1. Introduction
Understanding what sets the strength and geographical variability of oceanic diapycnal mixing is a critical issue in physical oceanography because of the central role that turbulent mixing processes play in the oceanic meridional overturning circulation and its impact on climate (e.g., Munk and Wunsch 1998). A large fraction of the energy available for diapycnal mixing is provided by the tides (Wunsch and Ferrari 2004), with satellite measurements indicating that the semidiurnal M2 barotropic tide dissipates one-third of its energy in the deep ocean globally (Egbert and Ray 2000, 2001). This dissipation is localized to specific hot spots in which enhanced tidally driven turbulent dissipation is revealed by in situ measurements, mostly over midocean ridges (Polzin et al. 1997; Rudnick et al. 2003) and near isolated seamounts (Lueck and Mudge 1997). The route to dissipation of the barotropic tide in the deep ocean primarily involves a conversion into baroclinic tides, that is, internal waves with tidal frequencies. Internal tides form a reservoir of turbulent energy, the dissipation of which results in irreversible diapycnal mixing. The fate of this reservoir—mainly, where and how internal waves break—is poorly understood on a global scale, yet is of key importance in setting the geography of diapycnal mixing (MacKinnon et al. 2017). Diapycnal mixing is heterogeneous and strongly impacts the distributions of tracers and water masses (Armi 1979) and the intensity and structure of the overturning circulation (Mashayek et al. 2015; de Lavergne et al. 2016).
This paper addresses the life cycle—from generation to dissipation—of semidiurnal internal tides over the Mid-Atlantic Ridge (MAR) sector south of the Azores by combining a theoretical model with multisource in situ and satellite data. Our primary goals are to document the key stages of the internal tides’ life cycle and to outline the energy budget of the internal tides in the region. The northern MAR is a relatively unexplored source of internal tides compared to the more widely studied Hawaiian Ridge system [as part of the Hawaiian Ocean Mixing Experiment (HOME; e.g., Rudnick et al. 2003)] and the southern MAR [under the auspices of the Brazil Basin Tracer Release Experiment (BBTRE; Polzin et al. 1997; Ledwell et al. 2000)]. However, recent theoretical (Melet et al. 2013; Lefauve et al. 2015) and numerical (Timko et al. 2017) modeling studies suggest that the northern MAR is an important site for internal tide generation and dissipation and, as such, provides an interesting point of contrast to the Hawaiian Ridge and southern MAR.
The work presented here is part of the RidgeMix project, which seeks to understand and quantify the upward supply of nutrients to the upper layers of the North Atlantic Subtropical Gyre. As part of RidgeMix, a mooring was deployed on the edge of the MAR, designed to resolve variability in velocity and temperature at tidal and higher frequencies throughout the entire water column with high vertical resolution. This mooring provides data with which local internal tide dynamics may be described for up to 10 baroclinic modes. In addition, direct measurements of turbulent energy dissipation from microstructure profilers were obtained above the MAR to assess the rate of dissipation of internal tides. Application of a 2D spectral model of barotropic-to-baroclinic energy conversion (St. Laurent and Garrett 2002) and analyses of tidal model estimates of barotropic tidal dissipation (Egbert and Ray 2000) and satellite altimetry-derived mode-1 horizontal energy flux data (Zhao et al. 2016) allow us to extend our understanding of the internal tides’ life cycle to a regional scale.
In sections 2 and 3, we introduce the data and methods used in this study, respectively. The characteristics of semidiurnal internal tides, characterized with a combination of a theoretical model, mooring data, and microstructure measurements, are presented in section 4. Our regional perspective of tidal energy conversion and dissipation is discussed in section 5. Our main conclusions are drawn in section 6.
