The relative strength and spatiotemporal structure of near-inertial waves (NIW) and internal tides (IT) are examined in the context of recent moored observations made 19 km south of Mendocino Escarpment, an abrupt ridge/step feature in the eastern Pacific. In addition to strong internal tide generation, steps and ridges give rise to the possibility of “shadowing,” wherein near-inertial energy is prevented from reaching depths beneath a characteristic intersecting the ridge top. A combination of two moored profilers and a long-range acoustic Doppler current profiler (ADCP) yielded velocity and shear measurements from 100 to 3640 m (60 m above bottom) and isopycnal depth, strain, and overturn-inferred turbulence dissipation rate from 1000 to 3640 m. Sampling intervals (20 min in the upper 1000 m and 1.5 h below that) were fast enough to minimize aliasing of higher-frequency internal-wave motions. The 67-day-long record is easily sufficient to isolate NIW and IT via bandpass filtering and to capture low-frequency variability in all quantities.
No near-inertial shadowing was observed. Instead, energetic near-inertial waves were observed at all depths, radiating both upward and downward. A strong upward internal tide beam, showing a pronounced spring–neap cycle, was also seen near the expected depth. Case studies of each of these are presented in depth and isopycnal-following coordinates. Except for immediately above the bottom and in the “beam,” where IT kinetic energy shows marked peaks, kinetic energy in the two bands is within a factor of 2 of each other. However, because of the redder NIW vertical wavenumber spectrum, NIW shear exceeded IT shear at all depths by a factor of 2–4. Dissipation rate was strongly enhanced in the bottom 1000 m and in the depth range of the internal tide beam. However, except for very near the bottom and possibly in one NIW event, no clear phase relationship was observed between dissipation rate and wave shear or strain, suggesting that turbulence occurs through a cascade process rather than by direct breaking at most locations.
Breaking internal waves are thought to provide the ≈2 TW of power hypothesized to be required to keep the deep ocean stratified (Munk and Wunsch 1998; Wunsch and Ferrari 2004). Because climate models are sensitive to the processes and spatial distribution of this mixing (Simmons 2004), the topic has received considerable attention in the last decade. Recent focus has been on the two most energetic internal-wave frequencies; namely, near-inertial waves (NIW) and internal tides (IT). The former are primarily generated when the wind blows on the mixed layer (D’Asaro 1985), whereas the latter arise when the barotropic tide flows over bathymetric features.
A natural question is, which is more important in mixing the deep ocean? Global integrals of the power input into each type of motion are similar [0.5–0.7 TW for NIW (Alford 2003b; Watanabe and Hibiya 2002) and 1 TW for IT, of which 0.8 TW is the M2 constituent (Egbert and Ray 2000, 2001)]. However, their different generation mechanisms should cause the temporal, vertical, and lateral distribution of the two to differ substantially. Beginning with the most basic expectations, internal tides are generated in the deep sea, whereas near-inertial waves must propagate from the surface. However, near-inertial waves often have greater shear, which is more closely related to mixing, but are also more intermittent because of their forcing by storms rather than the much more regular barotropic tides.
Observationally, the link between IT and deep mixing is fairly well established (e.g., Nash et al. 2007; Ledwell et al. 2000; Kunze et al. 2006a). However, Toole (2007) cautioned that the connection between the internal tide and mixing presented in Ledwell et al. (2000) was not clear-cut, noting a rich field of both NIW and IT motions in the deep Brazil Basin. Near-inertial waves have been tied to mixing in the upper ocean (Hebert and Moum 1994; Alford and Gregg 2001), and seasonal cycles of deep near-inertial energy (Alford and Whitmont 2007; Silverthorne and Toole 2009) make it clear that wind-forced NIW do make it to great depths. However, observations resolving the structure of NIW in the deep ocean are extremely rare. For both types of motions, much of the energy is input into low modes (D’Asaro et al. 1995; St. Laurent and Garrett 2002; Alford 2003a), which can propagate far from generation regions, so their fate remains a mystery.
Quantifying these statements is difficult because of the usual observational trade-offs between resolution and series length in both the vertical and time. Conventional moorings last a year or more but only resolve the first few modes. Vertical profiles, by contrast, are difficult to make fast enough to resolve the waves over a broad enough vertical aperture to conduct modal fits or for long enough to separate NIW from IT. The measurements presented here, a 67-day time series spanning the entire water column obtained from two “stacked” McLane moored profilers (MPs) and a long-range acoustic Doppler current profiler (ADCP), are a compromise between these extremes allowing a variety of calculations to be performed, including 1) separation of NIW from IT using bandpass filtering, 2) the modal content for each band, 3) kinetic energy and shear versus depth for each band, and 4) detailed investigation of individual wave packets. In addition, mixing estimates are also obtained from Thorpe scales (Thorpe 1977; Dillon 1982) in the range spanned by the McLanes (>1000-m depth) and compared to shear-based turbulence parameterizations from Gregg (1989), Gregg et al. (2003), and Kunze et al. (2006b).
The relative strength and importance of NIW and IT must depend on location. As a first step toward being able to make useful statements, the mooring was deployed in a place where internal tides would be expected to dominate, with the aim of establishing a lower bound on the relative NIW contributions. Mendocino Escarpment, a major transform fault in the western Pacific (Fig. 1), is a known strong internal tide generator (Althaus et al. 2003, hereafter AKS03). In addition, though the observations are in late winter (February–April), slab mixed layer models forced with National Centers for Environmental Prediction (NCEP) reanalysis winds (Kalnay et al. 1996) show that work done by the wind on near-inertial waves in the eastern Pacific is quite weak compared to the western Pacific, which is closer to the primary storm track (Alford 2001b, 2003b). Finally, escarpments and ridges are expected to “shadow” near-inertial energy propagating downward and equatorward as hypothesized by Garrett (2001) and Chiswell (2003) and observed by Aucan and Merrifield (2008). Because linear theory indicates that energy for a wave of frequency ω is expected to propagate along characteristics with slope
where f and N are the local inertial and buoyancy frequencies, equatorward-propagating waves with frequencies 1.01f and 1.08f would not be expected deeper than 2400 and 2750 m, respectively, at the mooring location (Fig. 2, gray and dashed lines).
