Passage is an identified hot spot of internal wave generation and turbulent mixing due to breaking internal waves (Sheen et al., 2013). We will assess the relationship of finescale turbulent mixing and internal wave properties (frequency and energy propagation) under different regimes, including the background stratification, current speed, the position of the ACC fronts, and topography. Our study will also employ a unique 4-year time series of bottommoored Current and Pressure recording Inverted Echo Sounders (CPIES) that span Drake Passage (Figure 1) to produce a time series of lee-wave energy radiation. A spatially denser subset of the CPIES array located downstream of the Shackleton Fracture Zone (Figure 1) is used to determine the relationship between the mesoscale field (via the geostrophic streamfunction and its derivatives), the turbulent mixing due to breaking internal waves, and the radiation of lee waves.

We expect that lee waves are generated in Drake Passage by the interaction of the near-bottom ACC flow with the abyssal topography. A few studies have used single full-depth in situ CTD/LADCP casts to estimate the energy radiation into lee waves and compared it to their depth-integrated (to 1,000 m above the bottom) dissipation rates (Sheen et al., 2013(Sheen et al., , 2014;;Waterman et al., 2013Waterman et al., , 2014)), assuming an isotropic form of the abyssal hill topographic spectrum from Goff and Jordan (1988). As noted above, the lack of anisotropy information in the small-scale topography could significantly impact the energy estimates. In this study, our estimates of lee-wave energy radiation employ the abyssal hill statistical parameters from Goff (2020) determined from global gravimetric measurements, including the anisotropy information in the topographic spectra. Moreover, we employ high-resolution multibeam (MB) bathymetric data for the Drake Passage region to estimate the abyssal hill statistical parameters. The MB data allow us to capture the smallscale abyssal hills (1-10 km), that is, the length scales predicted by linear lee-wave theory that are not captured by coarser resolution gravimetric data. The different topographic data sets and their statistical parameters allow us to assess the sensitivity of energy radiation estimates to the choice of statistical parameters that represent the 2D topographic spectra. In addition, we will calculate the energy loss to lee waves using the 1D isotropic topography of Nikurashin and Ferrari (2011) and compare to that calculated using the Goff (2020) and MB anisotropic topographies. This paper is structured as follows. Section 2 presents the data sets. An overview of the methodology to estimate dissipation rates, internal wave parameters, and lee-wave energy radiation is presented in Section 3. Section 4 presents the dissipation rates and wave parameters estimated across Drake Passage and their relationship with background stratification, shear, and the ACC frontal positions. Lee-wave energy radiation estimates are presented and compared with previous studies in Section 5. The spatial variability across Drake Passage of the lee-wave energy radiation and its time variability is also explored in this section. The effect of including the anisotropy in the topographic spectrum of the energy estimates is presented in Section 6. Section 7 compares the local turbulent dissipation rates and the local lee-wave energy radiation using different topographic data sets. We finalize with the summary and conclusions in Section 8.

As part of the cDrake project (Chereskin et al., 2012), full-depth CTD/LADCP casts were taken at 43 sites in Drake Passage during five annual cruises aboard the RVIB Nathaniel B. Palmer in late austral spring (November) Maximenko et al. (2009). The colored background shows the MB bathymetry from the Global Multi-Resolution Topography (GMRT) synthesis (Ryan et al., 2009). The 3 × 7 CPIES local dynamics array is located in the Polar Front Zone between the mean position of the SAF and PF. The Shackleton Fracture Zone (SFZ; thick dashed line) is indicated. The central position of the Yaghan Basin (YB), a topographic depression, is indicated. Black boxes delineate where statistical parameters were calculated using the multibeam data (see Table S1 in Supporting Information S1).

of 2007-2011 (Figure 1). Casts were performed within 20 m of the bottom when possible. A total of 177 casts were collected over the 4 years at the CPIES sites.

For the CTD casts, a SeaBird SBE 11-Plus was deployed; the instrument has an initial accuracy of 0.001°C and 0.003 psu for temperature and salinity, respectively, resulting in density estimates accurate to 0.003 kg m -3 . Bottle samples were taken during each cast at scheduled depths to validate salinity, and CTD calibrations were performed pre-and post-cruise for each year. The CTD downcast data used here were quality-controlled, despiked, and averaged to 1-dbar vertical resolution. Before implementing the finescale parameterization, we followed Whalen et al. (2012) and removed the upper-ocean mixed layer and the poorly stratified layer below the mixed layer (e.g., mode-water layers and pycnostads) from the CTD profiles using the density-based criteria of de Boyer Montégut et al. (2004). These weakly stratified regions exhibit high strain not due to internal waves, leading to spuriously high dissipation rates.

The LADCP current velocity profile at the location of the CTDs was obtained using a single downward-looking 150 kHz RDI Phase 3 broadband ADCP with 30° beam angles mounted on the CTD rosette. The LADCP sampled with a 16-m vertical bin and a staggered ping cycle alternating 1 and 1.6 s between pings. The staggered ping cycle results in a region of reduced sampling between 500 and 1,000 m above the bottom, but it avoids a complete data void arising from when the previous ping reflects off the bottom and so interferes with the current ping. Data were collected in beam coordinates. During each cast, two hull-mounted RD Instruments shipboard ADCPs recorded velocity data: a 150 kHz narrowband ADCP (NB150) on all five cDrake cruises (2007)(2008)(2009)(2010)(2011) and an Ocean Surveyor 38 kHz phased array (OS38) on the last three cruises (2009)(2010)(2011). The NB150 maximum profiling range is 300 m with a 8-m vertical resolution; the OS38 maximum profiling range is 1,000 m with a 24-m vertical resolution (more details about the data acquisition and processing are available in Firing et al. (2016) and Gutierrez-Villanueva et al. (2020)). Horizontal velocities (u, v) and vertical shears were obtained from the simultaneous CTD/LADCP profiles using the velocity inversion method of Visbeck (2002). In brief, for each LADCP cast, the method defines a system of linear equations constrained with bottom tracking, along with the ship-drift data and the hull-mounted shipboard ADCP profiles. The system of equations is solved using a standard least squares technique to yield absolute velocity profiles with a 15-m vertical resolution. Absolute velocity errors are relatively small (≤0.05 m s -1 on average). Data were excluded in depth bins where the error was equal to or larger than the absolute velocity. Finally, the barotropic tide predicted from the TPXO7.2 model (Egbert & Erofeeva, 2002) was averaged over the LADCP cast duration and subtracted from the velocity profile for the lee-wave energy radiation calculation (Section 3.4).

An array of bottom-moored CPIES spanning Drake Passage was deployed from November 2007 to December 2011 (Figure 1). The cDrake array consisted of a line of 20 CPIES spanning 800 km across Drake Passage (C-Line) and a local dynamics array of 3 × 7 (21 total) CPIES spanning 120 km cross-stream and 240 km downstream (Chereskin et al., 2012; Figure 1). Additional five CPIES (referred to as the H array) were placed along the Shackleton Fracture Zone during the observational program's final year in 2011. The CPIES were moored in water depths ranging from 500 m on the northern edge of the passage to 4,300 m in the middle. The shallowest 2 sites (C01 and C17), on the continental slope, are not used in this study. Each CPIES unit recorded bottom-tosurface round-trip acoustic travel time, pressure, and temperature at 0.5 m above the bottom, and velocity from an Aanderaa current meter tethered 50 m above the bottom. All instruments were sampled at hourly or shorter time intervals. To remove the barotropic tide and extract the slowly variant geostrophic flow, the near-bottom currents were 3-day low-pass filtered using a fourth-order Butterworth filter and subsampled to 12-hr intervals (Tracey et al., 2013). Tracey et al. (2013) describe in detail the processing of the pressure and acoustic travel time measurements. Here, we summarize the travel time corrections and how they are used to determine temperature, salinity, buoyancy b, and stratification N 2 full-depth time series. First, acoustic travel time was adjusted for the inverse barometer effect, the latitudinal effect of gravity, and the seasonal cycle. The acoustic travel time is then converted to travel time between the surface and 2,000 dbar using a second-order polynomial with depth-dependent coefficients determined from the historical hydrography (526 CTD and Argo float data) within Drake Passage. A constant offset for each CPIES site was determined from calibration CTDs made at the site (Chidichimo et al., 2014;Firing et al., 2014). The hourly time series of were filtered using a 3-day low-pass Butterworth filter; 24 hr at the beginning and the end of the records are removed to avoid transients. Subsequently, the filtered time series were subsampled to twice daily intervals.