2. Data
In this section, we briefly describe in situ data collection conducted during the RidgeMix cruise (Sharples 2016). We then document the global gridded datasets that we use to compute tidal energy–related quantities on a regional scale (section 3).
a. RidgeMix data
1) Mooring data
A mooring was deployed at 36.23°N, 32.75°W (Fig. 1a) on 26 September 2015 and recovered on 4 July 2016. It was equipped with 41 RBR self-logging thermistors, two Teledyne RD Instruments (TRDI) 75-kHz-long Ranger acoustic Doppler current profilers (ADCPs), and two Flowquest 75-kHz ADCPs. The positioning of thermistors and ADCPs along the mooring line is shown in Fig. 1b. The 36 thermistors monitored temperature with a sampling period of 15 s during the whole mooring deployment, whereas 5 thermistors stopped recording between a few days and a month after deployment. The spacing between thermistors was reduced where the stratification is maximum in order to capture high (up to 10) dynamical modes [section 3 and Fig. 2 (below)]. The ADCPs recorded hourly averaged horizontal velocity (over 50 and 150 pings for the TRDI and Flowquest ADCPs, respectively) with 8-m vertical bins. Their positioning allowed sampling of the entire water column down to ~100 m above the seafloor.
(a) RidgeMix experiment location. Background shading indicates bathymetry, orange circles are VMP stations, and the red star is the mooring location. (b) Mooring sketch; gray dots are thermistors, red triangles are ADCPs, and red segments are ADCP ranges.
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
Mean stratification N2 and first 10 baroclinic modes Πn for pressure and horizontal velocity. Vertical dashed lines represent x = 0 and x axes are normalized. Red dots are the positions of thermistors, and red lines are linearly interpolated between them.
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
2) Microstructure data
b. Global gridded datasets
1) SRTM30_PLUS
The Shuttle Radar Topography Mission dataset (SRTM30_PLUS; Becker et al. 2009) is a global bathymetry dataset at a 30-s resolution. SRTM30_PLUS is based on the 1-min Smith and Sandwell (1997) bathymetry and incorporates higher-resolution data from ship soundings wherever available. The MAR sector south of the Azores has been intensively surveyed (see Fig. 3 in Timko et al. 2017), and SRTM30_PLUS is significantly enriched by small-scale topographic features compared to the Smith and Sandwell (1997) dataset.
2) WOA13
Temperature and salinity data required to compute the buoyancy frequency are from the 1°-resolution World Ocean Atlas 2013 (WOA13) version 2 climatology2 (Locarnini et al. 2013; Zweng et al. 2013). This climatology is computed by objective analysis of historical hydrographic profiles from many different sources.
3) TPXO
Barotropic tide currents (amplitude and phase) were extracted from the 1/12°-resolution inverse tidal model for the Atlantic Ocean, the TPXO AO_ATLAS,3 a regional version of TPXO8 (Egbert and Erofeeva 2002). We hereinafter refer to this dataset as TPXO.
4) Mode-1 M2 energy fluxes and sea surface height from satellite altimetry
Mode-1 M2 internal tide horizontal energy flux and sea surface height (SSH) data at a horizontal resolution of 1/5° from Zhao et al. (2016) were used in this study to quantify the propagation of baroclinic tidal energy on a regional scale. Zhao et al. (2016) use a two-dimensional plane wave fit method to extract internal tides from satellite SSH and apply a modal decomposition that allows the inference of mode-1 internal tide pressure from SSH. Assuming that the energy partition between potential and kinetic energy components depends only on latitude and tidal frequency, the internal tide velocity is also estimated from SSH. Finally, vertically integrated horizontal energy fluxes 
3. Methods
In this section, we outline the methodology used in this study. First, we implement a theoretical model for the generation of internal tides (section 3a). This is followed with an analysis of mooring data to characterize internal tide properties (section 3b). Finally, we estimate the barotropic tidal energy loss on a regional scale from a tidal model (section 3c).
a. Theoretical model of barotropic-to-baroclinic energy conversion
In a stratified fluid, the interaction of a current with varying topography generates internal waves. Under different sets of flow characteristics and dynamical assumptions, models and parameterizations for internal wave generation have been developed (e.g., Baines 1998; Nycander 2005). When the current of interest is the barotropic tide, two dimensionless parameters mainly govern the nature of internal waves (St. Laurent and Garrett 2002; Garrett and Kunze 2007): the ratio of topographic slope s = ∇h to wave characteristic slope 
b. Energy density and horizontal energy flux from mooring data
Internal tide energy density E and horizontal energy flux F are estimated from mooring data following Nash et al. (2005). Here, we briefly recall the main steps of their procedure.
