1. Introduction
As part of the lower limb of the meridional overturning circulation, which is fundamental for Earth’s climate, the formation of Antarctic Bottom Waters (AABW) has important effects on the climate, such as through the release of oceanic heat loss to the atmosphere (Talley 2013). In recent decades, a substantial portion of the atmospheric warming due to the anthropogenic greenhouse gases participated in the warming of abyssal waters (Purkey and Johnson 2010) via the formation of bottom waters. In spite of the primary role played by AABW in the circulation of physical and biogeochemical properties, their pathways and the processes giving rise to the turbulent diapycnal mixing providing the buoyancy flux that is required to close the AABW cell (Munk 1966) are still subject to significant uncertainty. For example, in the early theoretical model of the buoyancy-forced abyssal circulation (Stommel et al. 1958; Stommel and Arons 1960), the deep currents are driven by a uniformly distributed upwelling. In spite of the apparent importance of this vertical flow, the spatial distribution of the upwelling required to close the overturning circulation remains largely unknown. In the case of spatially uniform upwelling, the model of Stommel predicts poleward flow in the ocean interior to balance western boundary currents. Abyssal float data from the Brazil Basin in the western South Atlantic are fundamentally inconsistent with this prediction, however, and indicate a mean circulation dominated by meridionally and vertically interleaved zonal currents flowing in both directions (Hogg and Owens 1999; Thurnherr and Speer 2004). St. Laurent et al. (2001a) hypothesize that the observed zonal mean flows in the interior of the Brazil Basin are related to forcing by the high levels of mixing observed over the western flank of the Mid-Atlantic Ridge (MAR; Polzin et al. 1997).
Microstructure and tracer observations collected during the Brazil Basin Tracer Release Experiment (BBTRE) in the 1990s indicate high levels of turbulence and mixing over the topographically rough MAR flank (up to two orders higher diapycnal diffusivity on the MAR flank than over the adjacent abyssal plain). Early analyses of the BBTRE data (Polzin et al. 1997; Ledwell et al. 2000b; St. Laurent et al. 2001a) emphasize the hypothesis that the breaking of tidally forced internal waves generated over rough topography (Bell 1975) provides the energy for the elevated turbulence. The principal argument for a tidal energy source of the elevated mixing on the MAR flank is provided by an apparent spring–neap modulation of the near-bottom dissipation rate of turbulent kinetic energy ε (Ledwell et al. 2000b; St. Laurent et al. 2001a). However, aliased sampling provides an alternative explanation for the observed variability in ε, as the BBTRE spring tide measurements were collected closer to the MAR crest, where turbulence levels are higher, than the neap tide measurements (Ledwell et al. 2000b; Toole 2007). To separate spatial from temporal patterns, a mooring was deployed in 1998 near 18°W inside a deep zonal canyon cutting across the MAR flank where the BBTRE tracer-release experiment was carried out (Ledwell et al. 2000b); we term this the BBTRE canyon.
A regional inverse model of the circulation on the western flank of the MAR near 20°S in the Brazil Basin based on the BBTRE microstructure and CTD data yields southwestward flow above the topography (St. Laurent et al. 2001a), consistent with float trajectories (Hogg and Owens 1999) and tracer advection (Ledwell et al. 2000a). The model also shows bottom water flowing eastward toward the MAR crest in the fracture zone (FZ) canyons, which corrugate almost the entire flanks of slow-spreading midocean ridges, including the MAR flank in the Brazil Basin (St. Laurent et al. 2001a). In the data of the model inversion, turbulence levels are significantly higher below the topographic peaks (i.e., within the FZ canyons) than above the “topographic envelope” (Fig. 3 in St. Laurent et al. 2001b). A steady-state heat budget of the BBTRE canyon indicates that the primary balance is between along-canyon advection and vertical eddy diffusion (St. Laurent et al. 2001b), similar to the situation in other sloping submarine valleys (Thurnherr et al. 2002).
The velocity data from the BBTRE mooring are qualitatively consistent with this heat budget, although they indicate mean up-canyon velocities of several centimeters per second (Thurnherr et al. 2005), nearly an order of magnitude above the heat budget–derived estimates. Thurnherr et al. (2005) interpret this discrepancy between the modeled and observed up-canyon velocities as evidence that mixing hotspots were insufficiently sampled during BBTRE. They suggest turbulence associated with hydraulic overflows across sills on the canyon floor as a hypothesized source of the “missing mixing” because of a strong association between the presence of sills between two hydrographic stations and the corresponding along-canyon density gradients. Overflow processes contribute significantly to the transformation of deep-water masses within narrow interbasin passages (Polzin et al. 1996; Mercier and Morin 1997; Ferron et al. 1998). The role of such passages is particularly relevant in the Brazil Basin, which, for AABW, is connected to other ocean basins via five confined channels (Hogg et al. 1996). Similarly, interbasin passages are known to affect the transformation of deep-water masses in the Pacific (Alford et al. 2013; Voet et al. 2015) and Indian Oceans (MacKinnon et al. 2008). The BBTRE canyon is not an interbasin passage, however, as it terminates at the MAR crest (Thurnherr et al. 2005). Even in such enclosed submarine valleys, hydraulic overflows are common (Thurnherr and Richards 2001; Thurnherr et al. 2002, 2008) and associated with high levels of turbulence and mixing (St. Laurent and Thurnherr 2007; Tippenhauer et al. 2015). Most overflows in the ocean display signs of hydraulic control (Turner 1973); the velocities increase greatly as the flow approaches the sill (or constriction) and accelerate for some distance downstream before returning to upstream levels fairly abruptly. Overflow processes known to be associated with high levels of turbulence include shear instabilities along the interface between the fast-flowing part of the overflow and the overlying water column as well as hydraulic jumps (Wesson and Gregg 1994). Additionally over shallower sills, the tidal modulation of internal hydraulic control was recognized in fjords (Farmer and Smith 1980; Staalstrøm et al. 2015) and in interbasin passages (Wesson and Gregg 1994); some of the barotropic tidal energy can radiate away as internal waves (Klymak and Gregg 2004) and affect the far-field turbulence in the ocean. Internal wave trapping (Gordon and Marshall 1976) can further intensify canyon mixing (Kunze et al. 2002; Carter and Gregg 2002) in the BBTRE canyon, where near-inertial waves are known to modulate the shear variance (Toole 2007).
With the Dynamics of Mid-Ocean Ridge Experiment (DoMORE) project, we aim to study the role of overflow processes in a 200-km-long section of the BBTRE canyon that includes the largest along-canyon density drop and turbulence levels (Thurnherr et al. 2005). Using data from hydrographic surveys and from several moorings, we study the influence of a large overflow on a 2-layer exchange mean flow and on along-canyon density gradients (section 3a). The spatial variability of the dissipation rate and its tidal dependence at the sill and away from it are investigated (section 3b). The survey suggests the occurrence of an overflow with enhanced downstream turbulence fortnightly modulated at the sill (section 3c). The moorings detect overturns (section 3d) and inform on the finestructure properties of internal waves (section 3e) at two locations: at the sill (mooring P1) and away from any topographic features (mooring P3). Consistent with the microstructure survey, large turbulent overturns around the 2-layer interface are phase locked with semidiurnal tides at spring tides at P1, reminiscent of a forming internal lee wave during slacking tides. Away from the sill, finestructure characteristics support the predominance of near-inertial waves with downward-propagating energy. In section 4, we quantify the dissipation rate at the sill and the energy radiated by internal waves, which both potentially contribute to remove the across-sill energy of the lower layer and of the barotropic tides.
