WW and GG platforms for both s1 and s2 surveys. The 30-min means also show that the GG dissipation estimates tend to be smaller than the VMP and WW estimates for s1 and below 35 m for s2, while they are more comparable to the VMP and WW estimates at depths less than 35 m for s2 survey. Despite the platform separation, there is a good agreement among the VMP- and WW-measured dissipation rates as indicated by the 30-min averages of ε that are within a factor of 2, 3, and 10 for 47%, 69%, and 95% of all considered ε from s1 and s2, respectively. Agreements between the GG- and WW-measured ε are relatively poorer, and are within a factor of 2, 3, and 10 for 27%, 45%, and 80% of ε, respectively. Weak agreements for s1 and s2 surveys are also among the rates from the VMP and GG platforms. However, when larger datasets of the TKE dissipation rates from the GG and WW platforms for the s3 survey are considered, a comparison of the survey-long means (Table A1) improves, and they are approximately within a factor of 2. The agreement between the WW- and GG-measured ε is also better for 30-min averages (Fig. A3). They are visually in good consensus and are within a factor of 2, 3, and 10 for 30%, 46%, and 81% of the considered rates.
Survey-averaged profiles and 30-min averages of the TKE dissipation rates from the VMP (εVMP; red lines and asterisks), WW (εWW; black lines and asterisks), and GG (εGG; blue lines and asterisks) for (a) s1 and (b) s2 surveys.
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
The 30-min-averaged profiles of TKE dissipation rates (W kg−1) from (a) the Wirewalker (εWW) and (b) the glider (εGG).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
Regardless of the locations and survey period, a majority of the TKE dissipation rate estimates are less than 10−8 W kg−1, indicating that low-turbulence waters were mostly sampled by the three platforms. Figures A2 and A3 show that weak turbulence was generally detected at depths below 20 m; hence, it is likely that all three platforms profiled concurrently very similar water masses with comparable levels of turbulence. An excellent agreement among, for instance, the VMP- and WW-measured ε in the water mass characterized by weak turbulence would point out that the Wirewalker/MicroRider package is a dependable platform to deliver quality microstructure observations. It is the case for the ε estimates from s1 and s2 surveys that are within a factor of 2, 3, and 10 for 50%, 74%, and 98% of the rates less than 10−8 W kg−1. The agreement is weaker for the GG- and WW-measured dissipation rates from the s3 survey, during which the dissipation rates are within a factor of 2, 3, and 10 for 31%, 46%, and 82% of ε less than 10−8 W kg−1. Discrepancies might be related again to the intermittency of turbulence and the platform separation. Overall, the presented results indicate that the Wirewalker/MicroRider package is able to deliver good quality microstructure velocity-shear observations and reliable TKE dissipation rates that are suitable for studies of short- and long-term mixing processes in the ocean.
APPENDIX B
Turbulent Horizontal-Velocity Variance
The slant beam angle from the vertical is 25° for all 300-kHz Sentinel V100 ADCPs that were deployed during the TGOM 2017 experiment, and, therefore, the first-order horizontal-velocity variance calculated from data collected by the Sentinel V100s is a better estimate when compared with that computed from ADCPs with a 20° slant beam angle. Figure B1 illustrates this point. It displays Ru as a function of kΔ/π for three θ angles (20°, 25°, and 30°), three φo phases (−90°, 0°, and 90°), four anisotropy ratios (0.3, 0.5, 0.6, and 1), and two depth ranges (15 and 100 m). For instance, the anisotropy ratio for Langmuir cells is often ≥ 0.5 and ADCPs with a 25° slant angle overestimate less than ADCPs with a 20° slant angle for small eddies with wavelengths L ≤ 100 m for the depth range of 15 m (Fig. B1a). In general, the response function shows that ADCPs with a smaller slant angle deliver better horizontal velocity variance estimates for highly anisotropic turbulence (wo/uo < 0.4), while they produce significantly larger overestimates than instruments with larger slant angles for wo/uo > 0.5 regardless of the depth range (Figs. B1a,b). Figures B1c and B1d illustrate effects of the phase for a fixed value of wo/uo = 0.5. For smaller depths (15 m) and L ≤ 100 m, the response for the slant angle of 20° is marginally preferable to those for 25° and 30° for phases between 0° and 90° but noticeably worse when the phase is negative. For larger depth ranges (Fig. B1d), the response depends strongly on L. For L = 200 m and depth of 100 m, an ADCP with an angle of 25° is preferable and an ADCP with 30° is better for L = 300 m whereas an ADCP with an angle of 20° shows poor responses for both wavelengths. Our TGOM 2017 observations indicate that wo/uo was generally between 0.3 and 0.6. The theoretical response function (Fig. B1) indicates that five-beam Sentinel V100 ADCPs are able to deliver reliable estimates of the first-order horizontal-velocity variance that are comparable to those calculated from data collected by a system with a 30° slant angle for wo/uo between 0.3 and 0.6.
Comparison of logarithmic response functions Ru for the first-order horizontal-velocity variance from instruments with slant beam angles from the vertical of 30° (solid thin lines), 25° (solid thick lines), and 20° (dotted lines); Ru is shown as a function of kΔ/π = 2Δ/L, where 2Δ(z) is slant beam pair separation at height z above the transducer and k and L are horizontal wavenumber and wavelength, respectively. Shown is variation with wo/uo of 0.3 (blue lines), 0.5 (green lines), 0.6 (red lines), and 1 (light-blue lines) and fixed phase of 0° (180°) at z of (a) 15 and (b) 100 m and variation with a phase of −90°(blue lines), 0° (green lines), and 90° (red lines) for fixed wo/uo = 0.5 at z of (c) 15 and (d) 100 m. The vertical lines mark L of 100 (magenta lines) and 300 (black lines) m in (a) and (c) and L of 200 (orange lines) and 300 (black lines) m in (b) and (d) for the slant angle of 30° (solid thin lines), 25° (solid thick lines), and 20° (dotted lines).
Citation: Journal of Physical Oceanography 51, 9; 10.1175/JPO-D-20-0248.1
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