The variables u′, p′, and ξ are then filtered at the M2 frequency ω using a bandpass fourth-order Butterworth filter in the bandwidth 
c. Barotropic tide energy loss using a tidal model
4. Structure of the semidiurnal internal tide
In this section, we use a range of measurements and a theoretical model to assess the life cycle of internal tides over the MAR at the location of the RidgeMix mooring—from generation (section 4a) to propagation (section 4b) and dissipation (section 4c)—before offering a summary of this local perspective (section 4d).
a. Theoretical estimates of internal tide generation
Figure 3 illustrates the method used to estimate barotropic-to-baroclinic energy conversion (section 3a) at the specific mooring location. First, the method interpolates the barotropic tidal ellipse from TPXO at the point of interest and extracts topography from SRTM30_PLUS around it (Fig. 3a). Second, topography is rotated along the ellipse’s axes (Fig. 3b), and its two-dimensional power spectrum ϕ is computed (Fig. 3c). Third, ϕ is directionally weighted by tidal currents and multiplied by a factor depending on the three frequencies of the system (f, ω, and Nb) to give the vertical energy flux Ef(K, θ) [Eq. (2) and Fig. 3d]. Finally, Ef is azimuthally averaged to get its distribution as a function of horizontal wavenumber (Fig. 3e) or equivalently its modal distribution [Eq. (7)]. Its cumulative sum eventually gives the total energy conversion (Fig. 3f). Alternatively, Ef can be integrated in the wavenumber direction to get its azimuthal dependence (Fig. 3g).
Illustration of the method used in the barotropic-to-baroclinic energy conversion model at the mooring location. (a) Bathymetry in longitude–latitude coordinates and barotropic tidal ellipse. (b) Bathymetry in the rotated coordinate system aligned with the major x and minor y axes of the ellipse. (c) Two-dimensional power spectrum of bathymetry ϕ (kx and ky are the wavenumbers in the x and y directions, respectively). (d) Vertical energy flux Ef(K, θ) from Eq. (2); θ = 0 in the x direction and rotates anticlockwise. (e) Azimuthally averaged vertical energy flux 
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
The model predicts an energy conversion at the mooring site that spans a wide range of equivalent horizontal wavenumbers, noticeably exhibiting a plateau between modes 1 and 5 and then gradually decreasing (Fig. 3e). Indeed, the rough topography of the MAR varies strongly on a wide range of scales, down to abyssal hill scales of O(1) km (Goff 1991). As a consequence, high-mode internal tides are expected to be radiated, as observed (St. Laurent and Nash 2004) and modeled (Zilberman et al. 2009) on the flanks of the MAR in the Brazil Basin. Superimposed on the theoretical model estimates is the spectrum of mooring-derived horizontal energy flux, converted to a vertical flux by multiplying by α, the wave characteristic slope, and dividing by the water depth. The energy flux is cut at mode 35, which is in theory the highest mode that can be resolved with 36 independent thermistors.4 It shows a good agreement with the theoretical model for modes higher than 5 but overestimates energy fluxes in modes 1–4 (Fig. 3e). Nonetheless, we do not expect a perfect match, as the mooring detects fluxes from remote sources—most likely propagating low modes—that are not taken into account in the model. The total vertical energy flux is 4.5 mW m−2 in the model and 9.1 mW m−2 in the mooring data. A factor of 2 discrepancy is also found by St. Laurent and Nash (2004). This may also relate to the model’s failure to take account of the subtidal circulation, which could introduce variability in internal tide generation (Kerry et al. 2014).
The model predicts the direction of the flux modulo 180° (Fig. 3g). The two preferential directions are almost perpendicular to the tidal ellipse’s major axis (θ = 0) and coincides roughly with the cross-fracture zone direction (Fig. 3a). The mooring-derived flux is mainly to the southeast and roughly fits in the prediction of the model (Fig. 3g). Again, we do not expect a perfect match since the model is local and cannot take into account remote modulation of the flux.