2. Data and methods
a. Study region
As is the case for most of the slow-spreading midocean ridges, the western flank of the MAR in the Brazil Basin is corrugated by FZ canyons, which are typically between 500 and 1000 m deep and spaced approximately 50 km apart (Tucholke and Lin 1994). For the DoMORE project, an ≈170-km-long stretch of one of these FZ canyons, the BBTRE canyon, was chosen (Fig. 1) to include both the location with the largest along-canyon density gradient near 14.6°W, where Thurnherr et al. (2005) inferred the existence of a major overflow as well as ≈100 km of canyon downstream from this overflow where the along-canyon density gradient observed during BBTRE was reduced compared with the gradient at 14.6°W. Along its axis, the BBTRE canyon is corrugated by meridionally elongated spanwise topographic structures that are called bathymetric hills and that form both sills and constrictions for any deep along-canyon flow (Fig. 1b). In terms of first-order topography (canyon width and depth, presence of topographic hills) as well as hydrography (along-canyon density gradients and stratification), the BBTRE canyon is similar to many other FZ canyons in the South Atlantic (Thurnherr and Speer 2003).
(a) Bathymetry in the South Atlantic of a midlatitudinal section on the western flank of the Mid-Atlantic Ridge and (b) over a fracture zone canyon around 21°S. (top) The 3900 m and (bottom) the 3900-, 4300-, and 4700-m isobaths are contoured. The insets display the topography over two sites (the overflow and downstream sites) with along- and across-sill tow-yo transects (orange lines), yo-yos (purple triangles), and CTD/LADCP profiles (black circles and stars), associated with DMP profiles (red and black triangles) and four moorings distributed with current meters (red triangles), two of which contain MMPs (red circles).
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
Over most of the DoMORE study region, the bathymetric hills are much more prominent along the northern canyon wall, which is considerably less steep than the southern sidewall, especially east of 14.2°W (Figs. 1b, 3c). A well-defined break in cross-canyon steepness along the southern wall is used to define a nominal canyon wall depth of 3900 m. The topographic data are acquired by a Kongsberg EM122 multibeam echo sounder with a horizontal resolution of 50 m and merged with the previous BBTRE survey (Ledwell et al. 2000a). Those data reveal deeper connections between the BBTRE canyon and its northern and southern neighbor canyons near 13.8° and 14.6°W, respectively (Fig. 1b). The average width of the BBTRE canyon in the DoMORE study region along the 3900-m isobath is ≈18 km. The maximum depth at each longitude is used to define the mean depth along the thalweg of ≈4760 m for the DoMORE study region. The BBTRE canyon reaches both its minimum width (≈10 km) and axial depth (≈4290 m) in the saddle of a particularly tall bathymetric hill near 14.6°W (Fig. 2). The basins on each side of the resulting sill are ≈4700 m deep; the estimated length of this sill is ≈8 km. At the sill, the topography is closed below 4000 m except for a 2-km-wide deep passage (Fig. 3a).
(a) Along-canyon isopycnals γn with the main sill located at 14.6°W. The thalweg (gray) and the canyon rim of the northern wall with a mean depth of 3860 m (black) are displayed. The isopycnal at the deep-water mass separation of AABW/LNADW (γn = 28.11) is indicated (thick). The along-canyon gradient of density ρx averaged in the bottommost 50 m above any intrusion of the thalweg is displayed below each station pair (red) as well as the density gradient uncertainty (black); ρx positive corresponds to decreasing density toward the MAR. (b) Turbulent dissipation rate estimated from the VKE εVKE inferred from LADCP profiles during two spring–neap cycles and averaged every 0.1° of longitude for the spring (red) and neap (black) tidal periods and integrated in height above bottom to 1000 m. The 95% confidence intervals are indicated based on bootstrapping.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
Topography of the cross-canyon sections (a) at the overflow site around the sill (moorings P1 and P2) with isopycnals from one tow-yo transect and (c) at the downstream site located 100 km eastward from the sill (P3 and P4). The current meter depths are indicated (crosses) as well as the MMP limits at P1 and P3 (thick lines). The ray paths are displayed for semidiurnal (dashed black) and near-inertial waves (dashed gray). Mean (thick red), standard error (pink), and 10th percentiles (dashed pink) of the zonal velocity (b) at the overflow site and (d) at the downstream site measured from the MMP and from the current meters (crosses, with the 10th percentiles error bars). A polynomial fit is applied on the temporal mean of MMP and current meter velocities (thin black), whereas another fit is applied on one LADCP profile (thin dashed black) taken within the sill passage in (b). The mean (green) and corresponding 10th percentiles of temperature (dashed green) at P1 and P3 are added in (b) and (d), respectively.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
b. Measurements
The BBTRE canyon region was visited twice with the R/V Nathaniel B. Palmer for the DoMORE project. During the first cruise (DM1) in July 2014, a topographic survey was carried out, lowered acoustic Doppler current profiler (LADCP) and conductivity–temperature–depth (CTD) profiles were collected (a combination of full-depth profiles and tow-yo and yo-yo casts), and an array of moored instruments was deployed. During the second cruise (DM2) in October 2015, the moored instruments were recovered, additional LADCP/CTD data were collected, and 41 microstructure casts were carried out with a deep microstructure profiler (DMP). The moorings were deployed at the location of the minimum canyon cross section near 14.6°W (overflow site) as well as in a similarly shallow area ≈100 km farther east (downstream site; Figs. 1–3), and most hydrographic profiles were collected between these two mooring sites. A total of 58 and 66 full-depth LADCP/CTD pairs were collected during DM1 and DM2, respectively; at 41 of the DM2 stations, simultaneous profiles of microstructure were collected as well. In addition to those full-depth pairs, 215 (140 and 75 for DM1 and DM2, respectively) partial-depth LADCP/CTD pairs below 3000 m were collected during several tow-yo transects both across the sill at the overflow site and meridionally across the BBTRE canyon at several locations (Fig. 1).
Temperature and salinity profiles were collected with a SBE 911plus CTD mounted on a SBE32 rosette using a wire speed of 50 m min−1. The tow-yo casts were collected with a mean vessel speed of 0.6 knots (1 knot = 0.51 m s−1); the package location was estimated from the ship’s location, wire out, and altimetry data. All CTD sensors were precruise calibrated, and there are no indications for significant drifts in any of the sensor data. The temperature uncertainty provided by the manufacturer is ±0.001°C. An accuracy of 0.001 for salinity is estimated from the results of salinometer calibrations using a Guildline Portasal SA10 for both cruises.