In spite of these factors favoring the IT, a major result of this paper is that that NIW and IT were nonetheless comparable in energy, except for immediately above the bottom and in the depth range of a strong internal tide beam, and the NIW had greater shear at all depths. No shadowing was observed; instead, a rich field of NIW was seen propagating both upward and downward at all depths. One of the packets resulted in nearly unstable shear values (even when smoothed over 80 m) and appeared to be associated with overturning. On the other hand, strong IT motions were seen at 1800 m, near the expected depth of the upward beam emanating from the ridge (Fig. 2, thin black line), and near the bottom, where the strongest mixing was observed. The observations are presented, and the implications are discussed.
2. Data and oceanographic context
Mendocino Escarpment is a prominent submarine feature in the eastern Pacific Ocean wherein a ≈10-km-wide ridge separates the smooth, deep abyssal plain to the south (≈3800 m deep) from the shallower and more variable seafloor to the north (Fig. 1). A fathometer survey at the longitude of our mooring indicates a ridge height of 2310 m (Fig. 2, gray line), substantially shallower and narrower than indicated from the Smith and Sandwell (1997) version 8.2 bathymetry (thin black line), which is contoured in Fig. 1. The ridge height increases moving westward, to its shallowest depth of 1200 m, where AKS03 made their measurements. Setting the mooring farther west where the escarpment is more sheer would have been desirable, but time did not allow this because the mooring was deployed and recovered during transits to and from another experiment.
Buoyancy frequency N(z) (Fig. 3) measured by the moored profilers and a CTD cast taken immediately after the mooring recovery agreed well with the climatological profile from Levitus and Boyer (1994), decreasing steadily from about 7 cycles per hour (cph) at 200 m to 0.5 cph near the bottom. Deep stratification was about 9 times the local inertial frequency of 1.29 cpd (18.5-h period) and 6 times M2 (dashed line).
The mooring was deployed in 3700 m of water on the sloping southern flank of the escarpment on 20 February 2009, and recovered on 29 April along the track shown in Fig. 1. It consisted of a subsurface syntactic float at 962-m depth housing an upward looking 75-kHz FlowQuest ADCP made by LinkQuest, Inc., and two McLane MPs crawling up and down the mooring wire below that, each of which carried a Sea-Bird Electronics CTD and a Falmouth Scientific acoustic current meter. An RDI-Teledyne Doppler volume sampler (DVS) at 2172-m depth measured velocity between the MPs at 4.5-min intervals for calibration purposes and to assess the effects of the MPs’ coarse temporal sampling. Pressure measured with a Sea-Bird Electronics 37 CTD at the subsurface float confirmed that mooring motion was quite weak, resulting in maximum pulldowns of 15 m.
Data were first corrected for clock errors assuming a linear drift (<3 min for all instruments). All compasses were calibrated by spin tests prior to the deployment and corrected for magnetic deviation at the site of +16.6°. The CTD on each profiler was calibrated before and after the deployment. Temperature and salinity were first edited for spikes usually associated with biota, which included two periods where the conductivity cell on the upper profiler was fouled and then cleared several days later. Salinity and density during these periods were discarded. After the first of these gaps, calibration was slightly in error, as evidenced by differences in salinity before and after. Salinity on the upper profiler after yearday 68.8 was therefore corrected by adding a depth-independent offset of 0.006 psu. This was consistent with the offset applied at the time of the postcruise calibration. Following these corrections and taking note of the differences in temporal and vertical resolution of each instrument (Table 1), data were combined by interpolating onto uniform depth–time grids of 2 m and 0.75 h, respectively.
An overview of the sampling duration and depth coverage is shown in Fig. 4 and Table 1. Velocity was measured from 140-m depth to 61 m above the bottom, with a 60-m gap near 1000 m above the shallow profiler. The range of the ADCP was sufficient to reach the surface, but values shallower than 140 m are discarded because of contamination by the reflection of the sidelobe from the surface. Isopycnal displacement (black lines) and dissipation rate from Thorpe overturns (green lines), computed as described in section 3, are measured by the MPs below 1000 m. Observed vertical striations are largely due to the internal tides, whereas several NIW packets are visible, such as a downward-sloping modulation in the early, shallow part of the record. A pronounced spring–neap cycle is observed in both velocity and isopycnal displacements, which are maximum near the bottom. However, a maximum in semidiurnal energy is visible near 1600–1800 m, the depth of the upgoing IT beam (Fig. 2). Tidal and near-inertial frequencies dominate the record, but lower-frequency modulation is observable: for example, the deep northward feature appearing near yearday 110. Many of these features will be examined in detail in later sections.
McLane profilers crawl at 25 cm s−1 (900 m h−1), a compromise between endurance and speed (Doherty et al. 1999). The upper profiler was standard, but the lower profiler had a modified gearbox with a lower reduction ratio, allowing it to climb at 0.33 m s−1 (≈1200 m h−1), with an extended pressure case carrying additional batteries to offset the extra drag associated with the higher speed. To ensure resolution of the semidiurnal internal tides and NIW, depth ranges of each profiler (1000–2142 and 2211–3639 m, respectively) were selected to give round trips every 3 h. The top and bottom profilers maintained this schedule until yeardays 94 and 100, respectively. After this, the voltage dropped on their lithium battery packs, resulting in slower speed. This in turn resulted in less frequent profiles and slightly reduced vertical coverage until they stopped profiling entirely on yeardays 110 and 117.6, respectively. In the following, quantitative analysis is restricted to the 43-day period from yearday 51 to 94 when all instruments were functioning optimally.