The gravest empirical mode (GEM) analysis relates to temperature, salinity, and calculated quantities, such as b and N 2 , by using the available hydrography mentioned above (Tracey et al., 2013). The GEM for each quantity was computed by fitting smoothing splines to the relationship between and temperature, salinity, b, and N 2 at a range of different pressure levels p from 4,000 dbar to the surface. The buoyancy GEM (Foppert et al., 2016) was constructed by first calculating neutral density following (Jackett & McDougall, 1997) with the temperature and salinity GEMs. Buoyancy was then estimated as =-

, where g = 9.81 m s 2 is gravity, 0 =1, 035 kg m -3 is the seawater density, and 0 = 28.5 kg m -3 is a deep neutral density. Subsequently, the N 2 GEM was calculated as . The GEM for each variable was then vertically interpolated to 10-dbar intervals using cubic splines. Consequently, low-pass 4-year, twice-daily time series of b(p, t) and N 2 (p, t) were obtained at each CPIES site by using () to look up b(p, τ) and N 2 (p, τ) in their GEM by linear interpolation. For the local dynamics array, near-bottom pressures and currents referenced to 4,000 dbar were objectively mapped satisfying the geostrophic relationship ∇ ⋅ fU = 0 (where ∇, f, and U are the horizontal gradient operator, Coriolis frequency, and horizontal velocity vector, respectively) to obtain geostrophic streamfunction and horizontal velocity (Firing et al., 2014). These 4,000-dbar absolute geostrophic fields are referred to as the depth-independent, barotropic component. Geopotential anomaly at each depth was objectively mapped to obtain the depth-dependent, baroclinic geostrophic streamfunction, and velocity and their gradients. This study uses the mapped geostrophic velocity where the mapping error is <0.08 m s -1 . Further information on the objective mapping methodology and validation of the mapped fields with numerical simulations and independent data sets is provided in Firing et al. (2014).

MB bathymetry data were obtained for the Drake Passage area from the Global Multi-Resolution Topography Synthesis (Ryan et al., 2009). This synthesis is maintained as a multi-resolution gridded global Digital Elevation Model that includes quality-processed ship-based MB sonar data at their full spatial resolution. The gridded bathymetry for the Drake Passage area includes the sonar data collected since 1,992, which includes the five cDrake cruises around the CPIES and the CTD/LADCP casts (Figure 1; Firing et al., 2016).

The ACC frontal locations are determined using the Mean Dynamic Topography from Maximenko et al. (2009) derived from a combination of 20 years of satellite altimetry, gravity measurements, and in situ data. We use each front's streamfunction values as defined by Gutierrez-Villanueva et al. (2020) to determine the CPIES and fine structure profile positions relative to the fronts in Drake Passage. There are 3, 26, 5, and 5 CPIES locations within the Subantarctic Front, Polar Front Zone, Polar Front, and Southern Drake Passage regions, respectively (Figure 1).

We infer finescale turbulent dissipation rates, ϵ, due to breaking internal waves by applying a finescale parameterization to the CTD/LADCP casts. The two key assumptions of the parameterization are (a) that both shear V z and strain ξ z at scales (10 -100) m are caused mainly by internal waves and (b) that nonlinear wave-wave interactions stimulate a downscale energy cascade resulting in internal wave breaking, leading to turbulent dissipation (Polzin et al., 2014 and references therein). Several studies have applied this parameterization to CTDs, LADCPs, and profiling float profiles in the Southern Ocean, revealing an energetic internal wavefield in the ACC (e.g., Frants et al., 2013;Garabato et al., 2004;Kunze, 2017;Kunze et al., 2006;Meyer et al., 2015;Sheen et al., 2013;Thompson et al., 2007;Waterhouse et al., 2014;Waterman et al., 2013;Wu et al., 2011). Here, we apply the finescale parameterization (Polzin et al., 2014)

(3)

where ϵ 0 = 6.37 × 10 -10 W kg -1 , N 0 = 5.2 × 10 -3 rad s -1 , 2 ∕ 2 0 are the canonical Garrett-Munk dissipation rate (Polzin et al., 2014), stratification, and buoyancy-normalized shear variance, respectively; f 30 = 7.3 × 10 -5 rad s -1 is the inertial frequency at 30° latitude, f is the local Coriolis frequency in rad s -1 , and is the mean stratification estimated by doing quadratic fits for each 320-m window of the buoyancy frequency (stratification) profile computed from individual CTD profiles N. In the absence of observations of the simultaneous frequency and wavenumber energy content, the only source of information for the frequency content of the internal wavefield is the shear-to-strain ratio

For a single wave frequency ω, R ω ≅ (ω 2 + f 2 )/(ω 2f 2 ), is a proxy for the ratio of horizontal kinetic energy to potential energy. For a Garrett-Munk internal wavefield, R ω = 3; larger values than Garrett-Munk indicate more near-inertial frequency content.

Shear and density profiles were broken into 320-m windows with a 50% overlap from the surface to the bottom.

For each 320-m segment of buoyancy-normalized shear variance 2 ∕ 2 , a linear fit was removed and a Hanning window was applied before Fourier transformation. Shear spectra were corrected due to smoothing associated with finite differencing, interpolation, and instrument tilting by using the Polzin et al. (2002) LADCP noise model. Next, shear variance was calculated by integrating the buoyancy-normalized shear spectra over specific limits of integration 2 ∕ 2 = ∫ max min [ ∕ ] , where m min , m max are the minimum and maximum (cutoff) vertical wavenumbers, respectively; S i [] indicates the vertical wavenumber spectra. The cutoff m max wavenumber corresponds to the wavenumber limit at which [ ∕ ] rolls off, indicating the transition from weakly nonlinear to strongly nonlinear wave-wave interactions (Gargett, 1990). We found that ∼90% of individual [ ∕ ] had a roll-off in the buoyancy-normalized spectra that started at 2π/106 rad m -1 (not shown). Consequently, we decided to integrate [ ∕ ] using 2π/320 and 2π/106 rad m -1 as the m min and m max , respectively. The Garrett-Munk shear variance (Cairns & Williams, 1976) was also integrated using the same limits of integration to obtain GM buoyancy-normalized shear variance.

Internal-wave strain ξ z is computed from the stratification profiles as

for each 320-m window. Strain variances were obtained by integrating the spectra over the specific wavenumber limits

2 = ∫ max min

[] ; the same limits of integration used for 2 ∕ 2 are also employed for 2 . Using fixed limits for both shear and strain avoids the need to normalize by their respective Garrett-Munk spectra.

We tested the sensitivity of the finescale dissipation estimates ϵ and shear-strain ratio R ω to different finescale parameterizations and limits of integration (Figures S1, S2 in Supporting Information S1). First, we employed alternative limits of integration as in Sheen et al. (2013) (2π/160 and 2π/64 rad m -1 ; see Figures S1a, S1d, S2a and S2d in Supporting Information S1). Using different limits did not significantly affect the amplitudes of either ϵ or R ω ; the spread of the cloud for ϵ is within one order of magnitude difference for 320-m estimates located near the surface (height above bottom >1,500 m). The medians (filled squares and gray error bars in Figures S1a, S1d, S2a and S2d in Supporting Information S1) show that half of the estimates align with the 1:1 relationship. The GUTIERREZ-VILLANUEVA ET AL.

7 of 25 R ω comparisons show that using larger wavenumber limits of integration brings the ratio down by a factor of three in general (filled squares in Figures S1d and S2d in Supporting Information S1), meaning that relatively short waves have less near-inertial energy content. On the other hand, comparing ϵ calculated with the strain-only parameterization with that estimated using the shear and strain estimates (for each 320-m window) shows the ϵ estimates do not vary significantly (Figures S1b and S2b in Supporting Information S1); a large number of points fall along the 1:1 line although some strain-only estimates are larger than the shear-strain estimates. Using larger wavenumber limits of integration for the strain-only parameterization gives dissipation estimates comparable to that of the shear-strain case (Figures S1c and S2c in Supporting Information S1). Consequently, in the following, we use the shear-strain parameterization and chose 2π/320 and 2π/106 rad m -1 as the m min and m max , respectively.

To avoid singularities when calculating ϵ (see Equations 1 and 2), R ω was set to 1.01 if the calculated R ω <1.01. Alternatively, Kunze et al. (2006) inferred that global shear estimates are dominated by noise rather than internal-wave energy in regions of weak stratification as indicated by a sharp increase in R ω where stratification decreases. We explored this shear noise contamination in our data sets by binning R ω as a function of for each individual cDrake cruise as well as combining all cruises (not shown). We concluded that shear measurements (and therefore ϵ and R ω ) appear to be unbiased due to low stratification. We also inspected the data for the possibility of shear contamination due to low ADCP range in regions of weak acoustic backscatter, but found no increase in R ω as the ADCP range decreased.