b. Internal tide properties from high-resolution mooring data
1) Energy density and energy flux
Time series of energy density E = KE + PE and horizontal energy flux F = ||F|| in modes 1–10 are shown in Figs. 4d and 4e. The energy density is mostly contained in mode 1 and gradually decreases with increasing mode number (Fig. 4d). The horizontal energy flux is, on the other hand, overwhelmed by mode 1, which is almost indistinguishable from the total energy flux (Fig. 4e). This picture is consistent with open-ocean mooring estimates of energy density and energy fluxes from the Internal Waves Across the Pacific experiment (IWAP; Zhao et al. 2010). Indeed, on the one hand, the wave velocity u′ and displacement ξ′ project qualitatively onto a few modes, between 1 and 10 (not shown). On the other hand, the wave pressure p′ results from the vertical integration of ξ′ and is hence smoother and thus is dominated by low modes. As a consequence, the kinetic [Eq. (16); Fig. 4b] and potential energy [Eq. (17); Fig. 4c] computed from u′ and ξ′ have some contributions from modes 1–10. In contrast, the horizontal energy flux [Eq. (18); Fig. 4e] computed from u′ and p′ is strongly dominated by mode 1. The time-mean and standard deviation of E and F as a function of mode confirm this distribution (Figs. 5a,b; Table 1). The mode-1 energy flux accounts for 83% of the energy flux of modes 1–10. However, mode-1 energy density accounts for only 45% of the energy density of modes 1–10. Our basic interpretation is that although the bulk of—potentially—propagating energy is in mode 1, mode 2 and above (modes higher than 10 are partially captured by the mooring) contain at least 55% of the energy ultimately available for local mixing.
Time series of (a) barotropic kinetic energy KEbt estimated from the moored ADCPs (black line) and from the TPXO combination of M2 and S2 tidal velocities (red line). Cumulated variables as a function of mode number: (b) KE, (c) PE, (d) E = KE + PE, (e) horizontal energy flux F, and (f) azimuth of mode-1 (thick line), mode-2, and mode-3 fluxes (colors follow the color bar). Gray lines in (d) and (e) are total E and F, respectively; no modal decomposition is performed. Gray shading in (a)–(e) represents spring tides. Notice that the flux from the total field can be smaller than the sum of the modal contributions as fluxes in different modes are not necessarily oriented in the same directions.
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
Time-mean (a) energy density E, (b) horizontal energy flux F, and (c) shear variance S in modes 1–10 (light gray bars) and in the sum of modes 2–10 (dark gray bars). Error bars are standard deviations from the mean.
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
Energy density E (kJ m−2), horizontal energy flux F (kW m−1), estimated group velocity 
The robustness and steadiness of mode-1 flux compared to higher modes is also demonstrated by the time series of their direction (Fig. 4f). The mode-1 flux is always directed between east and south directions and varies slowly, likely influenced by the surrounding mesoscale eddy field (Rainville and Pinkel 2006; Dunphy et al. 2017). On the other hand, the mode-2 and mode-3 flux directions vary through all azimuths on daily time scales. A similar variability is found for modes greater than 3 (not shown). This short time-scale variability might be attributed to interferences between waves arising from different sources, reflection, and scattering (e.g., Zaron and Egbert 2014). Two-dimensional histograms of modal horizontal energy fluxes further confirm the multidirectional nature of fluxes for modes greater than 1 (Fig. 6). This high directional variability is probably linked to the multiple sources of internal tides on the MAR around the mooring. The recent comparison of mode-1 and mode-2 horizontal energy fluxes from a high-resolution numerical model and historical moorings further demonstrates a poorer correlation and a higher variability in mode-2 fluxes compared to mode-1 fluxes (Ansong et al. 2017).
Normalized histogram of horizontal energy flux for (a)–(f) modes 1–6. The ranges of x and y axis differ between (a) and (b)–(f). Red solid and dashed lines in (a) represent the mean flux direction (azimuth 127.3°) and standard deviation (21.0°), respectively.