Because the profilers trace out a sawtooth pattern in depth and time, the effective sampling interval Δt ranges between 1.5 h at the center of each range to nearly 3 h at the ends (Fig. 3, dashed lines). At no depth does the associated Nyquist frequency ωN ≡ 1/(2Δt) (Fig. 3, solid lines) meet the desired criterion of ωN > N(z) (though it is within a factor of 2 at the center of the deep MP range), giving rise to the possibility of aliasing of higher-frequency internal-wave motions into our measurements. In addition, finite temporal sampling can lead to underestimation of higher-frequency motions, in the manner demonstrated by Niwa and Hibiya (1999).
The effects of the MP’s coarse temporal sampling on our measurements are therefore assessed by comparing rotary frequency spectra (Fig. 5) computed at the DVS and the upper 100 m of the lower profiler (the lower range of the upper profiler, not plotted, is similar). Additionally, the spectra provide a good characterization of the internal-wave environment at the site, which will be examined in the time domain in the remainder of the paper. Rotary frequency spectra (Mooers 1970; Gonella 1972), computed over yeardays 51–94 as the sine multitaper spectrum of complex velocity, u + iυ (Riedel and Sidorenko 1995), indicate clockwise (CW) and counterclockwise (CCW) rotation for negative and positive frequencies, respectively.
In the DVS spectra, prominent tidal peaks are seen at diurnal and semidiurnal frequencies, with nearly equal CW and CCW magnitudes (thick and thin black lines, respectively), indicating the strong orientation of the barotropic tidal flow in the north–south direction. The diurnal peak is dominated by barotropic motions, as expected because diurnal motions are evanescent at this latitude.
NIW appear as a prominent and strongly clockwise-polarized peak near f. Polarization thereafter decreases with increasing frequency, as expected from the internal-wave polarization relations (Gonella 1972). Additional prominent peaks are observed at f ± M2, associated with the heaving of near-inertial shear layers by internal tide displacements and/or nonlinear interactions as demonstrated by Alford (2001a) and Mihaly et al. (1998). The level of the spectrum is approximately 1.5 times the Garrett and Munk (1975) level, as modified by Cairns and Williams (1976, hereafter GM76), but shows the same slope. A decrease and break in the slope is observed at the local buoyancy frequency (dashed), as often observed (e.g., Pinkel et al. 1987), before whitening at about 100 cpd, because of contamination by a white instrument noise floor consistent with 0.9 cm s−1 RMS, approximately that expected given the ping rate of the instrument.
Clockwise spectra from the lower MP (gray) are in good agreement at the inertial and tidal frequencies but are lower than the DVS spectra for frequencies in excess of M2. This is taken as evidence that the MPs resolve the peaks well, but the slope and level of the higher-frequency continuum are underresolved because of the finite temporal resolution, with this effect evidently winning out over aliasing, which would tend to elevate the spectra in the resolved frequency range. Because of these uncertainties and because the NIW and IT are our focus, the higher-frequency motions are not discussed further.
Shear wavenumber spectra are also presented, to demonstrate the resolution and noise characteristics of each instrument (Fig. 6). The spectra from each instrument are averaged over the same time period (yearday 57.3–64.60) but are not directly comparable because each covers a different depth range. Differences in stratification are accounted for by Wentzel–Kramers–Brillouin (WKB) scaling velocity (Leaman and Sanford 1975) prior to computing the spectrum. However, because the intent is to show the wavenumbers where vertical resolution and noise become important, data are not WKB stretched. As a result, the spectrum observed at the lower MP falls off somewhat before the upper one. The ADCP spectrum (thin black line) is the highest, because it was taken during an energetic period in the upper water column. Broadly speaking, the spectra are about 2–6 times the GM76 spectrum (dashed line). Their greater excess relative to GM76 viewed in wavenumber over that in frequency (Fig. 5) is a statement that the motions are primarily near-inertial and internal tides, which are not included in the GM model.
The spectra from both McLane profilers (thick lines) reach the noise level at about k = 0.1 cycles per meter (cpm; 10 m), consistent with previous findings (Silverthorne and Toole 2009). A white noise in velocity with an RMS of 0.4 cm s−1 (dashed line) gives a +k2 spectrum in shear, similar in level to but somewhat steeper than the observed spectrum in the lower MP. The upper profiler’s noise spectrum is flatter, but both vary somewhat in time (not shown). The ADCP spectrum rolls off at about 80-m scales, consistent with the expected response, sinc4(zbk), for a Bartlett transmit pulse of length 2zb (dashed line; Alford and Gregg 2001), where zb = 16 m. When the ADCP spectrum is corrected for this modeled response (gray line), the falloff is less severe, with noise now apparent as a rise beginning at about k = 0.025 cpm. All quantities are henceforth smoothed to the resolution of the ADCP (80 m) to prevent complications resulting from depth-variable resolution.
d. Barotropic velocity
The velocity measurements span nearly the full water column, allowing an unambiguous separation between barotropic and baroclinic motions. These are defined as
Observed barotropic velocities are dominated by the tide and strongly polarized in the meridional direction, as demonstrated by plotting the first 23 days (Fig. 7, black lines). Consequently, meridional velocity is in good visual agreement with predictions (gray lines) by the Oregon State University TOPEX/Poseidon Global Inverse Solution (TPXO 7.1) model (Egbert and Erofeeva 2002). Tides are mixed, but predominantly semidiurnal. Spring tides (dashed line) will be marked on subsequent panels as indications of the strongest barotropic tidal flows. Nontidal flows are evident in zonal velocity (bottom panel), which modulate the flow with a period of several weeks.