Velocity profiles were collected with upward- and downward-facing Teledyne RDI Workhorse ADCPs mounted on the rosette. Horizontal velocities are calculated with the LDEO_IX implementation of the velocity inversion method (Visbeck 2002). Most of the DM1 LADCP profiles were collected with two 300-kHz instruments; during DM2 a downward-facing, 150-kHz ADCP was used together with an upward-facing, 300-kHz instrument. Because of weak acoustic backscatter, different bin sizes and blanking distances were tried; most of the profiles used here were collected with pulse and bin lengths of 32 and 16 m, respectively. LADCP data quality is assessed by comparing the upper-ocean horizontal velocities derived without the shipboard ADCP (SADCP) constraint to the corresponding SADCP velocities; based on data from many different regions, typical rms discrepancies for high-quality LADCP datasets are 4–6 cm s−1. Extremely weak acoustic backscatter in the DoMORE study region resulted in many LADCP profiles of insufficient or questionable quality. The horizontal LADCP velocities used here are all taken either from bottom-track solutions near the seabed (where acoustic backscatter is significantly greater than in the midwater column) or from profiles that passed careful visual inspection and using a 6 cm s−1 threshold for the rms LADCP–SADCP velocity difference. In addition to the horizontal velocities, the DoMORE LADCP data are also processed for vertical velocity (Thurnherr 2011). Because of the weak acoustic backscatter, the vertical velocities were processed in 40-m bins.
We used a Rockland VMP-6000 (RVMP), manufactured by Rockland Scientific International, Inc., to obtain profiles of microstructure from which ε is derived. Details of the RVMP instrument system can be found online (at http://www.rocklandscientific.com). The RVMP measures centimeter-scale shear of velocity u with depth z using airfoil probes, from which the dissipation rate of turbulent kinetic energy is estimated as ε = (15/2)ν〈(du/dz)2〉 (appendix A), where ν is the molecular viscosity of seawater and 〈⋅〉 is the integrated vertical wavenumber spectra. Here, we have invoked isotropy relations (Hinze 1975) to reduce the 9-component rate of strain tensor to a single microscale shear component.
Four moorings (Fig. 3; Table 1) recorded the mean flow, tides, and near-inertial waves at the overflow and downstream sites. Two McLane moored profilers (MMP), each equipped with an acoustic current meter (ACM) and a CTD from Falmouth Scientific, Inc., sampled the water column between ≈200 and 800 mab, crawling up and down the wire at approximately 25 cm s−1: P1 in the sill saddle at the overflow site (21.12°S, 14.58°W) and P3 in the deepest part of the canyon at the downstream site (20.92°S, 13.71°W), located ≈100 km east of P1. Both MMPs collected three, consecutive, 90-min-long temperature, salinity, and horizontal velocity profiles once every half-inertial period (16.7 h) concurrently during 8–10 months. ACM postprocessing includes compass calibration (Toole et al. 1999) and subsampling on a 2-dbar pressure grid. The accuracy of the derived velocity data is in the cm s−1 range (J. Toole 2016, personal communication), whereas the random noise of the raw path velocities mostly attributed to the instrument vibration is of ~1 cm s−1 (Doherty et al. 1999). Outliers above three median absolute deviations of the 0.05-Hz high-pass filtered conductivity, temperature, and pressure sampled at 2 Hz are replaced by the median over three consecutive points. A recursive filter (Mudge and Lueck 1994) is applied on the conductivity and pressure to minimize the effect of salinity spikes on the density. Each mooring had a Nortek Aquadopp acoustic current meter sampling the velocities every 10-min ≈10 m above the seabed as well as another instrument near the top of the MMP profile turnaround; on mooring P1, an additional current meter recorded the velocities near 3200 m. Both at the overflow and downstream sites, there were additional moorings (P2 and P4, respectively) with Aquadopp current meters both near the seabed and ≈800 m up in the water column; partway up on the northern canyon walls (Fig. 3).
Mooring locations at the overflow site (P1 and P2) and at the downstream site (P3 and P4) with each instrument (MMP and Nortek Aquadopp), depth, start, and end dates. The DoMORE surveys (DM1 and DM2) are indicated.
The barotropic tidal velocities from the ¼° TPXO7.2 tidal model (Egbert and Erofeeva 2002) are used to establish the phase of the spring–neap cycle at P1 and P3 and the phase of the semidiurnal tides at P1. A harmonics analysis (Pawlowicz et al. 2002) was conducted at P1c (at 3200 m, above the canyon walls) and at P3b (at 3600 m) with data from the shallowest current meters to reduce the effects of the baroclinic current arising from the local topography. The Greenwich phases of the M2 and S2 TPXO components (at the location of P1) are 131.63° ± 0.02° and 147.46° ± 0.05°, whereas they are 146.4° ± 3.9° and 155.1° ± 6.1° from the current meter at P1c; a lag of ~30 min is observed with the M2 tidal predictions. In addition, the observed M2 and S2 phases at P3b (149.8° ± 3.9° and 163.1° ± 14.8°) do not significantly differ from P1c. As such, we refer to the TPXO tides at P1 to distinguish the spring and neap tides in the DoMORE surveys and for each mooring. The spring tides with a period of dt = 14.79 days [1/(
c. Derived parameters
Based on an empirical link between the Ozmidov and the Thorpe scales, the length scale of density overturns can be related to patches of active turbulence (Thorpe 1977; Dillon 1982). The Ozmidov scale LO is the upper limit of the size of isotropic overturns in a stratified fluid. The Thorpe scale LT defines a vertical size of turbulent overturns from the root-mean-square of Thorpe displacement d′, estimated from the difference between the reordered gravitationally stable and observed density profile. The Thorpe scale has been shown to be highly correlated with the Ozmidov scale under conditions of internal wave–driven overturns in the well-stratified thermocline with LO = a〈(d′)2〉1/2, where angle brackets indicate an average over an unstable patch, and a is defined empirically at 0.8–0.95 (Dillon 1982; Wijesekera et al. 1993). In the case of turbulence driven by hydraulic and convective processes at regions where flow encounters sloping topography, the Thorpe scale can overestimate the Ozmidov scale (Mater et al. 2015). Each overturn is delimited from the zero crossings of the depth-integrated Thorpe displacements starting from the surface to the seafloor. Thorpe displacements are computed on potential temperature instead of density to remove the noise associated with salinity spikes; as the temperature–salinity (T–S) properties in the canyon are very nearly linearly related, this choice does not bias the results. A minimum overturn height of 5 m is chosen from the overturn resolution (Galbraith and Kelley 1996). A temperature noise level of 0.001°C is defined from the standard deviation of detrended profiles within homogeneous layers. To remove the effect of random noise on the detection of overturns in weakly stratified waters, intermediate profiles with temperature increments larger than the noise level are first constructed (Ferron et al. 1998; Gargett and Garner 2008) before determining Thorpe displacements.
An alternative indirect estimate for the turbulence levels is derived from finescale observations of vertical kinetic energy (VKE) estimated from the LADCP vertical velocity profiles (Thurnherr et al. 2015). We use version 1.2 of the public implementation available online (at http://www.ldeo.columbia.edu/LADCP). The resulting profiles of εVKE provide estimates for turbulent dissipation for the stations where no microstructure data were collected. Vertical wavelengths between 100 and 640 m were used to fit the VKE spectra. A comparison between εVKE and the corresponding microstructure-derived values in the joint DMP/CTD profiles indicates agreement within a factor of 2 (appendix B), consistent with previous data (Thurnherr et al. 2015).