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
2) Group velocity
Figure inspired by Fig. 1 in Alford and Zhao (2007b). (a),(c) Scatterplot of semidiurnal horizontal energy flux vs energy density (gray dots), mean and standard deviation of energy in each energy flux bin (red bars), and linear regression to these points (red lines) for mode-1 in (a) and mode-2 in (c). Group velocity is determined by the slope of this linear regression. The dashed and solid lines represent theoretical group velocity for propagating cg and standing 
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
The estimated mode-1 group velocity (1.09 ± 0.10 m s−1) agrees particularly well with the group velocity of a standing wave (1.08 m s−1; Fig. 7a and Table 1). Interestingly, the peaks of the bimodal-like shape of the PDF of F/E coincide with cg and 
The mode-2 group velocity shows a different picture, being inconsistent with both propagating and standing wave velocities (Fig. 7c). Estimates of 
We applied the same technique to modes 1–10 and report the estimated group velocity with their 95% confidence interval in Fig. 8. Apart from mode 4, which is more consistent with a propagating wave, all modes are either more compatible with standing waves or have even smaller group velocities than expected from a standing wave. Modes greater than 8 have very small group velocity because of vanishing fluxes, and their velocities thus gradually depart from theoretical values.
Binned average group velocity and its 95% confidence interval for modes 1–10, as determined as in Fig. 7 (red line). Theoretical group speeds for propagating cg and standing 
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
3) Spring–neap cycle
The energy density and horizontal energy flux both display a remarkable spring–neap cycle, mostly dominated by mode 1 (Figs. 4d,e). This spring–neap cycle is obviously related to the astronomical forcing, as seen in barotropic kinetic energy 
(a) Northbound and (b) southbound M2 mode-1 internal tides from the Zhao et al. (2016) dataset; color is SSH, and arrows are horizontal energy fluxes (fluxes smaller than 0.2 kW m−1 have been masked). The masked region in gray in the northwest corner is where mesoscale activity is too strong to be properly separated from internal tides (overlap in scales). The red arrow is the time-mean mode-1 horizontal energy flux from the mooring data. Black lines are the 2000- and 4000-m bathymetry contours. Green lines southward of 35°N are the 1000-m bathymetry contours highlighting the Atlantis-Meteor Seamount Complex, a chain of seamounts extending from the Great Meteor Seamount at its southern edge to the Atlantis Seamount at its northern edge (see also Fig. 1 in Searle 1987). Red and green stars are locations of the mooring and the Hyères Seamount, respectively. (c) Bathymetry (black line) and SSH (orange line) interpolated along the orange line in (a), stretching from the Hyères Seamount to the mooring location. (d) Theoretical group speed (light blue) and traveling time (green) of a M2 mode-1 internal tide propagating along the orange line in (a).
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
c. Local dissipation from microstructure measurements
Two 25-h stations with continuous tethered VMP deployments were carried out in the vicinity of the mooring site during spring and neap tides (section 2a). Mean profiles of the turbulent dissipation rate ε and the PDF of log(ε) for both series of casts are shown in Fig. 10. There is evidence for intensified dissipation during the spring tide, as highlighted by the spring tide PDF of log(ε) being skewed toward higher values compared to the neap tide PDF (Fig. 10b). Vertical profiles of ε also reveal a higher springtime dissipation at almost all depths with enhanced differences in the bottommost 500 m (Fig. 10a). In this depth range, ε reaches 10−9 W kg−1, as routinely observed over rough topography of the world’s oceans (Kunze 2017). Notice that the tethered VMP could not dive deeper than ~400 m above the seafloor (~2200 m) because of wire length limitations, and we expect dissipation to further increase with depth in excess of 1800 m.
(a) Vertical profile of 50-dBar binned dissipation ε (mean and std dev) and (b) PDF of log(ε) from repeated tethered VMP casts in the close vicinity of the mooring site during spring tide (red) and neap tide (blue).
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
The depth-integrated dissipation εz [Eq. (1)] is 1.3 ± 1.1 mW m−2 during spring tide and 0.7 ± 0.4 mW m−2 during neap tide. A similar factor of 2 difference between spring and neap tide dissipation has been observed on the Hawaiian Ridge (Klymak et al. 2006). Notice that εz is likely to be underestimated because of undersampling of the water column. Nonetheless, these high levels of dissipation may be due to the enhanced local generation of high-mode internal tides that carry most of the shear variance (Fig. 5c) and are prone to rapid breaking close to their generation site (in a similar fashion as on the Oregon continental slope; Nash et al. 2007). In addition, the spring–neap modulation and bottom intensification of dissipation suggests that the elevated turbulence may be triggered by a direct breaking of high-mode internal tides (Klymak et al. 2008). Note, however, that we are unable to verify that the spring–neap component of dissipation is phase locked with astronomical forcing.