The polarization ratio ϕ quantifies the dominant energy propagation of single frequency internal waves. It is an approximation of the ratio of upward to downward energy propagation; however, it may not indicate the energy flux vertical propagation in a multichromatic wavefield (Waterman et al., 2014). The ratio ϕ ccw/cw is calculated as

where ϕ ccw , ϕ cw , QS are the counterclockwise (ccw) and clockwise (cw) shear variance and the quadrature spectra, respectively; u, v are the zonal and meridional velocity components. In the Southern Hemisphere, a dominance of counterclockwise polarization (ϕ ccw /ϕ cw > 1) indicates a dominance of downward directed internal wave energy propagation. Conversely, a dominance of clockwise polarization (ϕ ccw /ϕ cw < 1) indicates a dominance of upward internal wave energy flux. We calculated ϕ by integrating the ccw, cw, and quadrature spectra, estimated from the 320-m buoyancy normalized shear variance windows, over the wavenumber limits used to calculate ϵ and R ω .

Assuming a stable density stratification N 2 , and both quasi-steady (slowly variant) U and tidal currents U t flowing over subcritical topography, the Bell (1975) linear theory gives expressions for the wave stress and associated energy radiation to lee waves. The wave stress integrated over the expected (linear) lee-wave scales

where k = (k, l) is the horizontal wavenumber, f is the Coriolis frequency, k ⋅ U is the Doppler-shifted frequency, ω t is the tidal frequency, P(k, l) is the 2D power spectrum of the abyssal hill topography, and ρ 0 is the seawater density. The parameter 2 0 is the Bessel function of order 0, and it is dependent on the tidal excursion parameter |k ⋅ U t |/ω t . Previous studies assumed that the barotropic tide is negligible in the ACC and did not remove it from GUTIERREZ-VILLANUEVA ET AL.

8 of 25 their LADCP profiles (e.g., Sheen et al., 2013;Trossman et al., 2015;Waterman et al., 2013Waterman et al., , 2014)). In this study, the barotropic tide was removed from the LADCP profiles and near-bottom current meters; therefore, J 0 (|k ⋅ U t |/ ω t ) = 1. Consequently, the wave stress (6) reduces to

The Bell (1975) linear lee-wave theory assumes subcritical topography so that critical/supercritical topography effects are not included in the lee-wave energy radiation. Critical and supercritical topography is defined by the

, where H rms is the root-mean-square (rms) height of the multichromatic topography (Nikurashin et al., 2014). The steepness parameter is a measure of the ratio between topographic height and the expected vertical wavelength of the lee wave. The steepness parameter also indicates when the near-bottom quasi-steady flow does not have enough kinetic energy to override the topographic features; therefore, the topography blocks the flow and does not generate internal waves. The √ 2 is a correction factor that stems from using a multichromatic topography. When a monochromatic topography is used, the steepness parameter reduces to the standard definition NH/|U|, where H is the height of the sinusoidal bump (Nikurashin & Ferrari, 2010b). In a 3D topography, the flow can be blocked and also split and go around topography (Nikurashin et al., 2014). To account for the critical to supercritical topography with respect to the flow, our stress estimates τ are corrected to

We use a critical steepness parameter s c = 0.4 to account for the nonlinear blocking and splitting of the flow around topography (Nikurashin et al., 2014).

To estimate the contribution from the eddy flow to the radiation of lee waves, we followed Yang et al. (2018) and decomposed the horizontal velocity = + ′ , where and ′ are the time-mean and eddy components, respectively. Similarly, we decomposed the wave stress into a mean and transient component = + ′ . The energy radiation (loss) of the quasi-steady total flow into lee-wave generation is then calculated as the work done by the lee-wave drag:

and the energy radiation from the near-bottom eddy flow to lee waves is

Note that the wave stress is a nonlinear function of the total velocity; thus, the eddy velocity contributes to the time-mean energy loss through this nonlinear dependence (Yang et al., 2018). We estimated 4-year lee-wave energy radiation time series using the low-pass time series of near-bottom currents U and stratification N 2 (inferred using the GEMS technique; Chidichimo et al., 2014;Tracey et al., 2013) estimated from the CPIES. We employed only the nearest-to-bottom N 2 time series at each CPIES for the lee-wave energy radiation estimates. To estimate lee-wave energy radiation from the CTD/LADCP data, we followed previous studies (Sheen et al., 2013;Waterman et al., 2013) and reduced high-frequency, short vertical wavelength variability in the CTD/LADCP casts by vertically averaging the velocity and stratification over 1,000 m closest to the bottom.

The horizontal scales of internal lee waves as predicted from linear theory are determined by the near-bottom flow and stratification: GUTIERREZ-VILLANUEVA ET AL.

where ν is the Hurst number, which characterizes the spectral slope at high wavenumbers, H rms is the topography rms, and Γ is the dimensionless norm of k defined by

where k s and k n are the wavenumbers in the strike and normal-to-strike direction of the topography, respectively,

) is the angle clockwise from true north to the wavenumber vector, and θ s is the strike angle measured clockwise from the north. In Equation 11, Q is a positive, symmetric matrix expressed in terms of its eigenvalues 2 ≥ 2 and its normalized eigenvectors and

Since the eigenvectors are orthogonal (i.e., =0 ), they depend on one orientation parameter, which is chosen to be the azimuth θ s of , the eigenvector in the strike direction (Goff & Jordan, 1988). Therefore, the 2D anisotropic model becomes

Nikurashin and Ferrari (2011) used ship-based single-beam echosound data, which provide global along-track 1D topography, and simplified the 2D anisotropic topography spectrum (Equation 14) to 1D by assuming isotropy:

where P 0 is the spectral level and μ = 2(ν + 1) is the topographic spectral slope at scales between 2 and 20 km. Nikurashin and Ferrari (2011) suggest that the isotropy assumption in the topographic spectra in Equation 15 has minimal implications in the rate of energy transfer from near-bottom flows to internal lee waves. They assumed that near-bottom flows over abyssal topography, dominated by transient eddies, can span the whole 360° direction during a few eddy turn-over times. Therefore, they concluded that the time-mean radiation is an average over geostrophic flows, impinging on rough topography at all possible angles.

The statistical parameters (k n , k s , θ s , H rms , and ν) in Equation 14needed to estimate the energy radiation to lee waves are obtained from three topographic data sets representing the abyssal hill morphology.

The first data set of statistical parameters is provided by Goff (2020) (G2020, hereinafter), an update from Goff (2010). The G2020 statistical parameters are based on the most recent global maps of the remotely sensed altimetric gravity field. The updated data set is significantly improved in the lateral and vertical resolutions of the global gravity map. Also, regions that previously had a low rms (i.e., where the small-scale gravity variance did not exceed the noise level) are improved. A key aspect of the data set is that it masks distinct features, such as seamounts, mid-ocean ridges (e.g., Shackelton Fracture Zone; Figure 1), and continental margins as they do not represent abyssal hills (Goff, 2010). The statistical parameters are available on a 1° × 1° longitude-latitude grid. Further details about the methodology employed to estimate these parameters can be found in G2020 and Goff (2010). For estimating E lee (Equation 9) and ′ (Equation 10), we assigned the statistical parameters from the grid box that contains each CPIES and CTD/LADCP casts. We exclude those CPIES and casts that are close to the South American or Antarctic shelf breaks as these topographic features are not abyssal hills. Table S1 in Supporting Information S1 shows the G2020 statistical parameters used for each CPIES location.

The topographic scales resolved by altimetric gravimetry (2.5-7.0 km alongtrack spatial resolution) are insufficient for determining the smallest expected lee-wave wavelengths. Hence, a second data set of statistical parameters is determined using the Drake Passage MB data to resolve these smaller length scales. The statistical parameters of the topographic spectra are estimated using a least squares fit of the 2D MB autocovariance (Goff & Jordan, 1988). However, this is only possible at 10 out of the 41 CPIES locations as either the noise-to-signal ratio from the MB-derived data set is high, or locations are adjacent to mid-ocean ridges, continental margins, or sea mounts. The statistical parameters obtained from the MB data are listed in Table S1 in Supporting Information S1. The H rms estimated from the MB data at these 10 CPIES locations is smaller than that estimated from the G2020 data, except at CPIES C11. The G2020 gravimetric data overestimate the H rms in Drake Passage since it cannot resolve the smaller topographic length scales that contribute to the lee-wave radiation.

Finally, to compare our lee-wave energy radiation estimates with that calculated assuming an isotropic abyssal hill topography, we use Equation 15 statistical parameters from Nikurashin and Ferrari (2011) (NF2011, hereinafter). NF2011 analyzed global shipboard single beam echo soundings with an along-track resolution of 2 km in a 3° × 3° grid. A least squares fit was used to estimate P 0 and μ. Interpolation was used for grid cells where topographic data are absent. Akin to the G2020 data sets, the grid box containing each CPIES location was used to characterize the topographic spectra as in NF2011.