For each DMP/CTD profile, the kinetic energy [EKE = 0.5ρ(〈u2〉 + 〈υ2〉)] and the available potential energy 
The ratio of the counterclockwise (CCW) to clockwise (CW) shear variance with depth for each MMP informs about the vertical direction of internal wave energy propagation (Waterman et al. 2013). A dominant counterclockwise (clockwise) component indicates downward-propagating (upward propagating) energy (Leaman and Sanford 1975). The shear-to-strain ratio 
3. Results
a. Time-averaged hydrography and flow in the canyon
Moorings P1 and P3 sampled an along-canyon, 2-layer mean flow composed of an up-canyon deep transport below an opposing flow (Fig. 3). Because of instrument configuration errors, sampling of the P1 MMP did not reach the maximal eastward velocity; the two interpolations displayed in Fig. 3b show different spline interpolations corresponding to the strongest and to mean zonal velocity profiles. The inferred vertical shear of the mean profile below the zonal velocity maximum is significantly greater for the interpolation at P1 than at P3. The mean sampled velocities in both layers were larger at P1 than at P3; the corresponding lower-layer velocities below ≈3900 m are 5.2 ± 2.0 and 1.8 ± 0.4 cm s−1. The velocity standard errors (pink lines in Figs. 3b and 3d) were calculated using the integral time scales (12 days, depth-averaged at MMP P1) of the 2-day low-pass filtered velocities to estimate the number of degrees of freedom (29, depth-averaged at MMP P1). The mean lower-layer velocity is indistinguishable from the average eastward velocity of 1.6 ± 1.3 cm s−1 in the bottommost 300 m recorded during a 2-yr deployment in the 1990s in a deep depression of the BBTRE canyon near 17.80°W (Thurnherr et al. 2005). [The data from the BBTRE mooring, which did not measure the top 500 m of the canyon below its rims, do not show any indication of the westward flow in the shallower layer.] Strong tides superimposed on the mean flow cannot regularly reverse the lower-layer flow below ≈4100 m (dashed pink lines in Fig. 3b). A cross-canyon hydrographic section at the overflow (contours in Fig. 3a) as well as near-bottom LADCP measurements (not shown) suggest that the lower-layer eastward flow at the overflow section extended across the canyon width. Based on the moored data (Figs. 3b,d), eastward flow in the lower layer is strongest near the thalweg, along the steeper and less corrugated southern canyon wall. The available hydrographic and LADCP data from the downstream section indicate a similar situation there (not shown). At P1, the westward mean flow of the upper layer extended above the canyon rims, at least up to the shallowest current meter (−0.8 ± 0.3 cm s−1 mean zonal velocity at 3200 m), whereas no significant zonal flow was observed above the canyon rims at P3.
The time-averaged separation between the two layers, based on the zero crossings of the mean zonal MMP velocities, occurs on the same neutral density surface (γn = 28.13) at both mooring sites. Because of the mean along-canyon density gradient between the two mooring sites, the interface is ≈50-m shallower (3870 m) in the overflow section at P1 than farther downstream at P3 (3920 m; Fig. 3). At P1, the mean density stratification in the lower layer is considerably higher than the corresponding stratification in the upper layer (Fig. 4b).
(a) Individual CTD density profiles taken west (black) and east (red) of the sill. The shallowest depth at the narrow deep passage over the sill 4290 m and the bifurcation depth at 3850 m are indicated (dashed lines); the vertical line indicates the 2-layer interface at 28.13. (b) Averaged buoyancy frequency and its standard error (shaded region) from CTD profiles west (black) and east (red) of the sill and at the mooring P1 (blue) and P3 (green).
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
Along-canyon isopycnals γn along the thalweg (stars in Fig. 1b) reveal the presence of a unidirectional along-canyon density gradient below ≈3500 m, with the largest gradient coinciding with the overflow (Fig. 2a). The cross-sill density drop there corresponds to a 0.2°C warming of AABW at P1 over less than 5-km along-canyon distance, about twice the magnitude of the entire warming between the overflow and the downstream moorings (≈100 km of canyon). The density drop in the overflow region implies markedly different stratifications east and west of the sill. The corresponding mean of CTD profiles (Fig. 4b) shows a pronounced buoyancy frequency maximum, with a peak value of 1.2 × 10−3 s−1 between 3800 and 4000 m, west of the overflow sill and noticed as far as 15.3°W. East of the sill no similar buoyancy frequency maximum was observed; the buoyancy frequency in the corresponding mean profile ranges around 10−3 s−1.
In the BBTRE data, a significant correlation between intensified along-canyon density gradients and high topographic peaks between station pairs persists across more than 1000 km of the canyon (Thurnherr et al. 2005). The red and black line segments along the bottom of Fig. 2a show the along-thalweg density gradients and their uncertainties, respectively. For station pairs where the blocking depth of abyssal hills is shallower than the shallower of the two bracketing profiles, the density is averaged in the 50 m above the blocking depth. Based on five yo-yo stations with six to eight profiles in the canyon (Fig. 1), the high-frequency density uncertainty, primarily of tidal and near-inertial origin, remains below 4 × 10−3 kg m−3, consistent with previous measurements in this region (Thurnherr and Speer 2003). At the spatial resolution of the along-canyon measurements (≈15-km average station spacing between 14° and 15°W in Fig. 2), the only density gradient rising above the high-frequency noise occurs in the overflow where the along-canyon density gradient reaches 1.6 × 10−6 kg m−4. Downstream of the overflow, the amplitude of the along-canyon density gradient in the near-bottom water remains below 2.9 × 10−7 kg m−4, which is indistinguishable from its uncertainty.
To estimate up-canyon volume transport, the time-averaged zonal velocity at P1 and P3 (Fig. 3) is integrated across the entire canyon width of 1.9 × 106 and 2.6 × 106 m2, respectively. The velocities along the thalweg are assumed representative in the across-canyon direction; frictional boundary layers along the sidewalls, in particular, are ignored. To estimate the velocity between the MMP profiles and the deep current meters, we apply a fourth- and seventh-order polynomial fit (Fig. 3) at P1 and P3, respectively. The resulting up-canyon transport of the deep layer in the overflow and downstream regions are 0.10 ± 0.03 and 0.04 ± 0.01 Sv (1 Sv = 106 m3 s−1), respectively. While this layer is mostly enclosed by the canyon sidewalls in the two mooring regions, there are deep passages cross cutting the canyon walls between the mooring arrays (Fig. 1). The inherent uncertainty arising from possible intercanyon exchange through these passages as well as diapycnal upwelling may contribute to the transport difference at the mooring sites.
Velocity spectra of Nortek current meter data are integrated over several different frequency ranges (Fig. 5) to quantify the kinetic energy of the subinertial flow (<0.8f, with an inertial period of 33.4 h), of semidiurnal tides (0.8M2–1.2M2), of near-inertial waves (0.8f–1.2f), and of high-frequency waves (1.2M2–N). As expected, the subinertial kinetic energy (KE) is highest in the overflow (P1). In the narrow passage of the sill, the subinertial KE is 35.0 cm2 s−2 ~10 m above the seabed (P1a); 770 m above the seabed at 3500 m (P1b), the subinertial KE is 16.9 cm2 s−2. In the deep instrument over the sill (P2a), the subinertial KE is 14.1 cm2 s−2; in the other instrument records, the subinertial KE remains below 10 cm2 s−2.