d. Summary of the local perspective
In summary, the high-resolution mooring data provide us with a detailed insight into internal tide dynamics on the northern MAR. The horizontal energy flux is highly dominated by mode 1 (0.83 kW m−1) and is rather steady in direction. Its intensity displays a strong spring–neap cycle lagging by 3.4 days from the astronomical forcing, hence pointing to a modulation by remote sources. The Hyères Seamount—a hot spot of mode-1 internal tide generation of the Atlantis-Meteor Seamount Complex—is a very likely candidate as it radiates an internal tide beam toward the mooring site, whose traveling time is close to the spring–neap cycle lag to the astronomical forcing.
The horizontal energy fluxes associated with modes 2–10 are very weak (<0.07 kW m−1) and vary strongly in direction, likely caused by the interactions of waves generated by numerous, distributed sources on the MAR. In turn, the energy density is more widely partitioned between modes, with mode 1 accounting for a smaller fraction of the total energy density than the sum of modes 2–10 (0.84 vs 0.95 kJ m−2). Examination of the propagation velocity revealed that most of the modes are compatible with standing waves. This implies that internal tide energy is likely to remain concentrated over the MAR and thereby become ultimately available for near-local turbulent mixing. In line with this result, microstructure measurements performed at the mooring site reveal elevated and bottom-intensified turbulent energy dissipation. The energy conversion model further confirms that high modes are expected to be generated. The model possibly underestimates conversion into low modes—although low modes diagnosed from mooring data may originate from remote sources (Figs. 9a,b)—but its agreement with mooring-derived fluxes for modes greater than 3 is remarkable.
5. Regional perspective
To get a broader view of internal tide dynamics over the northern MAR, we performed a regional energy budget using different data sources. The barotropic tide energy loss and internal dissipation should be equal in the absence of energy transport by internal tides. However, low-mode internal tides play a role in redistributing energy. In addition, energy entering low modes does not dissipate locally. In the following, the barotropic tide energy loss D is estimated via a tidal model (section 3c), the tidal barotropic-to-baroclinic conversion Ef is estimated via a two-dimensional spectral model (section 3a), and the conversion to mode-1 internal tide is also estimated via satellite altimetry 
The regional distribution of the total energy conversion 
Model estimate of barotropic-to-baroclinic energy conversion: (a) 
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
The energy conversion into mode 1 agrees well between the two independent estimates (Figs. 11b,e). As shown above, the Atlantis-Meteor Seamount Complex is the main source of mode-1 internal tides (see Figs. 9a,b). Another hot spot is the Azores Islands, which the satellite product misses likely because of the proximity of land. Importantly, both products concur on a very low mode-1 conversion at the MAR (<1 mW m−2). In contrast, strong generation of modes ≥2 occurs on the MAR and accounts for most of the energy conversion (cf. Figs. 11a and 11c). Using a different method for estimating energy conversion into normal modes, Falahat et al. (2014b) demonstrate a qualitatively similar distribution (their Fig. 6).
All quantities are further summed over the hatch-free area in Figs. 11a–e, where the ocean depth lies between 200 and 4000 m. This area isolates the MAR and does not include the Azores Plateau, where the assumption of small tidal excursion is likely to be violated. Two robust conclusions can be drawn from this budget (Fig. 11f). First, the close agreement between D (16.4 GW) and 
As a point of comparison, the Hawaiian Ridge system dissipates 20 GW of barotropic tidal energy (Egbert and Ray 2001), of which 6 GW (30%) is converted into mode 1 (Merrifield and Holloway 2002). The difference between the distribution of energy stems from the different topographic shapes of the two ridge systems. The Hawaiian Ridge has abrupt flanks that generate intense mode-1 tides, which may propagate far away from the ridge (Zhao et al. 2010). In contrast, the MAR has a wider rift valley (in the fracture zone direction, the direction perpendicular to the ridge edge) and hosts taller and steeper abyssal hills because of its slow spreading rate (Goff 1991). The latter are known to generate high-mode internal tides (Melet et al. 2013; Lefauve et al. 2015; Timko et al. 2017) that are prone to rapid breaking.