A direct comparison between the observed and TPXO7.1 barotropic tidal velocities is conducted using harmonic analysis with the MATLAB tidal analysis software (T-TIDE; Foreman 1996). The period spanning yeardays 51–94 is used for both observations and predictions. Agreement is quite good (Table 2), with the primary difference that the observed M2 tidal ellipses are slightly weaker and wider than predicted, as seen from the time series (Fig. 7).
3. Overturns and dissipation
Though moored microstructure measurements are possible (Lueck 1997), none were made on this mooring. However, numerous studies, beginning with Dillon (1982), have shown that the outer scale of turbulence (Ozmidov scale) is closely related to the overturning or Thorpe scale (Thorpe 1977) obtained from sorting measured potential density profiles. Though great care must be taken to detect spurious overturns resulting from noise and salinity spiking, methods have been developed for screening these (Alford and Pinkel 2000; Galbraith and Kelley 1996; Ferron et al. 1998; Johnson and Garrett 2004; Gargett and Garner 2008). When made simultaneously, turbulence dissipation rate estimates from overturns agree very well with those directly measured from microstructure (Dillon 1982; Moum 1996; Ferron et al. 1998; Alford et al. 2006).
Thorpe scales are estimated from the MP data following Alford et al. (2006). First, conductivity and temperature from each Sea-Bird CTD are carefully response matched and corrected for the thermal mass of the conductivity cell (Lueck and Picklo 1990). Every profile is visually screened and edited for spikes and then averaged in 2-m bins. Then, each potential density profile is sorted to a statically stable profile, and the Thorpe displacement is computed for each “reordering region” defined as in Galbraith and Kelley (1996). Because the run test and “water mass test” of Galbraith and Kelley (1996) reject too many valid overturns (Johnson and Garrett 2004; Gargett and Garner 2008), we instead require that overturns pass two tests. First, the measured Thorpe scale must be greater than the spurious inversion that would result from the instrument noise in the local stratification, LTρ = ρRMS/(∂σθ/∂z), computed using the sorted potential density profile over the reordering region. Using the local value is important because wave strain can modulate stratification appreciably relative to the mean, raising or lowering the noise floor. This is particularly key because most overturns occur when stratification is weaker than average (Alford and Pinkel 2000).
Second, to ensure that imperfect sensor matching did not produce the density inversion, the measured Thorpe scale from temperature and density are required to be within an empirical factor of 2 of each other, as done by Alford and Pinkel (2000). Though this test does not work inside thermohaline intrusions, where the temperature Thorpe scale can be large even when density is stably stratified, it is effective at screening spurious inversions in other regions. The temperature–salinity (T–S) relation is rather tight at our location, with the notable exception of the depth range ≈(2000–2600) m, where a substantial number of deep intrusions are seen. Because this depth range brackets the ridge crest depth, these are hypothesized to be structures that have resulted from blocking and/or mixing at the ridge crest and advected to our site. These intrusions prevent the reliable calculation of overturns from potential temperature in that depth range, preventing application of the second test there. However, the close agreement of the estimates from potential temperature and density above and below that range strongly bolster confidence in the density-based estimates at all depths.
Though we use potential density rather than temperature here, it is worth pointing out as a brief aside that potential temperature rather than temperature must be used at depth for detecting overturns when intrusions are absent. To demonstrate this, we zoom in on the deep portion of Fig. 4 during a spring tide (Fig. 8). During this period, the semidiurnal internal tide raises and lowers isopycnals by about 200 m (Fig. 8a). Temperature on this isopycnal increases about 0.02°C when isopycnals descend, which is due to adiabatic heating of the water during the vertical excursion. Potential temperature on the isopycnal, which removes the effect, remains constant (Fig. 8c). This is presumably a ubiquitous aspect of large vertical excursions in deep regions. Because static stability is relative to the adiabatic rather than the absolute gradient, use of temperature rather than potential temperature would result in overestimates of overturning scales. The same would of course be true for overturns computed from density rather than potential density.
Once the screened set of overturns is computed, the implied dissipation rate is estimated via the Dillon (1982) formula, ε = 0.64LT2N 3. Diapycnal diffusivity is then computed via the Osborn (1980) relation, Kρ = ΓεN−2, where Γ is the assumed mixing efficiency. The value and variability of Γ are the subject of considerable discussion (for a discussion, see Ivey et al. 2008, and references therein). However, direct comparisons between microstructure and dye-cloud values (Ledwell et al. 1993) support use of the traditional value of Γ = 0.2 in the thermocline. Lacking a reason to do differently, the commonly used value of Γ = 0.2 is used here.
The full set of overturns is visible in Fig. 4 (green), which are contours of ε = 1.5 × 10−8 W kg−1. The size and number of overturns clearly increases approaching the bottom and also (less obviously in Fig. 4) in a depth range near 1500–2000 m, as demonstrated by plotting the time-mean dissipation rate (Fig. 9c) and diffusivity (Fig. 9d). The dissipation rate reaches 7 × 10−10 W kg−1 in the middepth maximum, decreasing to 2 × 10−10 W kg−1 near 2200 m, before increasing over an order of magnitude to 5 × 10−9 W kg−1 near the bottom. The associated diffusivity is more strongly weighted toward the bottom because of the weaker stratification, reaching 10−3 m2 s−1.