In summary then, the MB and G2020 topographic data sets are used to derive the abyssal hills statistical parameters and represent a 2D anisotropic abyssal hill topographic spectrum (Equation 14). The NF2011 topography is used to derive the 1D isotropic form of the Goff and Jordan (1988) topographic model (Equation 15).

Finescale turbulent dissipation rates ϵ across Drake Passage show a consistent spatial pattern for the different cruises: higher values of ϵ in the northern half of Drake Passage (<58°S) indicate more vigorous internal wave activity and mixing due to breaking waves than in the southern part (Figure 2). The southern region shows background dissipation rates ϵ ≤ 1 × 10 -10 W kg -1 , whereas in northern Drake Passage ϵ ≥ 1 × 10 -8 W kg -1 . The northern Drake Passage elevated dissipation rates are concentrated between 500 and 1,500 m depth and in the Polar Front and Polar Front Zone. The Polar Front Zone also exhibits the largest frontal meandering and mesoscale eddy activity in Drake Passage (e.g., Lenn et al., 2011). Mesoscale eddies in the ACC can modify the propagation of internal waves (Kunze, 1985), which potentially affects the dissipation patterns (Meyer et al., 2015;Sheen et al., 2015). Near the bottom, the dissipation patterns in each of the different cruises suggest that breaking internal waves are less vigorous, likely because the region exhibits relatively smooth topography except for the stations near the Shackleton Fracture Zone (e.g., C10 in Figure 1). Using alternative limits of integration or the strain-only parameterization yields very similar ϵ estimates and spatial distribution for all cruises. As an example, Figure S3 in Supporting Information S1 shows the comparisons between different parameterizations and limits of integration for cDrake 2010. Our near-bottom turbulent dissipation values are on average an order of magnitude smaller than those from Garabato et al. (2004), who used finescale parameterizations to estimate dissipation from measurements made upstream of our study area. Sheen et al. (2013) also employed finescale parameterizations to estimate dissipation rates upstream of our study area (their T3 transect) and found more homogeneous and higher ϵ values (≥1 × 10 -9 W kg -1 ) in between the Polar Front and the Subantarctic Front compared to our estimates. Although the sample sizes in these studies are relatively small when studying a highly intermittent process like turbulent mixing, our results together with previous studies (Garabato et al., 2004;Sheen et al., 2013Sheen et al., , 2014) ) point to elevated mixing in Drake Passage relative to background global ocean dissipation.

Global ocean estimates of turbulent dissipation rates made from finescale observations often assume a constant shear-to-strain ratio R ω = 7 (Kunze, 2017;Kunze et al., 2006), which correspond to more near-inertial wave frequencies than the Garrett-Munk spectrum for which R ω = 3. However, our results suggest that the frequency content of the internal wavefield in Drake Passage, as indicated by R ω estimates, is less near-inertial and more like Garrett-Munk throughout the water column (Figure 3). There is some variability between years. For instance, the shear-to-strain ratios during 2008 and 2009 (Figures 3b and 3c) are closer to the Garrett-Munk value in the northern Drake Passage region than in other years. Our results do not show a latitude-dependent frequency content, that is, that internal waves are more near-inertial moving poleward as found by Sheen et al. (2014) stratification is weaker south of the Polar Front. Our results indicate that for high-latitude regions, such as Drake Passage, median values of R ω are closer to 3-4 in agreement with other estimates in the Southern Ocean (e.g., Meyer et al., 2015;Sheen et al., 2013;Waterman et al., 2013).

We explore possible sources of finescale mixing in Drake Passage by calculating the polarization ratio ϕ ccw/cw (Equation 5; Figure 4). The polarization ratio across Drake Passage is rather noisy and shows no latitude or depth dependence similar to the spatial distribution of R ω for the different years (Figure 3). However, some patches of high dissipation rates (ϵ > 1 × 10 -9 W kg -1 ) in the northern Drake Passage in the upper 1,500 m (Figures 2b and 2c) are associated with polarization ratios ϕ ccw/cw > 1, suggesting downward energy propagation. Meyer et al. (2015) showed that larger than average diffusivities were associated with larger than average polarization ratios (ϕ > 1), related to near-inertial energy in the upper 1,000 m at the Kerguelen Plateau in the Indian Ocean sector of the Southern Ocean. The authors associated this larger than average polarization ratio with wind-generated near-inertial waves propagating downward below the mixed layer. To determine possible sources of high mixing, we constructed average profiles of ϕ ccw/cw and R ω using all estimates of ϵ and separately for those of high mixing where ϵ > 1 × 10 -9 W kg -1 (Figure 5). We calculated the average profiles as a function of height above the bottom and also with depth in order to distinguish bottom-generated waves from below-mixed-layer-generated waves, respectively. In constructing the median profiles, we used all 177 available CTD/LADCP casts.

Over 50% of the profiles indicate downward energy propagation in the upper 1,000 m (blue line in Figure 5a) with median values of the polarization ratio greater than unity. The median shear-to-strain ratio in the upper 1,000 m lies between 3 and 4, consistent with Garrett-Munk (blue line in Figure 5b). When the shear-to-strain ratio is restricted to high dissipation values, the median exhibits a strong depth dependence, decreasing from a maximum of 5 at 750 m depth to a minimum of 1 at 2,000 m depth (red line in Figure 5b). The median profiles in the upper 1,000 m indicate downward energy propagation with more near-inertial frequency and are consistent with Meyer et al. (2015). High-amplitude near-inertial wave packets propagating down from the mixed layer, with vertical wavelengths of 200 m, have been observed west of Drake Passage in the upper 1,500 m (Kilbourne & Girton, 2015). The decay of the near-inertial frequency content and the counterclockwise rotation energy (Figures 5a and 5b) below 1,000 m suggests that near-inertial waves dissipate below the base of the ACC baroclinic jet, where the geostrophic shear is the largest. Under these conditions, waves could propagate downward until they are vertically trapped inside critical layers and dissipate. The near-bottom waves for the all data (blue lines) and the high-mixing profiles (red lines) are not statistically different and indicate more clockwise energy polarization (ϕ ccw/cw < 1) in 1,000 m closest to the bottom (Figure 5c). The R ω profiles indicate that fewer near-inertial waves are associated with high mixing levels (red line in Figure 5d), whereas over half of the profiles indicate that the waves are less near-inertial and more Garrett-Munk-like (blue line in Figure 5d). These results agree with those of Sheen et al. (2013) and Waterman et al. (2013) who attributed the high mixing patterns to less inertial, upward propagating internal lee waves.

To explore the broad relationship between finescale turbulent dissipation rates and internal-wave frequency content with the background stratification and shear in Drake Passage, dissipation rates and shear-to-strain ratios are bin averaged as a function of shear squared and stratification (Figure 6). Each bin average is calculated using all available 320-m ϵ and R ω estimates from the 177 CTD/LADCP profiles with their respective mean shear squared 2 and reference stratification

. Bins with less than five estimates (dissipation or shear-to-strain ratio) are omitted. The 1:1 relationship line indicated in Figure 6 marks where the large-scale Richardson number Ri

In general, low-shear, poorly stratified locations are associated with less internal wave activity as shown by the low dissipation values ϵ < 1 × 10 -9 W kg -1 (Figure 6a) and with less near-inertial waves R ω <5 (Figure 6b). Mixing due to breaking internal waves increases as the background stratification and shear increase; more near-inertial frequency content is associated with higher mixing (therefore, with higher stratification and shear). The highest stratification and shear levels are found in the upper 1,500 m in the northern Drake Passage within and between the Subantarctic Front and Polar Front (Figures 2 and 3). The higher mixing and more near-inertial energy associated with higher stratification and shear is consistent with wind-generated near-inertial waves propagating down from the mixed layer and dissipating in the upper 1,500 m (Figures 5a and 5b), below the base of the baroclinic fronts.

There is also high dissipation (ϵ > 5 × 10 -9 W kg -1 ) associated with Ri ≤1 (Figure 6). These low, large-scale Ri values are found in and north of the Polar Front in the bottom kilometer (not shown). The estimated Ri values that lie close to the stability threshold of the large-scale flow suggest that turbulent dissipation could occur near the bottom by physical mechanisms other than nonlinear wave-wave interactions, such as shear or convective instabilities; these latter processes are not captured by the finescale parameterization (Polzin et al., 2014). Therefore, our finescale dissipation estimates, although ( ) 2 + (

Topographic roughness in Drake Passage relative to the ACC front positions is shown in Figure 7. We computed topographic roughness by employing Equation 14for the 2D anisotropic topographic data sets of G2020 and MB, and the integral of Equation 15for the 1D isotropic NF2011 data set, and integrating them over the expect linear lee-wave wavenumber

Statistical parameters used for each CPIES location are shown in Table S1 in Supporting Information S1. Topographic roughness averaged for each frontal region mostly ranges from 60 to 180 m although some locations show > 200 m. Mean and individual topographic roughness estimates are within the typical values found by Sheen et al. (2013) in Drake Passage but an order of magnitude larger than values found by Waterman et al. (2013) in the Kerguelen Plateau region. Mean calculated for the 1D isotropic NF2011 and the 2D anisotropic G2020 abyssal hill topographies are not statistically different. The higher spatial resolution of the G2020 topographic roughness shows more variability within the Polar Front Zone than that from the NF2011 topography.