Horizontal kinetic energy of the subinertial flow (<0.8f) of near-inertial waves (0.8f –1.2f) of semidiurnal tides (0.8M2–1.2M2) and of high-frequency waves (1.2M2–N) for each Nortek current meter at moorings P1, P2, P3, and P4 (Fig. 3). P1a and P1b correspond to the current meters at 10 and 770 m (hab), respectively. The 95% confidence intervals, band averaged for each frequency range, are inferred from the equivalent degree of freedom of 50% overlapping segments after applying a Hanning window. The total horizontal kinetic energy summed over the four frequency ranges is indicated below each instrument. The black line separates the contribution of zonal (below) and meridional (above) velocities.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
In contrast to the subinertial flow, semidiurnal KE is highest in the bottom instrument of every mooring, with particularly high values in the overflow region (P1a and P2a). These observations indicate the presence of significant baroclinic tides in the canyon with amplitudes that increase with depth. Compared to P3 and P4, the internal tide is amplified both at P1 and P2, with the greatest amplification outside the deep overflow passage at P2a. Inside the narrow sill passage (at P1a), the semidiurnal and subinertial KE are of similar magnitudes and dominate the total energy. In the current meters on the same mooring but higher up in the water column, the subinertial flow contributes less and near-inertial oscillations contribute more to the total energy, which increases by a factor of 2 from the shallowest (P1c) to deepest (P1a) current meter.
In contrast to the subinertial and semidiurnal KE, both of which are strongest deep in the canyon, enhanced near-inertial KE is confined to the shallower current meters near the depth of the canyon rims at each site. At 10 m above the seafloor, the near-inertial energy is reduced in every record. The largest near-inertial peak was observed at 3500 m above the narrow sill passage (P1b) in the core of the upper-layer return flow near the depth of the canyon rims. With 18.4 cm2 s−2, near-inertial oscillations contribute to 29% of the total variance, whereas their contribution in the bottom layer (P1a) is only 2% (1.2 cm2 s−2). Above P1b, the near-inertial KE reduces upward, as illustrated by the P1c record collected ≈300 m higher up in the water column at 3200 m, where the near-inertial KE is 9.2 cm2 s−2. Downward decrease of near-inertial KE inside the BBTRE canyon was previously noted at a different site (Toole 2007) and potentially attributed to lateral constriction by the canyon walls and to the presence of a vertically variable shear and stratification.
b. Turbulent mixing inside the canyon
The along-canyon finestructure dissipation εVKE, depth averaged in the deepest 1000 m (Fig. 2b), reveals mean turbulence levels ranging from O(10−10) W kg−1 downstream from the overflow during neap tides to about 4 × 10−9 W kg−1 in the overflow during spring tides. Between the two mooring arrays, the observed averages are around 5 × 10−10 W kg−1. This pattern emphasizes the role of the sill in the deep-water modification, suggested by the large cross-sill density gradient around P1. At both mooring sites, the fortnightly tidal cycle modulates εVKE (by an order of magnitude in the overflow region and about a factor of 5 at P3). The reversed fortnightly modulation of εVKE near 14.5°W is likely an artifact of spatial variability, as more neap tide than spring tide measurements were collected over the corrugated northern canyon wall.
While LADCP-derived εVKE informs on the temporal and horizontal distribution of turbulence in the canyon, they are indirectly derived from energy estimates of the internal wave field. More direct and much higher vertical resolution estimates of turbulent dissipation are available from the microstructure survey (Fig. 1). Spring- and neap-averaged microstructure profiles were calculated for the overflow region and for the remainder of the canyon (Fig. 6). Profiles from the overflow region include the midcanyon cross sill and the northern wall transects (Fig. 1). In the overflow region below 3500 m (Fig. 6b), the averaged ε is one order of magnitude higher, 1.8 × 10−9 W kg−1 (95% confidence interval of 0.6–3.5 × 10−9 W kg−1), during spring compared to neap tides, 1.2 × 10−10 W kg−1 (0.6–2.3 × 10−10 W kg−1), and also compared to the rest of the canyon, 1.7 × 10−10 W kg−1 (1.0–2.6 × 10−10 W kg−1). This depth range of enhanced ε encompasses the 2-layer interface as well as the stratification maximum in the overflow. In the microstructure profiles, the neap tide dissipation rates in the overflow region are not significantly higher than the neap tide dissipation rates in the remainder of the canyon (Figs. 6a,b). Using Osborn’s model (Osborn 1980), κ = N−2Γε with a constant mixing efficiency (Γ = 0.2), we infer the diapycnal diffusivity κ (Fig. 6) from ε. The spring–neap cycle modulates κ below 3500 m at the sill, with a depth-averaged κ ranging between 3.8 × 10−4 (spring tides; 95% confidence interval of 1.4–7.5 × 10−4 m2 s−1) and 3.0 × 10−5 m2 s−1 (neap tides; 1.6–5.1 × 10−5 m2 s−1) with maxima of 3.8 × 10−3 m2 s−1.
Dissipation rate of turbulent kinetic energy ε from microstructure profilers (gray and light red for neap and spring tides, respectively) measured inside the canyon (a) away from the sill and (b) around the sill at the overflow site; ε is averaged for the spring (red) and neap (black) tides. (c),(d) As in (a) and (b), but for the diapycnal diffusivity κ. The terms ε and κ are averaged in potential temperature space before being converted back to depth space.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
Away from regions of internal wave generation, there is generally a close relationship between internal wave energy and turbulence (Gregg 1989; Polzin et al. 1995). Having observed a spatially varying dissipation rate enhanced at the sill, it becomes relevant to assess the relationship between an intensified ε and the internal wave field. Integrated microstructure dissipation rates times the density 
Total energy of the internal wave field inferred from CTD/LADCP profiles in 640-m segments vs depth-integrated dissipation rate of turbulent kinetic energy measured by microstructure profilers. Measurements at the overflow site (red) and away from the overflow site in the canyon (black) were taken at (a) 0–1 and (b)1–2 km hab.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
c. Overflow region
Further insight into the role of the sill is gained from four across-sill tow-yo sections and from microstructure profiles taken at middistance from the canyon rims (Fig. 1). Only one out of the four tow-yos sampled during spring tides; Fig. 8 displays the spring tide and one of the neap tide transects. In both sections the ship transited from east to west and both were timed for eastward tidal flow to occur during passage of the sill. Those sections reveal an asymmetric cross-sill spring–neap modulation of isopycnal displacements and dissipation rates. During spring tides (Fig. 8a), the isopycnals around the 28.12–28.14 neutral surfaces are squeezed on the upstream side of the sill, plunge down over the sill crest, and then rebound downstream of the sill with O(100) m vertical displacements, reminiscent of an internal hydraulic jump. The isopycnal displacements extending at least up to the 28.10 surface are perhaps related to a forming lee wave. The corresponding isopycnal surfaces are less disturbed during neap (Fig. 8b) than spring tides, independently of the semidiurnal tidal phase (clock symbols), as confirmed by the two additional neap tide sections. During spring tides, the stratification between the 28.12 and 28.14 neutral surfaces is increased both upstream and downstream of the sill, although the effect is much stronger upstream.