For comparison, dissipation rate and diffusivity are also estimated using the Gregg–Henyey (GH) parameterization (Gregg 1989; Gregg et al. 2003) as implemented by Kunze et al. (2006a). Briefly, shear wavenumber spectra are computed for each profile in 300-m windows. ADCP spectra are corrected for the Bartlett spatial response as noted above (see Fig. 6), before integrating out to a cutoff wavenumber of 0.025 cycles per meter (vertical dashed line in Fig. 6). Using different response corrections and several reasonable values of the integration cutoff had little effect on the results. Buoyancy frequency is from the shipboard CTD profile collected on recovery.
The time-mean parameterized dissipation rate and diffusivity (gray) in the upper 1000 m are close to the typically observed open-ocean value of ≈10−5 m2 s−1 (Gregg 1989). Below this, they are close to the overturn-inferred values above the middepth maximum and within a factor of 2 of them from 2400 to 2700 m. Parameterized and overturn-inferred values increase with depth at a similar rate in both depth ranges. Near the middepth maximum and near the bottom, the overturn-based ones exceed GH by factors of 3 and 10–30, respectively. Klymak et al. (2008) obtained similar results near the Hawaiian Ridge, interpreting the excess in directly measured turbulence as evidence that the usual cascade of energy through the spectrum, assumed by the GH parameterization, was being circumvented. In their case, direct breaking of the internal tide generated near the bottom was responsible.
The overturn-inferred diffusivities in the middepth maximum and near the bottom are one and two orders of magnitude greater than background oceanic levels, respectively. Values near the bottom are similar in magnitude to those observed in the lower 1500 m at various sites at the Hawaiian Ridge (Klymak et al. 2006). Indeed, the depth dependence of the near-bottom diffusivity is not unlike the fit they computed from their observations (dashed line), which decreases exponentially from 10−3 m2 s−1 at the bottom to 10−4 m2 s−1 at 1500 m above it.
This similarity to the Hawaiian Ridge, a major tidal conversion site, suggests that at least part of the mixing is connected to the tide. This is certainly true, as demonstrated by zooming in on a period near a spring tide (Fig. 10). The sawtooth sampling pattern of the lower MP is plotted (gray line), demonstrating the motions are well resolved.
During this period, isopycnals (black lines) rise and fall as the tide flows up and down the sloping bottom (Fig. 2). Overturns 50–100 m high (green) occur with a semidiurnal periodicity, with most occurring during southward flow when isopycnals are falling. Isopycnal displacements η are greater at depth, resulting in periods of weaker-than-average stratification or equivalently high strain γ ≡ ∂η/∂z during these periods. As noted, high strain generally precedes and accompanies overturns (Alford and Pinkel 2000). This phasing is similar to observations of breaking internal hydraulics in the South China Sea reported by Klymak et al. (2011) but different than that observed at several locations at the Hawaiian Ridge (Levine and Boyd 2006; Aucan et al. 2006; Alford et al. 2006). In addition, the relationship of the near-bottom dissipation to the tidal velocity and displacements is different or nonexistent during other times in the current record (not shown). There appear to be several mechanisms leading to these directly tidally forced, quasi-deterministic mixing phenomena (Klymak et al. 2008), that depend on parameters such as the criticality of the slope and the modal content of the internal tide. These require further study.
The time series of dissipation averaged over the bottom 400 m (Fig. 11) shows a hint of a spring–neap cycle, with maxima loosely occurring near spring tides (dashed lines). Superimposed on this modulation is a general downward trend in dissipation. Although its cause is unknown, sensor issues can be ruled out because calibration and sensitivity for the lower profiler were nearly identical at the beginning and end of the record. The depth of the midwater peak coincides with a maximum in semidiurnal energy (Fig. 9a). However, the time series of dissipation averaged over that depth range does not show a strong spring–neap cycle. Other factors than the internal tide appear to be important. The remainder of the paper will explore some of these in more detail.
4. Wave groups
We next zoom in on several periods and depth ranges in Fig. 4, beginning with a downward-propagating NIW near yearday 71 (Fig. 12). The zonal component of shear, smoothed as noted over 80 m, is plotted in the top panel. Phase propagation is upward, with a period close to the inertial frequency, indicating an NIW with downward energy propagation. However, the vertical displacements of the isopycnals (shown in black) heave the shear layers up and down as reported first by Sherman (1989). As noted above, this heaving results in Doppler-shifted spectral peaks at f ± M2 (Fig. 5; Alford 2001a).
This kinematic distortion is removed by transformation to an isopycnal-following or semi-Lagrangian reference frame (Anderson 1993). This is accomplished by selecting a set of isopycnals with constant mean spacing and computing shear along each by linear interpolation. In the bottom panel, zonal shear is again plotted, but with the vertical coordinate now the mean depth of each isopycnal. (Features following isopycnals would now appear as horizontal lines.) The distortion is much reduced, with the phase lines greatly straightened. Plane-wave fits computed by eye (bottom panel) yield a frequency slightly greater than inertial, ω = 1.03f, and a vertical wavelength of 350 m.
This wave is thus reminiscent of downgoing near-inertial packets seen in previous observations (Hebert and Moum 1994; Alford and Gregg 2001). However, its depth is significantly greater than similarly detailed past measurements, bolstering the conclusion of Alford and Whitmont (2007) and Silverthorne and Toole (2009) that near-inertial energy propagates to great depth. In addition, the present measurements indicate that at least some of the deep energy is associated with downward-propagating motions of relatively high vertical wavenumber (equivalent mode number ≈ 10).
