Eddy-Modulated Internal Waves and Mixing on a Midocean Ridge (2025)

Keywords: Diapycnal mixing; Eddies; Internal waves; Mesoscale processes; Subgrid-scale processes; Climate change

1. Introduction

Ocean mixing plays an essential role in driving the meridional overturning circulation (e.g., Munk and Wunsch 1998; Wunsch and Ferrari 2004) and for dispersing carbon, oxygen, and other biogeochemical tracers throughout the entire ocean. Outside of boundary layers, turbulent mixing in the ocean is closely related to internal waves (e.g., Munk 1981; Gregg 1989; Polzin et al. 1995). Although the importance of tidal forcing for driving internal waves and thus turbulence and mixing has been widely recognized for some time (e.g., Polzin et al. 1997; Egbert and Ray 2000; Ledwell et al. 2000; St. Laurent and Garrett 2002), recent theoretical and numerical studies imply that subinertial geostrophic flows can drive turbulent mixing in the deep ocean as well, especially near rough topography (Nikurashin and Ferrari 2010a,b). Numerical attempts to quantify the global internal-wave generation rate by subinertial geostrophic flows suggest that this process is also crucial to the global mechanical energy budget (e.g., Nikurashin and Ferrari 2011; Scott et al. 2011). However, because of a lack of suitable time series measurements, unambiguous observational evidence for such a connection has not yet been presented, as far as we are aware.

In the eastern tropical Pacific, satellite and in situ data from the upper ocean reveal the presence of westward-propagating mesoscale eddies near 10°N (e.g., Giese et al. 1994; Palacios and Bograd 2005; Willett et al. 2006). Recent studies indicate that these eddies also affect the flow at depth near the East Pacific Rise (EPR) crest in this region (Liang and Thurnherr 2011; Adams et al. 2011), where a tracer-release experiment (Jackson et al. 2010) and a microstructure survey (Thurnherr and St. Laurent 2011) indicate mean diapycnal diffusivities more than an order of magnitude above typical thermocline background values. Therefore, the EPR crest near 10°N is well suited for investigating possible energy transfer from mesoscale flows to small-scale processes.

In this study, we analyze measurements from a current meter and a McLane moored profiler (MMP) close to the crest of the EPR (section 2). The data reveal modulation with subinertial flows of the energy level and frequency content in the internal-wave band, of the vertical propagation of near-inertial motions, and of the susceptibility of the water column to shear instability (section 3). We interpret our observations as evidence for an energy transfer from low-frequency geostrophic flows, including mesoscale eddies, to near-inertial oscillations, turbulence, and mixing (section 4).

2. Data and methods

During a project funded by the National Science Foundation (NSF) called Larval Dispersal along the Deep East Pacific Rise (LADDER), moorings were deployed on and near the crest of the EPR between 9° and 10°N in November 2006 and recovered in November 2007 (Thurnherr et al. 2011). Here, we use data from two of the instruments moored at 9.5°N (Fig. 1) to investigate the connection between subinertial geostrophic flow, internal waves, and mixing inferred from the finescale measurements: 1) an Aanderaa RCM-11 current meter deployed on the “CA mooring” directly over the EPR crest at 2450 m, recording velocities every 20 min, and 2) an MMP, deployed on the “W1 mooring” ≈10 km off axis over the western ridge flank, recording temperature, salinity, and velocity profiles between 2300 and 2775 m [≈10 m above bottom (mab)] with a vertical resolution of 2 m, roughly 3 times per day. For additional information regarding the observations, refer to previous studies (Liang and Thurnherr 2011; Thurnherr et al. 2011).

To investigate the possibility of energy transfer from geostrophic flows to finescale variability, kinetic energy (KE) in the subinertial band and KE associated with finescale processes were estimated from the MMP data at W1. KE associated with subinertial flows was estimated from the moored velocity data by low-pass filtering with a fourth-order Butterworth filter with a cutoff frequency of 0.1 cycles per day. The local inertial period is ≈3 days. For the W1 MMP record shown in Fig. 2, subinertial KE time series at each depth (2-m resolution) were vertically averaged. An alternate estimate, calculated by low-pass filtering the vertically averaged velocities is nearly identical. To extract the KE associated with finescale processes, the MMP velocity profiles were firstly vertically high-pass filtered with a fourth-order Butterworth filter with a cutoff wavenumber of 0.02 cycles per meter. Finescale KE was then calculated from the high-pass-filtered velocities. Alternate estimates, calculated with cutoff wavenumbers ranging from 0.0025 to 0.1 cycles per meter, yield qualitatively similar results (not shown). To emphasize the low-frequency modulation of the finescale variability, we also applied a fourth-order Butterworth filter with a cutoff frequency of 0.1 cycles per day to the vertically averaged finescale KE.