We estimate the energy radiation from the total geostrophic flow into lee waves in Drake Passage using the three different topographic data sets and Equation 9. The steepness parameter is calculated as = √ 2 ∕|| where is shown in Figure 7. We analyze the spatial distribution of the energy radiation across Drake Passage and compare it to the 4-year mean low-pass near-bottom circulation (blue arrows in Figure 8a). The three northernmost CPIES (C03, C04, and C20; Figure 1) show strong northward flow associated with the mean position of the Subantarctic Front; the near-bottom flow is steered by the South American continental slope (Gutierrez-Villanueva et al., 2020). As in Chereskin et al. (2009) and Firing et al. (2016), the strong mean near-bottom currents located in the local dynamics array, that is, in the Polar Front Zone, are associated with strong meandering of the Subantarctic Front and Polar Front and transient eddies (Watts et al., 2016). The 1-year averaged currents at the five CPIES adjacent to the Shackleton Fracture Zone show deviation from the surface flow (gray contours in Figure 8a) due to topographic steering.

Here, we only show E lee for the G2020 topography as similar results were obtained when the MB and NF2011 topographies were employed. As expected, the 4-year average of lee-wave energy radiation from the total flow is collocated with where the strongest near-bottom currents impinge on rough topography (Figure 8a). E lee is largest where the Polar Front flows over the Shackleton Fracture Zone (243.0 mW m -2 , based on 1 year of data) and in the Polar Front Zone (322.2 mW m -2 , based on 4 years of data). The lowest mean energy estimates (0.91 mW m -2 ) are found in the Southern Drake Passage, where stratification and currents are the weakest (blue arrows in Figure 8a).

The high-spatial resolution of the local dynamics array in the Polar Front Zone (Figure 1) offers the opportunity to explore the spatial distribution of the energy radiation into lee waves from the total flow. We used the objectively mapped geostrophic currents at 4,000 m depth (black thin arrows in Figure 8a) and an averaged constant stratification N 2 = 6.38 × 10 -7 s -2 . The objectively mapped currents show good agreement with the near-bottom CPIES currents (blue arrows). Our energy-radiation estimates are not significantly different if the mean stratification (calculated at each CPIES location) nearest each mapped grid position is used instead. The energy estimates calculated from the objectively mapped currents are a factor of five smaller than those estimated directly from the near-bottom current meters (filled colored circles Figure 8). The differences are potentially due to the low-pass smoothing and adjusted depth employed for the mapped currents. The Polar Front Zone E lee varies by one order of magnitude. Surprisingly, the downstream region of the Polar Front Zone, characterized by a relatively smooth topographic depression (Yaghan Basin in Figure 1), displays relatively large energy radiation (E lee = 290.25 mW m -2 ; Figure 8a), associated with a deep, strong cyclonic circulation (blue and black arrows in Figure 8a).

Table 1 shows the mean statistics of the energy radiation from the total flow into lee waves per frontal region using the CPIES near-bottom current and stratification time series. We formed a 4-year time series for each frontal region by averaging together the energy radiation estimates from the CPIES located in that region. For the Polar Front, there is only one 4-year site (C10, Figure 1) as recall that the H-array CPIES only sampled for 1 year from October 2010 to November 2011. The standard error is calculated as ∕ √ ̂ , where σ and ̂ are the standard deviation and the degrees of freedom, respectively. Here ̂ is the ratio between the time series length (days) and the decorrelation time scale (days), determined to be the first zero crossing of the autocorrelation function for the time series in each front.

Our frontwise annual lee-wave energy radiation estimates are statistically stable as they show no significant year-to-year variability irrespective of the topography used (Table 1). The Polar Front Zone displays the largest lee-wave energy radiation for both the 1D NF2011 and 2D G2020 topographies. In this region, using both topographies, we found that over the last sampling period from October 2010 to November 2011, the average energy radiation drops by 30% with respect to the preceding sampling period. The Polar Front Zone is where the strongest bottom currents occur (Figure 8a) due to the meandering of the ACC fronts and deep eddy formation (Chereskin et al., 2009). Hence, the drop in the lee-wave energy radiation from October 2010 to November 2011 is likely a result of less meandering, causing a reduction in the mesoscale eddy formation during that period. Nonetheless, when the year-long records from the five H-array CPIES in the Shackleton Fracture Zone (Figure 1) are included over that period (October 2010 to November 2011) in the Polar Front, the energy radiation increases by a factor of 2-3 over the other sampling periods (Table 1).

The 4-year energy estimates in this study compare well with those of Brearley et al. (2013), who used a single year-long mooring record from the DIMES program in Drake Passage, located downstream of our region and just south of the Subantarctic Front (Polar Front Zone in our study). That study used a 2D isotropic topography and s c = 0.7, which accounts for flow blocking but not for splitting, therefore, suggesting that their lee-wave energy estimates are potentially biased high. Their annual-mean energy radiation from a single location is an order of magnitude lower than our four-year-mean and individual year-mean radiation estimates in the Polar Front Zone (Table 1).

Previous modeling studies that have estimated the lee-wave energy radiation from a global ocean model velocity time series averaged in the 500-1,000 m closest to the bottom potentially underestimate the lee-wave radiation from deep flows (Nikurashin & Ferrari, 2011;Scott et al., 2011;Yang et al., 2018). Nikurashin and Ferrari (2011) estimated lee-wave radiation energy of 14-42 mW m -2 from a global ocean model. Their estimates, however, are more homogeneous across the Drake Passage, whereas ours vary by one order of magnitude across the different frontal regions (see Figure 2 in Nikurashin and Ferrari (2013)). The Yang et al. (2018) Drake Passage averaged lee-wave radiation energy estimates determined from the year-long 5-day averaged model velocity field are a factor of three smaller than our 1D (NF2011) and 2D (G2020) energy estimates. The Scott et al. (2011) lee-wave energy model estimates are smaller by fivefold than our estimates for the 2D isotropic topography (Goff, 2010). et al. (2009). Small inset shows the % contribution from the energy radiation from the eddy flow to that of the total flow, both calculated from the CPIES data.

We estimate the lee-wave energy radiation from the near-bottom eddy flow ′ (Equation 10) and explore its relationship with the near-bottom eddy kinetic energy (EKE) in Drake Passage. The lee-wave energy radiation from the eddy flow and the EKE is calculated using the near-bottom current meters and mapped geostrophic velocities (Figure 8b). The easternmost-sampled region of the Polar Front Zone shows the smallest contribution of the energy radiation from the eddy flow to the total flow (% ′ ∕ ; small inset in Figure 8b); the energy radiation due to the mean cyclonic circulation in the Yaghan Basin contributes almost half of the total E lee . Conversely, the largest energy radiation due to eddies is localized close to the Shackleton Fracture Zone (H-array) and collocated with the maximum near-bottom EKE (Figure 8b, non-filled contours). In the western half of the sampled region of the Polar Front Zone, eddies are the major contributor to the generation of lee waves; lee-wave energy due to eddies is of the same magnitude as the total-flow energy radiation. This maximum lee-wave energy radiation due to the eddy flow coincides with the maximum poleward (divergent), horizontal eddy heat flux estimated by Watts et al. (2016). This horizontal flux caused by strong depth-independent currents crossing the upper baroclinic jet at an angle (and so favoring the growth of meanders of the ACC fronts) indicates baroclinic instability processes (Watts et al., 2016).

The deep EKE in the Polar Front Zone shows a similar distribution to that of the surface EKE (Foppert et al., 2017) with a second maximum located downstream (Figure 8b). The lee-wave energy radiation due to the eddy flow also shows patchy, but large values in the downstream region. While baroclinic instabilities dominate the eddy formation and growth in the upstream region, their growth is truncated downstream (Foppert, 2019). Foppert (2019) suggested that barotropic instabilities (downgradient horizontal eddy momentum fluxes) provide a nonnegligible path for eddies to grow by extracting kinetic energy from the mean flow and converting it to EKE. Mesoscale eddies generated by instability of the ACC are thought to lose energy through several mechanisms. Yang et al. (2018) showed that lee-wave radiation significantly weakens the eddy flow where the near-bottom eddy flow interacts with rough topography. The loss of energy from the eddy flow to lee waves may limit or taper the amount of energy available for eddy growth through baroclinic instabilities (conversion from potential energy to EKE) and barotropic (conversion from mean KE to EKE). The potential influence of lee-wave radiation on the energy pathways of the ACC and its implications for the MOC deserves further investigation.

