Abstract

The wind generation of near-inertial waves is revisited through use of the Pollard–Rhines–Thompson theory, the Price–Weller–Pinkel (PWP) mixed layer model, and KPP simulations of resonant forcing by Crawford and Large. An Argo mixed layer climatology and 0.6° MERRA-2 reanalysis winds are used to compute global totals and explore hypotheses. First, slab models overestimate wind work by factors of 2–4 when the mixed layer is shallow relative to the scaling H* ≡ u*/(Nf)^1/2, but are accurate for deeper mixed layers, giving overestimation of global totals by a factor of 1.23 ± 0.03 compared to PWP. Using wind stress relative to the ocean currents further reduces the wind work by an additional 13 ± 0.3%, for a global total wind work of 0.26 TW. Second, the potential energy increase ΔPE due to wind-driven mixed layer deepening is examined and compared to ΔPE computed from Argo and ERA-Interim heat flux climatology. Argo-derived ΔPE closely matches cooling, confirming that cooling sets the seasonal cycle of mixed layer depth and providing a new constraint on observational estimates of convective buoyancy flux at the mixed layer base. Locally and in fall, wind-driven deepening is comparable in importance to cooling. Globally, wind-driven ΔPE is about 11% of wind work, implying that >50% of wind work goes to turbulence and thus not into propagating inertial motions. The fraction into this “modified wind work” is imperfectly estimated in two ways, but we conclude that more research is needed into mixed layer and transition-layer physics. The power available for propagating near-inertial waves is therefore still uncertain, but appears lower than previously thought.

Abstract

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.

Abstract

The energy flux from the wind to inertial mixed layer motions is computed for all oceans from 50°S to 50°N for the years 1996–99. The wind stress, τ, is computed from 6-h, 2.5°-resolution NCEP–NCAR global reanalysis surface winds. The inertial mixed layer response, u _I , and the energy flux, Π = τ  · u _I , are computed using a slab model. The validity of the reanalysis winds and the slab model is demonstrated by direct comparison with wind and ADCP velocity records from NDBC buoys. (At latitudes > 50°, the inertial response is too fast to be resolved by the reanalysis wind 6-h output interval.)

Midlatitude storms produce the greatest fluxes, resulting in broad maxima near 40° latitude during each hemisphere's winter, concentrated in the western portion of each basin. Northern Hemisphere fluxes exceed those in the Southern Hemisphere by about 50%. The global mean energy flux from 1996 to 1999 and 50°S to 50°N is (0.98 ± 0.08) × 10⁻³ W m⁻², for a total power of 0.29 TW (1 TW = 10¹² W). This total is the same order of magnitude as recent estimates of the global power input to baroclinic M ₂ tidal motions, suggesting that wind-generated near-inertial waves may play an important role in the global energy balance.

Abstract

Internal waves advect vertical structure past Eulerian (fixed depth) sensors, leading to “fine-structure contamination,” wherein the intrinsic frequency spectrum is Doppler shifted by the advective motions. Shear, velocity, and isopycnal displacement records collected at low latitude (6.5°S, Coriolis frequency f = 1/4.4 cpd) with an ADCP and a loosely tethered vehicle are used to demonstrate this mechanism in a simple case. In contrast to the usual midlatitude situation where the intrinsic and advective frequencies are broadband and overlapping, the low Coriolis frequency at low latitude allows clear identification of heaving of near-inertial shear layers by the diurnal internal tide. Specifically, Eulerian shear and velocity frequency spectra show peaks at f ± K ₁, where K ₁ = 1 cpd is the diurnal tidal frequency. A simple two-wave model illustrates the mechanism and correctly predicts the magnitude of the shifted peaks. The shifted peaks are absent in spectra of quantities computed in an isopycnal-following frame since the advection effect is removed.