To investigate low-frequency effects on turbulence and mixing, first we used the W1 MMP record to derive a time series of Richardson number Ri,

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where N and S are the buoyancy frequency and vertical shear of horizontal velocity, respectively. To deal with measurement noise, the MMP velocity, temperature, and salinity profiles were first smoothed with 10-m-thick moving-average filters. From the smoothed velocity data, shear was calculated as

, where U_z and V_z are the vertical gradients of the horizontal velocity components, respectively. To go one step further, diapycnal diffusivities were estimated from the Ri time series using the simple parameterization method of Pacanowski and Philander (1981),

where K_m is the diapycnal eddy viscosity; K_ρ is the diapycnal diffusivity; and K_m0 = 10⁻⁴ m² s⁻¹ and K_ρ0 = 10⁻⁵ m² s⁻¹ are the background values for diapycnal viscosity and diffusivity, respectively. This model has been tested by Fer (2006), and the results show that, as long as suitable background values are used, the model can adequately reproduce microstructure-derived mixing levels.

To extract the modulation of near-inertial KE from the velocity time series, “standard” wavelet analysis (Torrence and Compo 1998) with Morlet wavelets was applied to the unfiltered KE time series calculated from velocity data at W1 and CA.

3. Results

Velocity data (low-pass filtered with a 10-day cutoff) from the instruments moored near the EPR crest at 9.5°N show significant low-frequency variability of KE (Fig. 2a). Previous studies have found strong correlations between the subinertial flow near the EPR crest and geostrophic flow near the surface and evidence that at least some of the subinertial velocity pulses at depth are directly related to westward-propagating mesoscale eddies spanning the entire water column (Liang and Thurnherr 2011; Adams et al. 2011). The finescale KE (Fig. 2b) is much smaller than the subinertial KE but is highly temporally correlated with it; in particular, the three largest maxima centered near yeardays −30, 45, and 70 agree in timing and approximately in relative magnitude between the two time series, suggesting eddy modulation of finescale processes in this region.

Finescale processes are closely linked to ocean turbulence and mixing (e.g., Munk 1981; Gregg 1989; Polzin et al. 1995). Consistent with the assumption that shear instabilities play an important role in this context, our data reveal a clear modulation of Ri with subinertial forcing (Fig. 2c): although 15%–20% of the water column sampled by the MMP at W1 is associated with (i.e., susceptible to Kelvin–Helmholtz instabilities) during times of strong subinertial forcing, the corresponding background fraction is only ≈5%. Given this modulation, it is not surprising that the parameterized diapycnal diffusivities derived from the Ri time series are highly correlated with the time series of subinertial and finescale KE (Fig. 2d). Although most of the time the inferred diapycnal diffusivity ranges between 1 × 10⁻⁴ and 2 × 10⁻⁴ m² s⁻¹, during episodes of strong subinertial flow the deduced mixing is intensified by about a factor of 3. Averaged over the half-year-long record, the two episodes of strong subinertial flow increase the average diapycnal diffusivity by ≈35%, from 1.46 to 1.97 × 10⁻⁴ m² s⁻¹. A tracer-release experiment carried out in the same region between yeardays −37 and 3 yields a mean diapycnal diffusivity of ≈2 × 10⁻⁴ m² s⁻¹ (Jackson et al. 2010). Although this is somewhat lower than the corresponding average of 3.1 × 10⁻⁴ m² s⁻¹ calculated from our indirectly inferred diffusivities for the same time period, the similarity in magnitude between the two estimates is encouraging, in particular considering that the tracer cloud spent a significant portion of the 40-day experiment over the western ridge flank, where the subinertial flows are markedly weaker than on axis (Liang and Thurnherr 2011). The mean diapycnal diffusivity of ≈10⁻⁴ m² s⁻¹ on the EPR flanks below 2300 m derived from a regional microstructure survey carried out during the mooring recovery cruise (Thurnherr and St. Laurent 2011) is also consistent with our parameterized estimates, because the survey was carried out during a time of weak subinertial forcing (see also section 4).