The 4-year time series of near-bottom currents and stratification offer an opportunity to investigate the time variability of the lee-wave radiation across Drake Passage. As for Figure 8, here we only show results for the G2020 topography as similar patterns were obtained when using the NF2011 topography. The time series of E lee (total flow) and s/s c are shown in Figure 9.

Selected stations representative of each frontal region are displayed along with time series of EKE and KE (solid gray line and dashed red line, respectively, Figures 9a-9d). In the Subantarctic Front and Polar Front Zone, EKE ≥ KE for most of the 4-year records; this relationship does not hold for the Polar Front and Southern Drake Passage regions. As expected, there is a strong correspondence between E lee and the near-bottom EKE and KE.

In the Subantarctic Front and Polar Front Zone, E lee has larger time variability as the mesoscale activity is more vigorous than in the Southern Drake Passage. More energy estimates that fall in the subcritical topography s < s c are found in the Polar Front Zone and Polar Front as the near-bottom flow is strong enough to override the rough topography and therefore radiate more lee waves.

Interannual variability of the expected E lee is evidently correlated to that of EKE and KE. The greatest changes in EKE (therefore, in the expected E lee ) are found in the Subantarctic Front and Southern Drake Passage (Figures 9a and 9d). For instance, lower than average EKE corresponds with a decrease in predicted internal lee-wave radiation during the first half of 2010 in the Subantarctic Front and western Polar Front Zone (Figures 9a and 9b). The weaker flow during this period results in more topographic blocking and splitting of the near-bottom currents, resulting in weaker lee-wave energy radiation. It is unlikely that the decrease in predicted lee-wave radiation during 2010 could be due to a migration of the fronts; no southern migration of the fronts has been found in Drake Passage (e.g., Kim & Orsi, 2014).

Investigating the physical mechanisms driving interannual variability of near-bottom KE and EKE (thus in expected lee-wave radiation) is beyond the scope of this study; nevertheless, it warrants future work.

To study the effect of different topographies, we compare the lee-wave energy radiation using the 1D isotropic abyssal hills topography of NF2011 and that calculated using the G2020 and MB 2D anisotropic topographies (Figure 10). We include the CTD/LADCP energy estimates (non-filled symbols in Figure 10) and plot them with the 4-year near-bottom CPIES estimates (colored dots in Figure 10). Only C07 is shown; other CPIES shows similar results (Figure S4 in Supporting Information S1). We also compared our energy estimates calculated using the NF2011 statistical parameters and those calculated using the G2020 statistical parameters averaged on a coarse of 3° × 3° box centered at each CPIES location. However, our results (not shown) are insensitive to the averaging of the G2020 parameters using a similar coarse resolution grid to that of the NF2011 topography. For energy estimates E lee > 10 -3 mW m -2 , the lee-wave energy radiation is not sensitive to the choice of topography.

The relationship between the lee-wave energy radiation estimates calculated using G2020 versus NF2011 topography (blue dots in Figure 10) and MB versus NF2011 case (red dots in Figure 10) shows that most of the dots fall within the one order of magnitude discrepancy (dashed lines in Figure 10), except for a small percentage (<10%) of dots for the NF2011 versus G2020 and MB cases (blue and red dots, respectively); these small clusters show NF2011 energy estimates being larger than the G2020 and MB estimates by more than threefold. Although the cases are fewer, the CTD/LADCP estimates (black triangles and squares in Figure 10) exhibit the same behavior as the CPIES energy estimates and occasionally are larger than those obtained by the CPIES. This study shows that the energy estimates are not sensitive to the choice of abyssal hill topography. Yang et al. (2018) showed that artificially changing the 2D anisotropic bathymetry to an isotropic form can lead to an increase in the energy radiation estimates up to an order of magnitude in Drake Passage.

Our comparison between the NF2011 1D topography and G2020/MB topography is within the Yang et al.'s (2018) range of discrepancy. We only find a small cluster with 2-3 orders of magnitude discrepancy between the 1D isotropic NF2011 and the 2D anisotropic G2020 in agreement with that determined by Trossman et al. (2015) using the CTD/LADCP casts from both the Southern Ocean fine structure experiment (SOFine) near the Kerguelen Plateau (Waterman et al., 2013(Waterman et al., , 2014) ) and from the DIMES experiment near Drake Passage (Sheen et al., 2013). Since Sheen et al. ( 2013) employed a 1D isotropic topography and only corrected their estimates for nonlinear blocking (but not for splitting), their energy radiation could potentially be overestimated.

We compare the energy radiation estimates calculated using the CTD/LADCP casts with those estimated from the CPIES near-bottom current meter and stratification at each CPIES location, employing the three topographic data sets (Figure 11). Here, each pointwise CTD/LADCP estimate is compared to the nearest CPIES estimate in space, averaged over a five-point window in time centered at the time of the CTD/LADCP cast. We expect differences in our results since the CTD/LADCP estimates represent a snapshot averaged over 1,000 m, while the CPIES estimates are obtained from near-bottom U and inferred N 2 at about 50 m above the bottom. The energy radiation estimates determined using the CPIES and the CTD/LADCP casts agree within two orders of magnitude using the three different bathymetries when both the CTD/LADCP and CPIES estimates are larger than 10 1 mW m -2 . The slope of the best fit in log 10 scale using only those estimates that agree within one order of magnitude is less than one for both NF2011 and G2020 topographies (blue and red solid lines in Figure 11, respectively), which indicates that the CPIES estimates are generally larger than the CTD/LADCP estimates. As both energy estimates decrease (i.e., moving down along the 1:1 line in Figure 11), the differences can be up to six orders of magnitude.

We also calculated the mean and standard error of the lee-wave energy radiation from CTD/LADCP and CPIES estimates (shown in Figure 11) over the five cDrake cruises for each of the five frontal regions (Table 2). The standard error is calculated as ∕ √ , where σ is the standard deviation and n = 5 is the number of cDrake cruises (i.e., degrees of freedom) using both the G2020 and NF2011 topographies. Not surprisingly, the CPIES energy estimates are higher than the CTD/LADCP estimates regardless of the topography used. The vertical averaging of the horizontal currents from the LADCP cast used to calculate the slowly variant near-bottom flow likely underestimates the energy radiation; the low-pass-filtered CPIES current better captures the geostrophic flow thought to be the main driver for lee-wave generation.

The Polar Front Zone and Subantarctic Front exhibits the largest lee-wave energy radiation estimates in Drake Passage for both G2020 and NF2011 topographies (Table 2). Sheen et al. (2013) estimated  (1-10) mW m -2 energy radiation estimates from CTD/LADCP casts in the Scotia Sea (downstream of Drake Passage) using a 1D isotropic topography spectrum (their estimates are corrected only for blocking, but not for splitting of the flow). Our estimates in the Polar Front Zone fall are one order of magnitude larger than those obtained by Sheen et al. (2013) in the same frontal region for the Scotia Sea (Table 2). The lower Sheen et al. (2013) estimates are potentially a consequence of quiescent mesoscale activity during their sampling period. Our study includes samples both along and across the Polar Front Zone in Drake Passage, and the stations are repeated five times, allowing better characterization of the deep flows and therefore also of the lee-wave energy radiation with more statistical robustness. Similar energy radiation estimates to ours are found by Waterman et al. (2013) for both instantaneous and transect-averaged cases over relatively smooth (1D isotropic) topography ( < 40 m) in the Kerguelen Plateau area.

Figure 10. Log 10 lee-wave energy radiation (E lee ) (mW m -2 ) calculated using the NF2011 1D isotropic abyssal topography versus log 10 lee-wave energy radiation calculated using a 2D anisotropic abyssal topography at Current and Pressure recording Inverted Echo Sounders (CPIES) C07 (Figure 1). Filled circles are energy estimates using the CPIES bottom current meters and stratification time series. Blue and red circles indicate that E lee (y axis) was calculated using the G2020 and multibeam (MB) statistical parameters, respectively. Open black squares and triangles are E lee (y axis) calculated using the G2020 and MB statistical parameters, respectively, using the conductivitytemperature-depth/Lowered Acoustic Doppler Current Profiler (CTD/ LADCP) stratification and velocity averaged in the 1,000 m closest to the bottom. Solid diagonal shows the 1:1 relationship. Dashed diagonals show the one order of magnitude limits.