The stability and mixing of the wave is examined next. Alford and Gregg (2001) observed that dissipation rate was associated with a shallow downgoing near-inertial wave in the Banda Sea. Mixing occurred once per wave cycle during high inverse Richardson number Ri−1 ≡ s2/N 2 (Miles 1961; Howard 1961), where S2 = uz2 + υz2 is shear squared. Shear was important for modulating Ri, but the strain resulting from divergent wave displacements was even more so. We investigate these concepts here by encircling regions in white where Ri < 1 in the top panel and where strain γ > 0.3 in the bottom panel. As before, contours of dissipation rate ε = 1.5 × 10−8 W kg−1 are plotted in green.
Though not as regular as seen in the Banda Sea, a similar process appears to be occurring here. Though the shear is a factor of 10 less, stratification is as well. Hence, the wave is sufficiently intense to yield Ri < 1 (white contours, top panel) nearly each cycle during each zonal shear minimum (blue), in spite of the heavy smoothing over 80 m. From the bottom panel, these are seen to coincide with periods of high strain, as in the Banda Sea. Dissipation rate (green) also appears to occur during these periods, though the data are not sufficient to constitute a definitive proof. Still, the observation of a deep downgoing near-inertial wave that is associated with near-unstable values of Ri and possibly mixing indicates that NIW may indeed play a role in mixing the deep sea.
Our density measurements do not span the water column, precluding determination of energy flux (Nash et al. 2005; Kelly et al. 2010). However, the phase between shear and strain can be used to determine the horizontal propagation direction of the wave (Winkel 1998). For this wave, zonal shear is 180° out of phase with strain, indicating a propagation direction toward due south. Returning to Fig. 2, the wave is observed near the maximum depth expected for a southward-propagating wave of the observed frequency. Because the wave characteristic connects the observed depth and the ridge top, the wave could have barely cleared the ridge top as it propagated downward and toward the equator from farther north. Alternately, it could have been generated at the ridge crest by an adjustment process there.
The second wave packet considered (Fig. 13), near the upper end of the MP profiling range, is plotted in the same format as the previous example, except that now a lower strain value, γ > 0.2, is contoured. Shear in this example is stronger, at least partly because of the greater stratification at the shallower depth. It differs from the previous wave in that it shows downward phase propagation, implying upward energy propagation. Because NIW are thought to be generated at the surface, NIW radiation is generally thought to be dominantly downward, as often observed (beginning with Leaman and Sanford 1975). Hence, a clear upgoing wave packet is contrary to expectations, apparently implying either a deep source or that surface-generated NIW can survive reflection from the bottom rather than being scattered from a rough seafloor or dissipated in bottom boundary layers.
The wave is distorted as before by tidal heaving, but not as strongly as in the first example. Plane-wave fits to the wave in the isopycnal-following frame (bottom panel) indicate a shorter vertical wavelength (130 m) and slightly greater frequency. Determination of its propagation direction is not possible because strain (white) is irregular. Mixing, if present, is too weak to be detected with our techniques. Consistent with this, Ri > 1 everywhere during this period.
A second upgoing wave was observed near the end of the mooring record (Fig. 14). Because the wave is above the MPs, no isopycnal information is available, so only the first panel is plotted. Shear toward the end of the period plotted, after the mooring was recovered (yearday 118.6), is from the 75-kHz shipboard ADCP while it was stationary during the mooring recovery. Agreement is good between the two datasets. Because tidal heaving did not appear to be too great, plane-wave fits (dashed) give reasonable results, indicating a wave of frequency 6% greater than f propagating upward toward the surface.
Without strain information, no estimate of propagation direction is possible for this wave from the moored data. However, some spatial information is available from shipboard shear on the transit to recover the mooring (track in Fig. 1). Because the transit took 20 h, slightly greater than an inertial period, the data are inertially “backrotated” by multiplying observed complex shears uz + iυz by eif (t−tr), where tr = 118.6 is a reference time. The observed backrotated shear, plotted in Fig. 2, shows a feature intersecting the mooring latitude at the observed depth of the upward-propagating feature. Assuming it is the signature of the wave, the feature extends upward toward the southeast at the expected slope for a wave of ω = 1.08f, close to ω = 1.06f inferred from the time series. Though the wave’s propagation direction cannot be precisely determined with these 2D data, the time series and spatial data together indicate the wave is propagating upward toward the equator.
Where do these waves come from? From their frequency and vertical wavenumber, the vertical group velocity of the three waves is computed from the dispersion relationship as −28, 14, and 24 m day−1, respectively. Each wave would have been in contact with the surface or the bottom O(100) days ago. If the third wave emanated from the surface, reflected from the bottom, and intersected the mooring, the total time would have been about 200 days, with a generation site several hundred kilometers to the northwest. Hence, the waves could have been generated by storms occurring the previous October–January. Uncertainty in tracing the waves back to their origin is too great to say more.
b. Internal tide beam
We next examine a spring–tide period (Fig. 15) in the depth range bracketing the expected depth of the upward IT beam plotted in Fig. 2. The format is the same as the NIW figures just presented. However, the sloping shear features are here of semidiurnal rather than near-inertial period. Their downward phase propagation is indicative of upward energy flux, as expected.
Transforming to isopycnal coordinates (Fig. 15b) removes the self-advection of the wave, allowing plane-wave fits. The resulting vertical wavelength is 700 m, twice as long as the longest of the NIW packets. Strain (white) is in phase with uz, which for a linear wave with downward phase propagation indicates propagation toward the south, also as expected given its generation at the ridge top to the north.