(a),(b) Neutral density across the sill measured by two 8-h tow-yo sections during (left) spring and (right) neap tides. (c),(d) Dissipation rate ε sampled by microstructure profilers around the sill during (left) spring and (right) neap tides. The term ε is displayed in logarithmic scale from 10−11 to 10−8 W kg−1. The time relative to the maximum eastward tidal flow referenced at 1200 UTC is indicated below each profile. The dashed line of the bottom subplots corresponds to the upper limit of the upper subplots.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
Elevated dissipation rates during spring tides, up to 1.8 × 10−7 W kg−1 in individual profiles (Fig. 8c), are found over the sill crest within 1.7 km east of the sill, that is, in the same region where the isopycnals show large vertical displacements. While there are clear spring–neap differences in flow and turbulence in this region, there is no apparent correlation between the semidiurnal tidal phase (clock symbols) and ε in the four spring tide profiles. Even though it is based, in part, on a single profile collected ≈2.3 km west of the sill saddle, the observed pattern of turbulence across the sill is consistent with a unidirectional hydraulically controlled overflow, where high turbulence can arise from shear instabilities in the supercritical region downstream of the sill and from the transition between a supercritical to subcritical regime (hydraulic jumps). In the latter case, an exchange from kinetic to potential energy occurs in the lower layer as the isopycnal rebounds.
Applying this 1.5-layer model to the continuously stratified ocean requires estimates for g′ and hu. Following Whitehead (1998), g′ = 2.0 × 10−4 m s−2 is estimated from the maximum upstream–downstream density difference (Δρ = 0.02) above the sill depth in two profiles straddling the sill (orange stars in Fig. 1), and the thickness of the lower-layer hu = 440 m is taken from the depth difference between the sill saddle and the so-called bifurcation depth, where upstream and downstream density profiles diverge (Fig. 4). The passage width W = 2 km, usually defined at the bifurcation depth, is approximated at P1 by the width of the narrow deep passage, which constrains most of the lower layer. The Rossby radius L = (2g′hu/f2)1/2 = 10 km, with f = 5.2 × 10−5 s−1, confirms that the overflow passage is narrow. With these parameters expression 1 yields a transport estimate of 0.14 Sv in good agreement with the observed mean transport at P1, especially considering the model’s simplifying assumptions that include no friction and mixing as well as a rectangular channel geometry (Whitehead 1998).
One of the defining characteristics of hydraulic control is that the flow speed at the control point (a sill or narrows) is equal to the horizontal speed of gravity waves, in which case the flow is called critical. Using the parameters given above, the corresponding 1.5-layer gravity wave speed c = 
To determine whether this uplift is sufficient to transport the deepest upstream water across the sill, we derive an order of magnitude estimate for the blocking depth U/N at P1. Using N = 10−3 s−1, the blocking depth during maximum eastward tidal flow (u ≈ 25 cm s−1) is 250 m, similar in magnitude to the elevation of the sill above the upstream basin (≈400 m at the thalweg); we infer that there is no significant topographic blocking of eastward-flowing deep canyon water in the overflow. During maximum westward tidal flow (u ≈ −5 cm s−1), on the other hand, the blocking-depth estimate is only 50 m, that is, tidal reversals of the overflow affect only the top of the lower layer. The lower-layer water downstream of the overflow is topographically constricted to flow unidirectionally up canyon, independently of the tidal phase.
d. Tidal modulation of turbulence
Using data from the two MMPs, P1 at the overflow site and P3 at the downstream site, we investigate the tidal modulation of turbulent patches in the canyon with a Thorpe-scale analysis (Fig. 9). Elevated depth-averaged Thorpe scales 〈LT〉, assuming zero turbulence where no overturns are observed (LT = 0), occur in the overflow with a mean and standard error of 2.8 ± 0.1 m, compared to 0.9 ± 0.02 m at P3. Overturns are observed in 20% of the measurements at P1 as opposed to 5% at P3. The largest 〈LT〉 occurs at P1 with 28% values larger than 10 m compared with 19% at P3. The observed maximum height of static instability was 200 m at P1. In addition to the intensified mean 〈LT〉 at P1, spring–neap tides modulate 〈LT〉 by a factor of 2–3, whereas Thorpe scales at P3 are not significantly modulated on this time scale. Despite the presence of fortnightly modulated overturns and microstructure ε, a comparable periodicity in the lower-layer subinertial eastward flow potentially arising from the buoyancy forcing of the downstream enhanced turbulence (St. Laurent et al. 2001a) could not be ascertained.
(a) Depth-averaged zonal velocity at MMP P1 (red dots), at MMP P3 (black dots), and from TPXO (black line, for the eight components M2, S2, N2, K2, K1, O1, P1, and Q1); the gray shading indicates the spring tides. Zonal velocity (colors) minus the depth-averaged velocity, isopycnals (black lines), depth of maximum shear (black dots), and occurrence of temperature overturns (yellow) at (b) P1 and (c) P3. (d) Depth-integrated Thorpe scales at P1 (red dots) and P3 (black dots) with the 7-day low-pass filtered values (lines).
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
Along with the fortnightly modulation of Thorpe scales, we investigate the presence of a semidiurnal cycle in the occurrence of large overturns at P1. A composite analysis based on semidiurnal tidal phase, taken from the hourly TPXO tidal prediction, reveals elevated 〈LT〉, by up to factors of 2 and 4 during neap and spring tides, respectively, occurring during westward tidal flow (Fig. 10). During this semidiurnal tidal phase, the maximal westward tidal flow reverses the mean up-canyon flow almost to its deepest measurement at MMP P1 around 4100 m, as seen from the 10th percentiles of velocities (Fig. 3b). During times of westward tidal flow, advection of warmer (downstream) water reduces the stratification in the overflow (Fig. 11c). Many of the largest overturns were observed in all three consecutive profiles collected during every MMP sampling burst, implying decay time scales greater than 3 h, consistent with the period of increased 〈LT〉 composite.
(a) Zonal velocity, (b) buoyancy frequency squared, (c) shear variance, and (d) Thorpe scales depth-averaged from 3800 to 4000 m at varying semidiurnal phase (0 and 3π/2 correspond to southward and westward tidal flow, respectively) for spring (red) and neap (black) tides at MMP P1.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
(a) Zonal velocity, (b) Thorpe scales, (c) buoyancy frequency, (d) shear, and (e) fraction of Richardson number below criticality averaged for a semidiurnal eastward and westward tidal flow at spring and neap tides at MMP P1. Shading represents 95% confidence intervals inferred by bootstrapping.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
During eastward tidal flow, 
The microstructure observations from the lee of the overflow sill (Fig. 8c) suggest that hydraulic jumps contribute to the overall turbulence, including to its vertical structure with its middepth maximum, in the overflow region. The apparent absence of semidiurnal modulation in microstructure observations (Fig. 8c) implies that other processes than hydraulic jumps must affect 
e. Internal wave properties
The internal wave field in the overflow and downstream regions (P1 and P3, respectively) is analyzed using the counterclockwise-to-clockwise polarization ratio of shear variance and the shear-to-strain variance ratio Rω. The polarization ratio at P3 (Fig. 12a) is dominated by the counterclockwise component throughout the entire profile and decreases with increasing depth. The internal wave field in this region away from the overflow is therefore predominantly associated with downward-propagating energy. The large shear-to-strain ratio at P3 (Fig. 12b), which is also associated with a decrease with increasing depth, indicates dominance of near-inertial waves outside the overflow. The downward-decreasing importance of near-inertial waves apparent in the finestructure properties is consistent with the vertical decrease in near-inertial energy inside the canyon (Fig. 5) and with possible trapping (Gordon and Marshall 1976; Hotchkiss and Wunsch 1982) and/or with lateral constriction of near-inertial waves in the canyon (Fig. 3). The importance of near-inertial waves away from the overflow agrees with elevated near-inertial finescale shear found at another site away from any overflow in the BBTRE canyon (Toole 2007).