Figure 12 shows the bivariate probability distribution function of the steepness parameter s with respect to the flow and the geostrophic streamfunction Ψ in Drake Passage using the near-bottom current meters and stratification from the CPIES time series. In general, the steepness parameter distribution is similar for both the 2D anisotropic GF2020 (Figure 12a) and the 1D isotropic NF2011 (Figure 12b); the 5-95 percentiles interval spans 0.20 ≤ s ≤ 5; however, s has been known to be as large as (10) (Yang et al., 2018). Both the 1D isotropic and 2D anisotropic cases show that for the Subantarctic Front and within the Polar Front, more data fall within the critical/supercritical topography (s ≥ s c ), where topographic blocking and/ or flow splitting effects limit the energy radiation to lee waves. In contrast, subcritical topography (s ≤ s c ) dominates within the Polar Front Zone for either topography. If an s c = 0.70 is used (instead of s c = 0.4), more estimates in the Polar Front Zone fall within the subcritical topography for the NF2011 topography (Figure 12b) than for the G2020 (Figure 12a). This is partly because the larger s c = 0.7 only accounts for the topographic blocking but not for splitting. The Polar Front Zone coincides with where the highest mesoscale activity is found in Drake Passage (Foppert et al., 2017). Strong bottom flows (0.20-0.40 m s -1 ), due to the meandering of the ACC fronts and deep eddy formation in the Polar Front Zone (Chereskin et al., 2009), impinge on the relatively smooth topography potentially contributing to the subcritical topography in this region.

The s estimated using the near-bottom CTD/LADCP current speed and stratification for the G2020 and NF2011 topographies (open black squares in Figure 12) mostly falls within the critical and supercritical topography everywhere in the Drake Passage. For G2020, only three casts located in the Polar Front Zone are in the subcritical topography (Figure 12a). Around 20% (37) of all casts are in the subcritical topography for the NF2011 topography with the biggest cluster found in the Polar Front Zone (Figure 12b). All stations for the MB s (open magenta circles in Figure 12) are in the supercritical topography. Having a time series of near-bottom current and stratification allows us to characterize the time-variable steepness parameter s in Drake Passage at more statistical robustness than was attainable in previous studies.

Figure 11. Log 10 lee-wave energy radiation using the conductivitytemperature-depth/Lowered Acoustic Doppler Current Profiler casts (E lee CTD/LADCP) (mW m -2 ) versus log 10 lee-wave energy radiation using the Current and Pressure recording Inverted Echo Sounders (CPIES) near-bottom current meter and stratification (E lee CPIES) (mW m -2 ). Lee-wave radiation is estimated using the NF2011 (filled blue circles), G2020 (filled red squares), and multibeam-inferred (filled black triangles) statistical parameters. Red and blue solid lines are the linear fit in log 10 scale for the NF2011 and G2020 topographies, respectively. Only estimates falling within one order of magnitude are used for the linear fit, which amounts to 60% and 52% of total number of all estimates (177) for the NF2011 and G2020 topographies, respectively. Solid diagonal shows the 1:1 relationship. Dashed diagonals show the one order of magnitude limits.

Frontal region G2020 NF2011 CPIES (mW m -2 ) CTD/LADCP (mW m -2 ) CPIES (mW m -2 ) CTD/LADCP (mW m -2 ) Subantarctic Front (SAF) 56.15 ± 22.24 29.51 ± 22.98 36.47 ± 12.24 14.39 ± 6.90 Polar Front Zone (PFZ) 59.48 ± 24.49 39.44 ± 5.66 21.25 ± 10.06 15.38 ± 2.98 Polar Front (PF) 9.26 ± 5.25 a 8.82 ± 4.40 b 15.82 ± 1.69 c 5.10 ± 3.77 d Southern Drake Passage (SDP) 4.97 ± 0.72 5.90 ± 3.52 3.36 ± 1.53 1.42 ± 0.70 Note. Estimates for the Polar Front that also include the one-year-long H-array are given in the footnotes. Bold numbers indicate that CPIES energy estimates are statistically different from the CTD/LADCP estimates when using the same abyssal hills topography. a 52.42 ± 38.98 when the H-array is included. b 11.63 ± 4.65 when the H-array is included. c 36.23 ± 20.56 when the H-array is included. d 5.73 ± 1.93 when the H-array is included.

Table 2 Mean ± Standard Error Lee-Wave Energy Radiation Estimates (mW m -2 ) per Frontal Region Calculated From Currents and Stratification From the Contemporaneous Current and Pressure Recording Inverted Echo Sounders (CPIES) and Conductivity-Temperature-Depth/Lowered Acoustic Doppler Current Profiler (CTD/LADCP) Estimates Shown in Figure 11

We calculate the fraction of lee-wave energy that is locally dissipated through nonlinear wave-wave breaking (Figure 13). We integrated the finescale dissipation estimates from near the bottom to the base of the second mixed layer (see Section 2.1). In interpreting our results, caution is advised as turbulent mixing is not only caused by breaking lee waves; for example, downward-propagating near-inertial internal waves breaking near the pycnocline can also enhance turbulent dissipation (Meyer et al., 2015). Also, waves generated upstream can travel horizontally (Baker & Mashayek, 2021) or can be advected by the geostrophic flow (Waterman et al., 2014(Waterman et al., , 2021) ) and dissipate downstream of topography (Zheng & Nikurashin, 2019), therefore breaking the assumption that lee-wave energy dissipates locally. Advection by the flow and remote dissipation are more likely to occur in and north of the Polar Front where the strongest flows are found.

The ratio between turbulent dissipation and lee-wave energy radiation indicates that on average, only a small percentage (<10%) of the lee-wave energy dissipates locally, regardless of the topography employed for CPIES and CTD/LADCP estimates (gray symbols in Figures 13a-13c). Although a small fraction of the expected lee-wave energy estimates are sensitive to the choice of topography, the percentage of lee-wave energy locally dissipated remains invariant to topography. Furthermore, these expected energy estimates are too small to significantly impact the energy budget. Using the strain-only finescale estimates of turbulent dissipation only brings the percentage up to 30% (Figure S5a in Supporting Information S1) and is <10% when the shear-strain parameterization with alternative limits is employed (Figure S5b in Supporting Information S1). The small percentage agrees with Sheen et al. (2013) who found an order of magnitude discrepancy between their direct estimates of turbulent dissipation from VMPs integrated in the bottom kilometer and lee-wave energy radiation estimates at a site upstream of our study. However, perfect agreement between lee-wave energy radiation and local dissipation is not expected. Nikurashin and Ferrari (2010b) showed from numerical simulations using parameters tuned for Drake Passage (Garabato et al., 2004) that the ratio of turbulent dissipation vertically integrated over the bottom kilometer and the energy extracted by the lee waves from the geostrophic flow is 50% for critical to supercritical topography, reducing even further to ∼10% for subcritical topography. Despite doing a full-water-column integration of the turbulent dissipation estimates, our results show that the percentage is smaller than that obtained by Nikurashin and Ferrari (2010b) for critical-supercritical topography. When subcritical topography (log 10 (s/ s c ) ≤ 0 in Figures 13a-13c) dominates (therefore, linear lee-wave theory applies), the percentage of lee-wave energy that dissipates locally (<10%) is consistent with Nikurashin and Ferrari (2010b). Waterman et al. (2014) found that finescale parameterizations overpredict their estimates of turbulent dissipation at a subset of locations where large lee-wave energy radiation coincides with upward propagating, high-frequency internal waves, and shear profiles with maximum values near the bottom and decreasing with height (above the bottom). It is unlikely that the omission of inertial oscillations in the linear lee-wave theory brings the lee-wave energy radiation closer to the local dissipation since the modified theory that takes account of energy lost to inertial oscillations is thought to reduce the energy available for lee waves by only 15% (Nikurashin & Ferrari, 2010a). Therefore, the excess lee-wave energy must either propagate or be advected by the geostrophic flow and dissipate elsewhere (Zheng & Nikurashin, 2019) and/or be reabsorbed back into the mean flow (Kunze & Lien, 2019). On the other hand, including the interaction of the barotropic tide harmonics with the near-bottom flow (Shakespeare, 2020) may reduce the expected lee-wave energy radiation, thus bringing the energy radiation closer to the energy dissipated locally.