As noted, time-mean dissipation shows a peak in this depth range, which is presumably associated with the IT beam as observed by Lien and Gregg (2001). Increased overturning is indeed seen during this period (green), but without a clear phase relationship with the shear. In addition, Ri−1 is more stable than in Fig. 12, only exceeding unity near the end of the period. Hence, the mechanism leading to the increased mixing is not clear.
5. Bandpassed records of near-inertial waves and the internal tide
a. Time series
Now that we have shown specific examples of NIW and IT, we next examine their relative strength more systematically by bandpass filtering. Following previous work (Alford 2003a; Alford and Zhao 2007), this is achieved in the time domain with a fourth-order Butterworth filter, run forward and backward on the time series at each depth to minimize phase distortion. Frequency limits for each band were 0.8 and 1.25 times the inertial and M2 frequency, respectively. These are wide enough to capture frequency differences in each band such as varying frequency content of different NIW events and the spring–neap modulation but narrow enough to separate them from each other and from the diurnal motions. The time series is easily long enough to do this without concern for leakage or ringing.
The separation is demonstrated in Fig. 16, in which zonal velocity is plotted because meridional velocity was already plotted previously. The total field shows the same rich blend of mesoscale, NIW, and IT motions, whereas the separated near-inertial (Fig. 16b) and internal tide fields (Fig. 16c) emphasize wave motion in the respective bands. Note that only the baroclinic portion of the signals is plotted in Figs. 16b,c. The events plotted in Figs. 12 –14 are clearly seen in Fig. 16b, whereas the IT beam is evident in Fig. 16c as stronger velocities from 1500–2000 m. These show a pronounced spring–neap cycle, indicating stronger generation during the stronger barotropic forcing at spring tides (dashed lines).
b. Energy and shear
A cursory glance indicates that NIW and IT velocities are of similar magnitude. A more quantitative statement is obtained by calculating the baroclinic kinetic energy in each band,
where and are the bandpassed baroclinic velocities in each band. The time mean of each quantity is plotted in Fig. 9a, together with the total energy,
Time-mean energy in both bands (heavy gray and black lines) show general decreases with depth by a factor of 5–10. The decrease in these is consistent with WKB scaling of velocity with depth (Leaman and Sanford 1975), which predicts energy should scale as N(z) (light gray). By contrast, total energy (thin black lines) has a strong contribution from the barotropic tide and therefore has a different vertical structure.
The values of KENIW and KEIT are nearly equal from the surface to 1500-m depth, at which point KEIT increases by about a factor of 5 until about 2200 m. As evident from Figs. 15 and 16, this is the signature of the upward-propagating IT beam propagating upward from the ridge crest, occurring near but slightly below the depth where the characteristic intersects the mooring (1610 m, upper dashed line, and Fig. 2; black line). Interestingly, near-inertial energy increases somewhat in this depth range as well, but KEIT is about 3 times greater. Below the beam, KENIW and KEIT are nearly equal again until about 3200 m. Both quantities increase sharply before the bottom, but KEIT increases more so, exceeding KENIW by a factor of 5 at the deepest measurements. The bottom enhancement begins at about the depth at which the downward IT beam intersects the mooring (3245 m, lower dashed line, and Fig. 2; black line), but it is unknown whether the beam or other bottom-enhancement processes lead to the increase.
The story for shear (Fig. 9b) is somewhat different, with shear in both bands again decreasing in depth but less sharply than N 2 (plotted divided by ten on the same axes, thin gray). As in energy, shear in both bands is enhanced in the depth range of the beam and near the bottom, but now NIW shear exceeds IT shear at all depths except immediately above the bottom.
In neither energy nor shear is evidence for shadowing of NIW by the ridge apparent. Indeed, a maximum is seen at 2500–3100 m, the depth of the wave shown in Fig. 12, perhaps suggesting a generation process at the ridge top. The lack of shadowing is potentially explained by waves obliquely propagating in from the west, although that possibility was excluded for the first wave shown, because it was propagating directly southward.
c. Modal partition
The greater energy in IT but greater shear in NIW is consistent with a redder wavenumber spectrum for IT, because the shear operator emphasizes higher wavenumbers. To quantify this, a modal decomposition is computed for each bandpassed quantity. Following Alford (2003a) and Alford and Zhao (2007), a set of orthogonal modes Φ(z) valid over a flat bottom is first computed by numerically solving the Sturm–Liouville equation,
where ce is the eigenspeed. Bandpassed velocity at each time is then projected onto each mode by solving a least squares problem. Because the data span nearly the whole water column, the inverses are stable up to at least the first 20 modes, but the calculation is stopped there to avoid resolution concerns that would appear near mode 46 [water depth (3700 m) over vertical resolution (80 m)]. For comparison, the equivalent mode numbers of the waves in Figs. 12 –15 are 10, 28, 23, and 5, respectively. The time-mean kinetic energy is then plotted for both bands as a function of mode number (Fig. 17). As expected, IT energy exceeds NIW energy at the lower modes by a factor of 2 or so, more so for the first mode. The strong first-mode response is as expected for a knife-edge model of generation (St. Laurent and Garrett 2002). However, NIW exceeds IT energy at the highest modes that dominate the shear.
d. Richardson number
Returning to the depth profiles (Figs. 9c,d), the similarity of the parameterized and overturn-inferred mixing above and below the beam indicates that the usual internal-wave cascade processes may be occurring in those depths. However, the peaks in dissipation near the beam depth and near the bottom, which are not captured by the parameterization, are likely related to processes not modeled by the GH parameterization. Internal tides appear implicated, but NIW energy and shear are also elevated in the beam depth range, giving rise to the possibility of interactions as suggested by Aucan and Merrifield (2008). Furthermore, the deep turbulence extends much farther up into the water column than the bottom enhancement of energy or mean shear, and deterministic relationships between dissipation and the IT motions are the exception rather than the rule. Other processes than direct breaking of the internal tide as observed by Klymak et al. (2008) appear to be responsible.