(a) Ratio of the counterclockwise to clockwise component of the shear variance at MMP P1 and MMP P3 averaged for spring and neap tides; a positive ratio indicates downward-propagating energy of internal waves. (b) Shear-to-strain ratio Rω at P1 and P3 averaged for spring and neap tides; near-inertial waves are characterized by a large Rω. In (a) and (b), the 95% confidence intervals (horizontal bars) are indicated based on bootstrapping. Clockwise (red) and counterclockwise (black) spectra of the shear filtered at M2 and S2 frequencies at (c) P1 and (d) P3.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
In contrast to P3, the polarization ratios at P1 are close to zero, indicating that there is no preferred vertical propagation direction for the internal wave energy in the overflow. The corresponding shear-to-strain ratios in the overflow above 3900 m are close to 5, that is, 2–3 times lower than Rω at P3, indicating lesser dominance of near-inertial waves and a stronger influence of high-frequency waves in the overflow region. Both the negative CCW/CW polarization and the lower Rω in the shallowest sample at P1 during spring tides, compared to neap tides, suggest the presence of internal tides in the overflow at P1. In that case a lower shear-to-strain ratio is expected, and the dominance of a single wave to relate Rω to the frequency content of the internal wave band may no longer be valid. To separate the semidiurnal tide from the remainder of the variability, least squares harmonic analysis (Thomson and Emery 2014) with the M2 and S2 tidal frequencies is used. Rotary spectra of the resulting semidiurnal shear (Figs. 12c,d) indicate the prevalence of the clockwise component with the upward-propagating energy characteristic of internal tides at vertical wavelengths above 90 m at P1. On these wavelengths, the semidiurnal shear spectra are red everywhere but characterized by higher energy at P1 versus P3.
4. Discussion: Energy of the overflow region
In the overflow region below ≈3800 m, the isopycnal surfaces are deeper east than west of the sill (Fig. 8), with the implied decrease of lower-layer potential energy across the sill accelerating the flow. Both interfacial shear instabilities and boundary friction near the seabed extract kinetic energy from the overflow. Internal waves (internal tides and quasi-steady lee waves) arise from flow–topography interactions (St. Laurent and Garrett 2002) and are likely generated at hydraulic jumps downstream of the overflow sill. These locally generated internal waves redistribute some kinetic energy by radiating energy out of the sill region. A local mechanism of energy loss at the hydraulic jump is accounted for by the drop in Bernoulli function B = (1/2)u2 + gz + P/ρ across the sill, with P and z the pressure and the distance from the bottom, respectively.
The energy equation (Baines 1995) can be applied to the barotropic tides or to the overflow at the sill 
a. Energy loss across the sill
In a steady-state flow, the energy flux is first compared with the measured energy dissipation integrated in the volume V of oriented surface S around the sill, 
In addition, the frictional boundary layer affects through the bottom stress τ0 the energy of the lower layer differently over the sill, where higher bottom velocities are noticed, than within the canyon away from the sill. This effect is evaluated from CTD/LADCP profiles in the sill passage, assuming a layer of constant stress defined by the bottom stress τ0 with 
The contribution of the spatially integrated measured dissipation rate with the frictional boundary layer estimate accounts for 2% of the lower-layer energy loss. This underlines that high dissipation may have been undersampled or that additional mechanisms may play a substantial role near the sill, such as horizontal eddy shedding around the three-dimensional topography (MacCready and Pawlak 2001). As noticed over a different sill (Klymak and Gregg 2004), the radiated energy by internal waves can account for a significant fraction of the barotropic energy loss when the measured dissipation rate remains low in comparison to the Bernoulli drop. In the deep fracture zone over the sill, internal waves may not only be generated by the barotropic tides but also by the steady-state overflow and participate in the drop in the Bernoulli function. The tidal advection across the sill may, however, hinder a clear distinction between those waves.
b. Internal wave radiation
We evaluate the internal wave energy flux around the sill from the wave characteristics measured at P1. In the narrow sill passage, the tidal excursion length 
To estimate the total energy phased locked with semidiurnal tides, we select the velocity of 0.05 m s−1 and the buoyancy frequency of 0.9 × 10−3 s−1 depth averaged around the 2-layer interface at westward tidal flow (Fig. 10). Amplitudes of isopycnal displacements of 50 m are selected in a similar manner through the M2 cycle. The total energy density E becomes 3.6 J m−3, which yields vertical and horizontal energy fluxes of 0.05–0.29 and 0.05–0.30 W m−2, respectively. The total flux, that is, the sum of the vertical flux integrated horizontally across the overflow area (3.4 km × 19 km; 3.4 km is the across-sill width that encompasses the largest isopycnal displacements in Fig. 8a) and the horizontal fluxes integrated across the two cross-canyon sections (both S = 0.6 km × 19 km), is 4.1–25.8 MW. The energy radiated away by internal tides is comparable to the lower-layer energy loss.
In addition, the linear theory of internal tides and lee waves (Gill 1982) predicts a vertical energy flux 
5. Conclusions
We carried out an analysis of data collected during the DoMORE project in one of the many fracture zone canyons corrugating the western flank of the MAR in the South Atlantic. The primary results emphasize the effects of a variety of mechanisms affecting the turbulent mixing of deep water in the canyon:
A deep 2-layer exchange mean flow transports 0.04–0.10 Sv of AABW eastward in the deepest layer, which is laterally confined by the canyon walls below ~3900 m.
The along-canyon density gradient reaches a maximum in a region where a tall abyssal hill restricts the canyon both laterally (constriction) and vertically (sill) and where the mean lower-layer velocity is larger (5.2 cm s−1) than ≈100 km east of the sill (1.8 cm s−1). The semidiurnal tides are not strong enough to reverse the entire lower layer, indicating that the overflow acts like a check valve for up-canyon flow below ≈4000 m.
Consistent with the hypothesis of a tidally modulated, hydraulically controlled overflow, the largest dissipation rate ε ≈ 10−7 W kg−1 and diapycnal diffusivity κ ≈ 10−3 m2 s−1 were observed east of the sill crest below 3500 m. The isopycnal rebound east of the sill is reminiscent of a hydraulic jump.
Large overturns in the sill passage (P1) occur primarily during westward semidiurnal tidal flow. Those overturns, intensified around 3800–4000 m, relate to the reduced stratification observed at the sill during westward tides.
Internal tides with upward-propagating energy are generated specially in the vicinity of the sill. In contrast, at the downstream mooring site (P3), the internal wave field is dominated by near-inertial waves with downward-propagating energy.