An inverse relationship is observed between the fraction of energy radiation and subcritical/critical topography: the more subcritical the topography is, the larger the lee-wave energy radiated (Figures 13a-13c, blue shading). Conversely, critical-to-supercritical topography dominates for small energy radiation to lee waves for both 13a and 13b), and also for the MB (2D anisotropic) topography (Figure 13c) although fewer stations are available. While turbulent dissipation varies by two orders of magnitude, the lee-wave energy radiation varies by almost six orders of magnitude. The fraction of energy locally dissipated, therefore, is limited predominantly by the saturation of the energy flux due to topographic blocking and splitting. As discussed by Nikurashin and Ferrari (2010b), when the bottom flow does not have enough kinetic energy to surmount large topography (s ≥ s c ), the stagnant fluid downstream and below the height of the topographic feature thickens and so reduces the vertical displacement of the water flowing on top of it. Consequently, the lee-wave energy radiation saturates. It is possible that this critical-to-supercritical topography with respect to the flow drives highly nonlinear breaking downstream of the topography (due to nonradiating internal waves and acceleration of the flow in these regions), which could be higher than that for the subcritical topography (Klymak, 2018;Klymak et al., 2021). Whether this breaking downstream of topography could be suitable for weakly nonlinear wave-wave cascade of energy and breaking requires further investigation. Trossman et al. (2015) noted that pointwise discrepancies between lee-wave energy estimates and direct estimates of dissipation in the SOFine and DIMES regions can be large. However, the authors found that statistical agreement between the energy estimates and dissipation rates is achieved when averaging all locations and when the 2D anisotropy is accounted for in the abyssal hill topographic spectrum. Here, we take a similar approach and averaged our energy E lee and depth-integrated ϵ estimates by the frontal region. The front-wise averaging potentially reduces the nonlocal effects, such as wave advection and mean flow-wave interactions of the energy and dissipation estimates; these effects are not encapsulated in the Bell (1975) theory and finescale parameterizations (Waterman et al., 2014). Our results are shown in Figure 13d for the CPIES (circles) and CTD/LADCP (triangles). For the CPIES estimates, both NF2011 and G2020 topographies (blue and red circles, Figure 13) show one-to-two orders of magnitude higher energy conversion over the dissipation within all frontal regions. Notably, the CTD/LADCP energy estimates for the NF2011 topography (blue triangles circles, Figure 13) show better agreement with the depth-integrated inferred dissipation than the CPIES estimates. In the Southern Drake Passage, dissipation exceeds the expected lee-wave energy radiation by a factor of 2, which is likely owing to the fact that inferred dissipation is not only due to lee waves breaking at their site of generation.

Radiation and breaking of internal lee waves are thought to play a significant role in the energy budget of the Southern Ocean. However, uncertainties remain regarding the amount of energy converted from ACC deep flows into lee waves and how much of this energy dissipates locally. In this study, we analyzed the spatial distribution of finescale turbulent mixing and internal lee-wave energy radiation in Drake Passage using three different abyssal hill topographies. Moreover, we quantified the percentage of radiated lee-wave energy that dissipates locally from near-the-bottom to the base of the pycnocline. Turbulent dissipation was estimated using a shear-to-strain finescale parameterization calculated from a series of CTD/LADCP casts at repeated locations across Drake Passage. Drake Passage is a known hot spot of internal wave activity and breaking. Our results consistently showed higher turbulent dissipation due to breaking internal waves north of the Polar Front. In the upper 1,500 m, higher dissipation was associated with downward propagating near-inertial waves dissipating in the thermocline of the Subantarctic Front and Polar Frontal Zone. However, we found that turbulent dissipation was less vigorous near the bottom across much of Drake Passage, mainly due to the relatively smooth topography in our study region. The internal wave frequency content in Drake Passage is less near inertial than what was assumed for the global ocean by Kunze (2017) who used R ω = 7 (i.e., ω ∼ 1.15f).

The energy extraction from the geostrophic flow to internal lee waves across Drake Passage was estimated using a unique 4-year time series of near-bottom currents and stratification from an array of CPIES. The Bell (1975) linear lee-wave theory, corrected for critical to supercritical topography with respect to the flow, was used to determine the lee-wave energy radiation using both near-bottom current meter and CTD/LADCP casts. Lee-wave energy was calculated from three abyssal hill topographies: two were 2D anisotropic (G2020 and MB), and one was 1D isotropic (NF2011). The Polar Front Zone comprises multiple strong deep flows associated with the frequent meandering of the Subantarctic Front and Polar Front. These strong flows impinging over small abyssal hills characterized subcritical topography for generating lee waves (and therefore more linear energy radiation). In the Southern Drake Passage region, the energy radiation was small due to weaker flow and stratification.

Lee-wave radiation was collocated with strong near-bottom EKE. The maximum radiation of lee-wave energy was localized in the Polar Front and the Polar Front Zone. In the Polar Front Zone, the maximum expected radiation was collocated with a maximum in downgradient eddy heat flux observed by Watts et al. (2016). A second maximum in the expected lee-wave radiation was localized downstream (in the Polar Front Zone) and coincided with a second EKE maximum. Yang et al. (2018) showed that radiation of lee waves due to the interaction of the deep ACC flow with topography represents an important sink of EKE in a year-long global climate model output. Our estimates from observations also indicated significant loss of energy from the eddy flow to lee waves. Further work with idealized simulations with lee-wave-resolving resolution could further clarify and quantify the effect of lee-waves on the Southern Ocean EKE pathways.

This study was motivated by previous studies (Trossman et al., 2015;Yang et al., 2018) that suggested that estimates of lee-wave energy radiation and near-bottom turbulent dissipation in the ACC potentially come to a close agreement (less than one order of magnitude in discrepancy) by employing a two-dimensional anisotropic abyssal hill topography. Previous studies estimated lee-wave energy radiation by assuming an isotropic topography in Drake Passage (Sheen et al., 2013) and the Kerguelen Plateau (Waterman et al., 2013); these studies found an order of magnitude discrepancy between their lee-wave energy estimates and turbulent dissipation. In contrast, the statistical parameters from the G2020 gravimetric and MB data used in our study showed that the abyssal hills in Drake Passage are highly anisotropic as k n > k s by a factor of 4-5. Trossman et al. (2015) suggested that while pointwise discrepancies between the expected lee-wave energy and dissipation estimates were large (without statistical agreement), averaged energy estimates and direct estimates of dissipation from VMPs were in statistical agreement when the 2D anisotropy was accounted for in the abyssal hill topographic spectrum. Our study showed that on average less than 10% of the lee-wave energy radiation dissipated locally regardless of the abyssal hill topography employed. Nikurashin and Ferrari (2010b) found that for critical to supercritical topography (s ≥ s c ), numerical simulations showed that half of the radiated energy dissipates locally in Drake Passage, and it reduced to ∼10% for subcritical topography. Our study showed that lee-wave energy estimates were one to two orders of magnitude larger than the local turbulent dissipation for both 1D isotropic and 2D anisotropic bathymetries in agreement with the expected percentage found by Nikurashin and Ferrari (2010b) for subcritical-to-supercritical topography. This excess of wave radiation was associated with critical to subcritical topography, that is, more linear lee-wave energy radiation. The percentage of expected lee-wave energy that locally dissipates by wave-wave cascade does not increase even if turbulent dissipation is integrated from the bottom to the base of the pycnocline. In the absence of critical layers, upward-propagating lee waves can reflect back from the base of the pycnocline, and energy transfer from the sheared flow to the waves is enhanced, therefore enhancing wave breaking and mixing (Baker & Mashayek, 2021).

Several caveats come with this study. Some of the near-bottom current meters may have been located within the bottom boundary layer. The lack of direct estimates of turbulent dissipation prevented us from estimating true dissipation rates due to breaking internal waves. Mean dissipation rates could be substantially biased due to sampling in a hot spot of turbulent mixing (Klymak, 2018). Some of our dissipation estimates from finescale parameterizations were inherently overpredicted due to physics that are not encapsulated by the parameterization (Waterman et al., 2014). Also, the statistical representation of the abyssal hill topography might be inaccurate for some regions in Drake Passage; the MB data revealed topography that is smoother compared to the single beam (NF2011) and satellite gravimetry (G2020). For example, the Polar Front Zone is characterized by abyssal plains rather than by abyssal hills. In this region, the energy sink due to the bottom boundary layer might have been more important than lee-wave generation. Higher precision mapping of the global ocean topography is required for more accurate statistical representations of the abyssal topography, thus enabling more realistic representations of the energy deposition from geostrophic flows to lee waves.

Despite the above-mentioned limitations, the main take away of this study suggests that only a small percentage of the expected lee-wave energy dissipated locally in the full-water column through nonlinear wave-wave interaction as also found in various recent studies (Brearley et al., 2013;Nikurashin & Ferrari, 2010a;Sheen et al., 2013;Waterman et al., 2013). Specifically, the finding that the scatter between the amount of energy radiated and local dissipation remained invariant even if the full 2D anisotropic topography was employed showed that the lack of isotropy was not a definitive aspect for explaining the small fraction of theoretical lee-wave energy radiation that dissipates locally. Therefore, our study suggests that alternative fates must be considered for the paths of the excess lee-wave energy. The theoretical lee-wave energy could be either advected by the geostrophic flow and dissipate elsewhere (Zheng & Nikurashin, 2019) and/or be reabsorbed back into the mean flow (Kunze & Lien, 2019). In addition, the interaction of the slowly variant flow with the barotropic tide over small-scale abyssal hill topography could suppress the energy radiated into lee waves (Shakespeare, 2020). Future work using idealized numerical simulations tuned for the range of parameters (such as steepness) found in this study could shed light on the fates of the excess of lee-wave energy radiation.