The VMP data allow us to gain some insight into the distribution in turbulent dissipation levels across and beyond the MAR (Fig. 12). The most notable feature is the strong on- versus off-ridge contrast, with increased dissipation occurring above the rough topography of the MAR [as also evidenced in the Brazil Basin by Polzin et al. (1997) and Ledwell et al. (2000)]. Pointwise dissipation rate is often ≥10−9 W kg−1 over the ridge and decays to O(10−11–10−10) W kg−1 off the ridge (Fig. 12b). The vertical distribution of ε is beyond the scope of this study, and we focus on the depth-integrated dissipation εz from 50 m (to exclude turbulence related to mixed layer processes) to the seafloor [Eq. (1); Fig. 12a]. The dissipation εz and the local energy conversion 
(a) Depth-integrated dissipation εz (black line) and barotropic-to-baroclinic energy conversion 
Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0121.1
The fraction of the local dissipation to the total energy conversion 
6. Conclusions
A multisource analysis of the life cycle of semidiurnal internal tides on the MAR sector south of the Azores has been conducted. The main conclusions are as follows:
Mooring data on top of the MAR reveal that the internal tide horizontal energy flux is dominated by mode 1, which is steady in intensity and direction (to the southeast). The mode-1 horizontal energy flux undergoes a strong spring–neap cycle that likely stems from interaction with remotely generated internal tides. Energy fluxes for modes greater than 1 are extremely variable in intensity and direction, probably because of interactions with ubiquitous, distributed sources on the MAR.
Energy density is more widely distributed among the modes. Specifically, modes 2–10 contain more energy than mode 1 alone. High-mode generation is supported by spectral estimates of energy conversion.
Estimates of modal group velocity indicate that most modes are compatible with standing internal waves. Given conclusion 2, this implies that energy is concentrated above the MAR and ultimately dissipates locally. This is supported by the strong energy dissipation inferred from microstructure measurements.
A simplified regional energy budget outlines qualitative differences with the well-studied Hawaiian Ridge system (Merrifield and Holloway 2002; Klymak et al. 2006), which dissipates a similar amount of semidiurnal barotropic tide energy (16 GW over the MAR versus 20 GW around Hawaii). Namely, only 9% (vs 30% in Hawaii) of the energy is converted into mode 1, the only mode that may radiate energy away. Consistently, the fraction of energy locally dissipated is higher over the MAR, q = 0.49 ± 0.35 versus 0.08–0.25 in Hawaii (Klymak et al. 2006). This measure is, however, rather uncertain given the modest number of direct dissipation measurements. Note that these results are in line with differences in internal tide characteristics between the two systems highlighted in St. Laurent and Nash (2004). Falahat et al. (2014a) also found a higher q in the Atlantic Ocean than in the Pacific Ocean. They attribute this difference to the extended sharp topography of the MAR as compared to the knife edge shapes of the Hawaiian Ridge and isolated seamounts in the Pacific Ocean.
A final perspective of this work is provided by the regional validation of the spectral estimate of energy conversion, which can be extended globally. This model is, by construction, more accurate than parameterizations (e.g., Nycander 2005; Green and Nycander 2013; and references therein) and gives additional information on the modal content and direction of the internal tide energy flux.
Acknowledgments
RidgeMix is supported by the U.K. Natural Environment Research Council through Grant NE/L004216/1. We are grateful to the technicians, officers, and crew of RRS James Clark Ross for their invaluable role in data collection. ACNG further acknowledges the support of the Royal Society and the Wolfson Foundation. ZZ was supported by NASA Ocean Surface Topography Science Team (OSTST) Award NNX17AH57G. The regional computation of energy conversion uses Python’s mpi4py message passing interface library (Dalcin et al. 2008, 2011; https://mpi4py.scipy.org/docs/mpi4py.pdf). The code is available on request. Discussions with Christian Buckingham and Rob Hall are greatly appreciated. We appreciate the criticism of two reviewers that helped to improve the quality of the manuscript.
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