To investigate, depth–time series of inverse Richardson number are computed in Fig. 18 using total shear (top), near-inertial shear (middle), and IT shear (bottom). In spite of being smoothed over 80 m in the vertical, Ri−1 approaches unity an appreciable portion of the time as the bottom is approached. However, much of the contribution to it is due to other frequencies than NIW and IT, as seen by the much more stable values for the bandpassed quantities. In both bands, Ri−1 appears to increase with depth but is much less than the total.
These statements are quantified in Fig. 19, where time-mean Ri−1 is plotted for each band and the total on the left and the fraction at each depth for which each quantity exceeds 0.2 is plotted on the right. The time-mean values are quite low, as expected given their averaging over many stable and unstable periods and the large interval over which they are computed. However, the plots demonstrate a general increase in the tendency for instability in the depth range of the beam and toward the bottom.
This paper has presented detailed observations from a profiling mooring near Mendocino Escarpment, a major internal tide generation site previously investigated by AKS03. With two stacked McLane moored profilers and a long-range ADCP, velocity and shear were measured over nearly the whole water column each 1.5 h for 67 days. The measurements are sufficiently resolved to separate internal tide (IT) and near-inertial wave (NIW) contributions via bandpass filtering, to examine their modal content, and to examine specific wave packets. Dissipation rate was also measured via overturns and compared to energy, shear, and Richardson number in each band. The main findings are as follows:
(i) Dissipation rate ε agreed well at middepth with estimates from the Gregg–Henyey shear parameterization but was greatly enhanced in 1) the bottom 1000 m and 2) 1500–2000 m, the expected depth range of an upgoing IT beam (Fig. 9c, d). Here, ε was tidally modulated near the bottom (Fig. 10), with a suggestion of a spring–neap cycle (Fig. 11), but not in the depth range of the beam (Fig. 11).
(iii) NIW packets were observed at all depths, moving both upward and downward (Figs. 12, 14). No evidence of near-inertial shadowing was found (Fig. 9a), implying that some NIW energy impinged on the site laterally where the escarpment does not block it.
(v) The modal partition was computed for IT and NIW and found to be redder for NIW (Fig. 17), consistent with their greater shear.
We are left rather uncertain regarding the specific mechanisms leading to the mixing at our site. However, some statements can be made. Tidal processes are certainly important at our site in generating some of the mixing observed. In the bottom few hundred meters, direct breaking of internal tides locally generated over the sloping bottom is seen, though the mechanism requires further study. Though there is a rough spring–neap cycle, the phasing between the internal tide flows and the mixing appears to vary with time, as does the intensity and timing of the peaks at the different springs.
At the depth of the internal tide beam, the observed peaks in dissipation rate at the same depth as that in IT kinetic energy also implicates the tide there, but no similar deterministic relation is seen between the IT and dissipation as there is near the bottom and there is not a clear spring–neap cycle. The collocated maximum in near-inertial shear may implicate an interaction between the two frequencies, as suggested by Aucan and Merrifield (2008).
Near-bottom mixing is enhanced well above the “directly breaking” ITs. Here, the general falloff away from the bottom has the same decay constant as inverse Ri for the IT band (Fig. 19a), but other frequencies are also likely responsible because total Ri−1 is much greater than that for just the IT or NIW. It is possible that enhanced IT and NIW energy triggers instabilities of other waves in the continuum. These instabilities would not be well resolved by our measurements either in frequency because of our 1.5-h sampling or in wavenumber because of our 80-m smoothing. Alternatively, the waves could undergo a spectral cascade as argued by Polzin (2004).
The question of modal content is a central one for both the IT and the NIW because the energy is generally input into the low modes, but the higher modes are those relevant for mixing because of their potential for higher shear. The distinction is particularly poignant for NIW, where observations of low-mode energy flux show energy traveling over great distances (Alford 2003a) but where the most striking observational features are the high-mode ones such as those described in Alford and Gregg (2001) and here. The latter have approximately one-tenth the energy of the lower modes but appear more directly tied to mixing than the low modes.
The dominance of low wavenumbers even for NIW is likely key to the observed seasonal cycles in deep near-inertial energy (Alford and Whitmont 2007; Silverthorne and Toole 2009), because higher wavenumber motions would take large and variable fractions of a year to reach the abyss, washing out their seasonal cycle. The observations of high-wavenumber NIW in the abyss does, however, present a puzzle for how they could have gotten there. Perhaps they can survive the O(100–200) days it apparently took them to get there. Furthermore, the observation of upgoing packets implies that they can also survive bottom reflections.
Regarding the role of NIW in mixing the deep ocean, no strong conclusions are offered. We have demonstrated the dominance of NIW shear over IT shear at nearly all depths and demonstrated that deep NIW may lead to nearly unstable values of Ri, even at 80-m scales, and we may have observed mixing tied to the passage of such an event in like manner to Alford and Gregg (2001). Stronger conclusions would require more highly resolved observations, ideally coupled with direct turbulence measurements. However, the importance of NIW at this site, which strongly favors IT, may call for a more important role for NIW at other sites such as beneath storm and typhoon tracks.
The author is grateful to John Mickett, Eric Boget, and Andrew Cookson for their skill in designing, deploying and recovering the mooring and to the captain, crew, and marine technician of R/V Wecoma for their expert ship handling, hard work, and flexibility, which made the operations possible. This work was supported by the Office of Naval Research and the National Science Foundation.
Corresponding author address: Matthew H. Alford, Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98105. Email: firstname.lastname@example.org