Abstract

Global estimates are presented of the fraction q of wind-generated near-inertial wave power available for local turbulent dissipation under the assumption that modes 1–3 propagate “far” and the higher modes remain to eventually break. Using climatological stratification profiles and mixed layer depth, the modal distribution of near-inertial energy flux is computed following Gill's classic 1984 work by projecting a slab flow in the mixed layer onto the dynamical modes. Global maps and zonal-mean profiles are presented, which show a global-mean value of q = 0.63 and 0.75 for winter and summer profiles, respectively. The simplicity of the calculation makes it of potential use in parameterizations of near-inertial breaking in climate simulations.

Abstract

Temporal and spatial patterns of near-inertial kinetic energy (KE_moor) are investigated in a database of 2480 globally distributed, moored current-meter records (deployed on 690 separate moorings) and compared with the distribution of wind-forced mixed-layer energy flux F _ML. By computing KE_moor using short (30 day) multitaper spectral windows, the seasonal cycle is resolved. Clear winter enhancement by a factor of 4–5 is seen in the Northern Hemisphere for latitudes 25°–45° at all depths <4500 m, in close agreement with the magnitude, phase, and latitudinal dependence of the seasonal cycle of F _ML. In the Southern Hemisphere, data coverage is poorer, but a weaker seasonal cycle (a factor of 2) in both KE_moor and F _ML is still resolvable between 35° and 50°. When Wentzel–Kramers–Brillouin (WKB) scaled using climatological buoyancy-frequency profiles, summer KE_moor is approximately constant in depth while showing a clear decrease by a factor of 4–5 from 500 to 3500 m in winter. Spatial coverage is sufficient in the Northern Hemisphere to resolve broad KE_moor maxima in the western portion of each ocean basin in winter, generally collocated with F _ML maxima associated with storm forcing. The ratio of depth-integrated KE_moor to F _ML gives a replenishment time scale, which is about 10 days in midlatitudes, consistent with 1) previous estimates of the dissipation time scale of the internal wave continuum and 2) the presence of a seasonal cycle. Its increase to ≈70–80 days at lower latitudes is a possible signature of equatorward propagation of near-inertial waves. The seasonal modulation of the magnitude of KE_moor, its similarity to that in F _ML, and the depth decay and western intensification in winter but not in summer are consistent with a primarily wind-forced near-inertial field for latitudes poleward of ≈25°.

Abstract

Observations are reported of the semidiurnal (M ₂) internal tide across Kaena Ridge, Hawaii. Horizontal velocity in the upper 1000–1500 m was measured during eleven ~240-km-long shipboard acoustic Doppler current profiler (ADCP) transects across the ridge, made over the course of several months. The M ₂ motions are isolated by means of harmonic analysis and compared to numerical simulations using the Princeton Ocean Model (POM). The depth coverage of the measurements is about 3 times greater than similar past studies, offering a substantially richer view of the internal tide beams. Sloping features are seen extending upward north and south from the ridge and then downward from the surface reflection about ±40 km from the ridge crest, closely matching theoretical M ₂ ray paths and the model predictions.

Abstract

Extending an earlier attempt to understand long-range propagation of the global internal-wave field, the energy E and horizontal energy flux F are computed for the two gravest baroclinic modes at 80 historical moorings around the globe. With bandpass filtering, the calculation is performed for the semidiurnal band (emphasizing M ₂ internal tides, generated by flow over sloping topography) and for the near-inertial band (emphasizing wind-generated waves near the Coriolis frequency). The time dependence of semidiurnal E and F is first examined at six locations north of the Hawaiian Ridge; E and F typically rise and fall together and can vary by over an order of magnitude at each site. This variability typically has a strong spring–neap component, in addition to longer time scales. The observed spring tides at sites northwest of the Hawaiian Ridge are coherent with barotropic forcing at the ridge, but lagged by times consistent with travel at the theoretical mode-1 group speed from the ridge. Phase computed from 14-day windows varies by approximately ±45° on monthly time scales, implying refraction by mesoscale currents and stratification. This refraction also causes the bulk of internal-tide energy flux to be undetectable by altimetry and other long-term harmonic-analysis techniques. As found previously, the mean flux in both frequency bands is O(1 kW m⁻¹), sufficient to radiate a substantial fraction of energy far from each source. Tidal flux is generally away from regions of strong topography. Near-inertial flux is overwhelmingly equatorward, as required for waves generated at the inertial frequency on a β plane, and is winter-enhanced, consistent with storm generation. In a companion paper, the group velocity, ĉ _g ≡ F E ⁻¹, is examined for both frequency bands.