The correlations between subinertial KE, finescale KE, Ri, and inferred diapycnal diffusivity in the W1 record shown in Fig. 2 are consistent with the hypothesis that some of the oceanic turbulence is driven by low-frequency geostrophic motions, rather than by tidal flows (Naveira Garabato et al. 2004). Theoretical and numerical investigations of this hypothesis indicate that the energy transfer from low-frequency flows to turbulence involves vigorous near-inertial waves generated on steep slopes (Nikurashin and Ferrari 2010a,b). Both time series of KE in the near-inertial band from the W1 MMP and the significantly longer CA velocity record (Fig. 3c) reveal low-frequency modulation of near-inertial KE with a characteristic time scale similar to that of the corresponding subinertial KE near the ridge crest (Fig. 3b) and of sea surface height anomalies (Fig. 3a). To make the data from W1 and CA directly comparable, the subinertial KE time series from W1 shown in Fig. 3b is calculated from velocity data at 2450 m, whereas the corresponding time series in Fig. 2a shows vertically averaged values.

A careful comparison between the modulation of near-inertial KE with the corresponding subinertial KE reveals, however, that there is no one-to-one correspondence between the two: although each of the large peaks in near-inertial KE is associated with a corresponding pulse in low-frequency KE, the reverse is not true. This observation implies that the ratio of near-inertial KE to subinertial KE varies with time; that is, the spectra of the velocity do not have the same shape for the whole observed period. Furthermore, our data indicate that the intensity of near-inertial waves near the EPR crest in this region is modulated primarily by low-frequency flows but that not all low-frequency flow pulses cause a corresponding increase in near-inertial KE. Figure 4 reveals that, in addition to flow speed, the intensity of the near-inertial KE depends on the flow direction relative to the orientation of the EPR crest. In particular, there is a strong correlation between the near-inertial KE and the magnitude of the along-ridge flow, whereas cross-ridge flows do not appear to have a strong effect on the near-inertial oscillations sampled by our moored instruments.

Vertical propagation can provide insight into the nature of the observed near-inertial oscillations, because bottom-generated near-inertial oscillations initially propagate upward, whereas surface-generated ones initially propagate downward. We therefore examine profiles of bandpass-filtered (0.75f–1.5f) zonal velocity at W1 during periods of weak and strong subinertial flow. A similar procedure has been used to investigate vertical propagation of internal waves in previous studies (e.g., Alford 2010). Two representative sample periods are shown in Fig. 5. During the period from yearday −10 to 0, when the subinertial flow was weak, the near-inertial zonal velocities show upward-propagating phase, which indicates that the dominant near-inertial energy was propagating downward (Fig. 5a), as expected for near-inertial oscillations generated at the sea surface (e.g., Garrett 2001). However, during the period from yearday 66 to 76, when a strong pulse of subinertial flow affected our research region, the near-inertial zonal velocities show downward phase propagation, which implies that upward-propagating near-inertial energy was dominating. The observation of predominantly upward-propagating near-inertial energy during subinertial flow pulses suggests that during this period the near-inertial oscillations are most likely generated at the seafloor by the subinertial flow.