The DoMORE data confirm the existence of a lower layer flowing zonally toward the MAR in the BBTRE canyon (St. Laurent et al. 2001a; Thurnherr et al. 2005). Similar up-canyon currents toward the ridge crest were inferred for many other canyons in the western South Atlantic (Mercier et al. 2000; Thurnherr and Speer 2003). Since abyssal hills are intrinsically associated with seafloor spreading, similar dynamics with elevated turbulence and mixing occurring primarily near tidally modulated overflows are expected to occur in many of the FZ canyons corrugating the global slow-spreading midocean ridge system. If each FZ canyon hosts one major sill comparable to the one described above, ≈1.3 GW of energy is dissipated in the ≈40 canyons of the Brazil Basin (Thurnherr et al. 2005). This number can be compared with the 2.7–4.8 GW of energy dissipated in the Strait of Gibraltar (Wesson and Gregg 1994) in a region of remarkably high dissipation rate.
Acknowledgments
The DoMORE project was supported by NSF under the Grant OCE-1235094. The author thanks J. M. Toole for his assistance in the processing of MMPs and J. R. Ledwell for commenting the manuscript. Suggestions by two anonymous reviewers greatly improved the manuscript. The effort of J. Zhao and of colleagues from LDEO, WHOI, and the crew of the R/V Nathaniel B. Palmer was greatly appreciated prior and during the two DoMORE cruises.
APPENDIX A
Dissipation Rate from Deep Microstructure Profiler
The methodology for computing the dissipation rate from airfoils has a long history that is described in detail in the literature; Lueck et al. (2002) give a comprehensive review. Considerable details of the analysis methodologies are described by the Rockland Scientific Technical Note 28 (available online at http://www.rocklandscientific.com). A contemporary innovation involves the concurrent use of high-frequency motion sensing through multiaxis analog accelerometers. Using cospectral analysis, we remove the platform-induced vibrations from the probe records using the method of Goodman et al. (2006). Typically, this correction applies to frequencies between about 10 and 60 Hz. In the resulting “clean” shear spectra, coherent vibrational energy between the profiler platform and the shear records has been removed. For the RVMP system, this allows us to measure dissipation rates as low as about 3–5 × 10−11 W kg−1 (Fig. A1).
Microstructure shear spectra of one DMP profile (vad005) averaged over the two probes taken for three depth bins at 21.08°S and 14.64°W. The black dashed lines represent the universal velocity shear spectra inferred from the Nasmyth (1970) spectra. The upper-wavenumber limit is denoted by the triangle.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
To estimate the dissipation rate from the cleaned spectra, we follow the spectral analysis procedure described by Gregg (1999). In practice, the microstructure records were examined in 2048-element windows over which a 1024-element FFT was employed. Adjacent 1024-element bins are treated using a Hanning window employed with 50% overlap. For the typical fall speed of 0.75 m s−1, this results in spectral variance estimates at 1.5-m depth intervals of each microstructure shear record. The limits of integration are taken from the lowest wavenumber to an upper-wavenumber cutoff calculated as either 100 cpm or a lesser wavenumber representing the transition between the dissipative subrange and the blue portion of the high-wavenumber spectrum dominated by electronic noise. In practice, the noise-limited wavenumber nearly always applies. This cutoff wavenumber is found through identifying the corresponding root of the fifth-order polynomial fit to the spectral curve. No corrections are applied to the shear spectra, as the inertial subrange and dissipative rolloff are always well resolved in these data. Dual shear probes were always used and the dissipation rate reported is typically the mean of the independently estimated dissipation rates from each probe signal.
As a measure of fidelity, each spectrum is compared to the canonical spectral form derived by Nasmyth (1970) for the calculated value of the dissipation rate. Measured spectra generally show good agreement with Nasmyth (Fig. A1). In cases where the measured spectra deviate substantially, we flag them as suspect and do not include them in the dissipation estimates. In the final analysis where we combine the CTD data with the dissipation estimates, we compute the Ozmidov wavenumber as (N3/ε)1/2 (Thorpe 1977). As the Ozmidov wavenumber corresponds to the lowest wavenumber for the dissipation integral, we reexamine the dissipation estimate by integrating each Nasmyth spectra from its associated Ozmidov wavenumber to infinity. This allows us to examine the uncertainty caused by missing variance in the data spectral estimates, both at the lower and upper ends of the spectrum. We flag cases where the resulting estimate of integrated variance differs by more than 10% from the data estimate. These cases represent less than 0.1% of all estimates and are not included in further estimates.
APPENDIX B
Vertical Kinetic Energy Finestructure Parameterization Method for TKE Dissipation
Turbulence measurements with free-falling microstructure profilers are expensive and time consuming to collect. Since there is a close relationship between internal waves and turbulence, it has become common practice to estimate turbulence and mixing levels with “finestructure parameterization methods” from internal wave signals measured with standard oceanographic CTDs and ADCPs (Kunze et al. 2006). Here, we use a recently developed method that is based on LADCP-derived vertical kinetic energy (Thurnherr et al. 2015) to elucidate spatial and temporal patterns of turbulence along the BBTRE canyon (Fig. 2). The VKE method is empirical and has been found to yield estimates consistent within a factor of 2 with simultaneous microstructure measurements in a suite of datasets taken between 10° and 70° of latitude and that include both Luzon Strait, a region of extreme internal wave activity, and the open South Pacific, where internal waves and turbulence levels are considered oceanic background. Importantly, there are no indications of significant biases of the VKE method applied in regions of internal wave generation; that is, the method is expected to work well in the BBTRE canyon. Consistent with this inference, individual profiles of microstructure and VKE-derived dissipation in the DoMORE-2 data are generally similar, although the errors associated with the individual VKE samples can exceed a factor of 5 (insets in Fig. B1). A scatterplot of VKE- versus microstructure-derived ε indicates agreement within a factor of 2 when suitably averaged, in agreement with Fig. 2 of Thurnherr et al. (2015), and the corresponding dataset-averaged mean profiles are also mutually consistent within a factor of 2 throughout the water column (not shown).
VKE finestructure parameterization diagnostic plots from two profiles with available microstructure data. The insets show the VKE-derived dissipation profiles in blue and the identically averaged corresponding microstructure data in orange. The main panels show the corresponding normalized VKE spectra in the same shades of blue used in the inset; no εVKE estimates are produced for the dotted spectra, which fail one or more of the consistency checks built into the processing software. The station-averaged VKE spectra are shown in salmon color with a thicker line in the finescale range used for the spectral fits; the green band shows the empirical VKE spectrum with a factor of 2 uncertainty. (left) Example profile 28 with strong bottom-intensified turbulence. (right) Example profile 48 with low turbulence levels throughout the water column.
Citation: Journal of Physical Oceanography 47, 8; 10.1175/JPO-D-16-0264.1
The VKE parameterization method is based on the observation that vertical wavenumber m finestructure spectra of vertical ocean velocity have a universal m−2 slope that, in contrast to the Garrett–Munk model, does not vary with latitude, density stratification, or the bandwidth of the internal wave field but only with local turbulence levels (Thurnherr et al. 2015). This power law usually holds on vertical scales between a low wavelength cutoff, which varies with the VKE energy level and LADCP data quality but which is typically around 100 m and usually extends to vertical scales in excess of 500 m. The quality of the parameterization estimates depends primarily on how well the empirical m−2 spectrum can be fit to the observations. Most of the individual DoMORE-2 VKE spectra are consistent with an m−2 power law on vertical wavelengths below 500 m down to vertical scales between 100 and 200 m (Fig. B1, main panels). On shorter wavelengths, LADCP measurement noise becomes significant and flattens the spectra.
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