Abstract

The time sequence of events that lead to internal wave breaking and ocean turbulence is investigated. Data are obtained from depths 100–400 m with a repeat profiling CTD and a coded-pulse Doppler sonar. The instruments were deployed from R/P FLIP during February–March 1995 while stationed 30 km west of Point Argüello, California, as an aspect of the Marine Boundary Layer Experiment. Although the water depth at the site is 1500 m, both rms shear and diapycnal diffusivity, as inferred from the average rate and size of overturning events, increase with depth below 250 m. A deep source of wave energy is implied.

Depth–time series of 6.4-m shear S, 2-m strain (γ ≡ N ² /N ², where N is the buoyancy frequency), 6.4-m gradient Richardson number Ri ≡ N ²/S ², and 2-m “effective strain rate”

(the depth derivative of CTD-inferred vertical velocity ŵ) are obtained at 4 minute intervals over a 9-day, 100–400 m domain. The occurrence of overturns, static instabilities of vertical scale ≥2 m in the observed density profiles, is monitored. Data are examined in both Eulerian and isopycnal-following (semi-Lagrangian) reference frames.

Over two thousand overturns are detected and mapped relative to the background shear, strain, Ri, and strain rate fields. Correspondence between low values of 6.4-m Ri and overturns is indeed significant. However, 2-m strain and effective strain rate appear to be better indices of overturning: γ ≥ 2 in 60% of all overturning events, and |∂ŵ/∂z| is greater than average in 80% of overturns.

Depth–time maps of effective strain rate show wavelike features on vertical scales 5–20 m, which extend coherently across isopycnal surfaces. Time series of depth-averaged ∂ŵ/∂z variance (expressed as a dissipation rate), and depth-averaged dissipation rate ε _T , estimated from observed overturning scales are highly correlated. Time-mean = 8.6 × 10⁻⁹ W kg⁻¹, implying an eddy diffusivity K _ρ = 0.89 × 10⁻⁴ m² s⁻¹. Mean dissipation rate and diffusivity computed from 10-m shear display comparable magnitude ( = 6.8 × 10⁻⁹ W kg⁻¹, K _ρ = 0.70 × 10⁻⁴ m² s⁻¹) and similar dependence upon mean stratification and shear to the overturn-inferred quantities. It is suggested that the overturns seen at this site result from breaking of these high ∂ŵ/∂z waves.

Abstract

New estimates of mode-1 M ₂ internal tide energy flux are computed from an extended Ocean Topography Experiment (TOPEX)/Poseidon (T/P) altimeter dataset that includes both the original and tandem tracks, improving spatial resolution over previous estimates from O(500 km) to O(250 km). Additionally, a new technique is developed that allows separate resolution of northward and southward components. Half-wavelength features previously seen in unseparated estimates are shown to be due to the superposition of northward and southward wave trains. The new technique and higher spatial resolution afford a new view of mode-1 M ₂ internal tides in the central North Pacific Ocean. As with all altimetric estimates, only the coherent or phase-locked signals are detectable owing to the long repeat period of the tracks. Emanating from specific generation sites consistent with predictions from numerical models, internal tidal beams 1) are as narrow as 200 km and 2) propagate a longer distance than previously observed. Two northward internal tidal beams radiating from the Hawaiian Ridge, previously obscured by coarse resolution and the southward Aleutian beam, are now seen to propagate more than 3500 km across the North Pacific Ocean to reach the Alaskan shelf. The internal tidal beams are much better resolved than in previous studies, resulting in better agreement with moored flux estimates.