4. Discussion

Intense ocean mixing is known to occur over rough bottom topography and is usually mainly attributed to the breaking of internal waves generated by topography–flow interactions (e.g., Polzin et al. 1997; Ledwell et al. 2000). However, what motions contribute to the generation of internal waves and how much they contribute are still open questions. Although much of recent related observational work has emphasized the role of tides in this context (e.g., Polzin et al. 1997; Egbert and Ray 2000; Ledwell et al. 2000; St. Laurent and Garrett 2002), our observations, in particular the striking modulation of finescale and near-inertial KE with the background low-frequency variability as well as the association of upward-propagating near-inertial KE with pulses of low-frequency flows, are highly suggestive of energy transfer (i.e., a “cascade”) from mesoscale flows to near-inertial oscillations. Although covariance of KE in different frequency bands is also possible when the spectral shape does not change (i.e., without an energy transfer), this would imply constant ratios between the KE in different frequency bands. Therefore, we interpret the fact that the shape of the KE spectra derived from our data varies quite significantly with time, as apparent in the varying ratios of near-inertial KE to subinertial KE as well as of semidiurnal KE to subinertial KE (Fig. 3), as evidenced for energy transfer between different frequency bands. Both the modulation of finescale KE with subinertial forcing and the opposite vertical propagation of near-inertial kinetic energy during times of weak and strong subinertial forcing support this inference. Perhaps more importantly, our observational inference of an energy transfer is also consistent with theoretical and numerical predictions of energy transfer from subinertial to near-inertial motions (Nikurashin and Ferrari 2010a,b). In our interpretation, the modulation of Ri with low-frequency forcing and, in particular, the common occurrence of layers with during times of strong subinertial flow strongly suggests that the energy transfer from mesoscale flows to near-inertial waves continues all the way to turbulence and mixing. This interpretation implies that, in addition to winds at the sea surface (e.g., Garrett 2001; Alford 2003; Alford and Whitmont 2007), geostrophic currents flowing over topography constitute another important energy source for near-inertial oscillations and mixing in the ocean.

Our data indicate that, near the crest of the EPR, along-ridge flow is more effective in modulating the near-inertial KE than across-ridge flow (Fig. 4). In our interpretation, a likely explanation for this somewhat unexpected result is provided by the fact that in the cross-ridge direction the near-axial topography of the EPR is dominated by the ≈20-km-wide crest (Fig. 1, bottom), whereas the along-ridge topography is associated with undulations with characteristic horizontal and vertical scales of ~5 km and 50–100 m, respectively (not shown). The observation that along-ridge flows with magnitudes of ~10 cm s⁻¹ are associated with significant near-inertial KE but that across-ridge velocities of the same magnitude are not is consistent with the prediction, from linear theory, that significant lee wave radiation is only expected for topographic roughness with horizontal scales less than U/∣f∣ (e.g., Nikurashin and Ferrari 2011; Scott et al. 2011), which yields a cutoff of ~4 km in our case.

In addition to near-inertial waves, our observations also reveal a modulation of semidiurnal KE with the background subinertial flow (Fig. 3d). This could be due to eddy-modulated energy conversion from barotropic to baroclinic tides, as has been inferred in a recent observational and numerical study on the Hawaiian Ridge (Zilberman et al. 2011). There, the modulation is caused by phase variations of the perturbation pressure associated with changing stratification and/or cross-ridge currents. This suggests that the influence of subinertial flows on internal waves is not restricted to the near-inertial band but also involves baroclinic tides.

In spite of the fact that not all low-frequency KE pulses on the EPR crest in our study region can be unambiguously associated with westward-propagating eddies apparent in sea surface height data (Liang and Thurnherr 2011), Fig. 3 indicates a close connection between geostrophic currents at the sea surface and near the EPR crest. The time period after yearday 240 is particularly noteworthy in this context, because it was a quiet period when both the low-frequency and near-inertial KE at depth were weak and there was no clear westward propagation of sea surface height anomalies. This implies that the turbulence measurements carried out in the context of a regional microstructure survey during yeardays 319–335 (Thurnherr and St. Laurent 2011) sampled this quiet period and cannot be considered representative for the longer-term regime. This points to an important shortcoming of microstructure and other quasi-synoptic mixing surveys, because the temporal context is usually not known.

In conclusion, we interpret our observations from the EPR crest near 9.5°N as evidence for an energy transfer from mesoscale eddies propagating westward across the ridge crest to internal waves, turbulence, and mixing in the deep ocean. To the best of our knowledge, these observations constitute the first observational evidence for such a downscale energy transfer that is only expected to take place in regions of rough topography. Our interpretations suggest that, in addition to topographic roughness and tidal forcing, parameterizations of deep-ocean mixing should also take forcing by subinertial flows into account. Furthermore, because the frequency and intensity of mesoscale eddies depend on the state of the climate (e.g., Palacios and Bograd 2005; Meredith and Hogg 2006; Böning et al. 2008; Qiu and Chen 2010; Farneti et al. 2010), the observed eddy-modulated internal waves as well as the expected eddy-modulated mixing connect climate change and climate variability to physical and biogeochemical dynamics in the deep ocean and imply the possibility of a hitherto unexplored feedback mechanism potentially affecting the global climate system.