Rapid changes in winds drive rotating currents known as inertial oscillations. In a stratified ocean, these oscillations can then initiate subsurface near-​inertial internal waves that propagate laterally and vertically and are refracted by horizontal gradients in vorticity. We report on a process study of wind forcing and ocean response in the Iceland Basin of the North Atlantic using arrays of profiling floats measuring temperature, salinity, horizontal velocity, and turbulence. Three arrays with four to eight floats each sampled spatial gradients in both high-frequency (internal wave) and low-frequency (mesoscale) currents in order to clarify the dynamical coupling between these distinct categories of oceanic phenomena.

The observations are qualitatively consistent with theory for wave-​mesoscale interactions: immediately following each wind event, a surface inertial oscillation appears that initially matches a simple slab mixed-layer model in both amplitude and phase, but diverges over several cycles to become a super-inertial internal wave. The surface oscillation decays over several days, while near-inertial energy appears below the surface layer two to three days after the surface motion. Lateral phase gradients estimated from the inertial cycle at each float show that the deeper energy has shorter horizontal wavelengths and tends to propagate toward anticyclonic (negative) vorticity.

These case studies illustrate both the strengths and limitations of Lagrangian (flow-following) arrays for the study of the energetics of air-sea interaction. High-resolution observations of this kind are not feasible globally, but examples in a variety of wind and ocean eddy environments can improve our understanding and verify estimates of wind-energy input and mixing from numerical models and theory.

An 18-month deployment of moored sensors in Iceland Basin allows characterization of near-inertial (frequencies near the Coriolis frequency f with periods of ~14 h) internal gravity wave generation and propagation in a region with an active mesoscale eddy field and strong seasonal wind and heat forcing. The seasonal cycle in surface forcing deepens the mixed layer in winter and controls excitation of near-​inertial energy. The mesoscale eddy field modulates near-inertial wave temporal, horizontal, and vertical scales, as well as propagation out of the surface layer into the deep permanent pycnocline. Wind-forced near-inertial energy has the most active downward propagation within anticyclonic eddies. As oceanic surface and bottom boundaries act to naturally confine the propagation of internal waves, the vertical distribution of these waves can be decomposed into a set of "standing" vertical modes that each propagate horizontally at different speeds. The lowest modes, which propagate quickly away from their generation sites, are most enhanced when the mixed layer is deep and are generally directed southward.

Across the stable density stratification of the abyssal ocean, deep dense water is slowly propelled upward by sustained, though irregular, turbulent mixing. The resulting mean upwelling determines large-scale oceanic circulation properties like heat and carbon transport. In the ocean interior, this turbulent mixing is caused mainly by breaking internal waves: generated predominantly by winds and tides, these waves interact nonlinearly, transferring energy downscale, and finally become unstable, break and mix the water column. This paradigm, long parameterized heuristically, still lacks full theoretical explanation. Here, we close this gap using wave-wave interaction theory with input from both localized and global observations. We find near-ubiquitous agreement between first-principle predictions and observed mixing patterns in the global ocean interior. Our findings lay the foundations for a wave-driven mixing parameterization for ocean general circulation models that is entirely physics-based, which is key to reliably represent future climate states that could differ substantially from today's.

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We construct a generalized slab model to calculate the ocean’s linear response to an arbitrary, depth-variable forcing stress profile. To introduce a first-order improvement to the linear stress profile of the traditional slab model, a nonlinear stress profile which allows momentum to penetrate into the transition layer (TL) is used (denoted 'mixed layer/transition layer,' or MLTL stress profile). The MLTL stress profile induces a two-fold reduction in power input to inertial motions relative to the traditional slab approximation. The primary reduction arises as the TL allows momentum to be deposited over a greater depth range, reducing surface currents. The secondary reduction results from the production of turbulent kinetic energy (TKE) beneath the mixed layer (ML) related to interactions between shear stress and velocity shear. Direct comparison between observations in the Iceland Basin, the traditional slab model, the generalized slab model with the MLTL stress profile, and the Price-Weller-Pinkel (PWP) model suggest that the generalized slab model offers improved performance over a traditional slab model. In the Iceland Basin, modeled TKE production in the TL is consistent with observations of turbulent dissipation. Extension to global results via analysis of Argo profiling float data suggests that on the global, annual-mean, ~30% of the total power input to near-inertial motions is allocated to TKE production. We apply this result to the latest global, annual-mean estimates for near-inertial power input (0.27 TW) to estimate that 0.08 ± 0.01 TW of the total near-inertial power input are diverted to TKE production.

Six profiling floats measured water-mass properties (Т, S), horizontal velocities (u, v) and microstructure thermal-variance dissipation rates χT in the upper ~1 km of Iceland and Irminger Basins in the eastern sub-polar North Atlantic from June 2019 to April 2021. The floats drifted into slope boundary currents to travel counterclockwise around the basins. Pairs of velocity profiles half an inertial period apart were collected every 7–14 days. These half-inertial-period pairs are separated into subinertial eddy (sum) and inertial/semidiurnal (difference) motions. Eddy flow speeds are ~O(0.1 m s^-1) in the upper 400 m, diminishing to ~O(0.01 m s^-1) by ~800-m depth. In late summer through early spring, near-inertial motions are energized in the surface layer and permanent pycnocline to at least 800-m depth almost simultaneously (within the 14-day temporal resolution), suggesting rapid transformation of large-horizontal-scale surface-layer inertial oscillations into near-inertial internal waves with high vertical group velocities through interactions with eddy vorticity-gradients (effective β). During the same period, internal-wave vertical shear variance was 2–5 times canonical midlatitude magnitudes and dominantly clockwise-with-depth (downward energy propagation). In late spring and early summer, shear levels are comparable to canonical midlatitude values and dominantly counterclockwise-with-depth (upward energy propagation), particularly over major topographic ridges. Turbulent diapycnal diffusivities K ~O(10^-4 m² s^-1) are an order of magnitude larger than canonical mid-latitude values. Depth-averaged (10–1000 m) diffusivities exhibit factor-of-three month-by-month variability with minima in early August.

Diapycnal mixing shapes the distribution of climatically important tracers, such as heat and carbon, as these are carried by dense water masses in the ocean interior. Here, we analyze a suite of observation-based estimates of diapycnal mixing to assess its role within the Atlantic Meridional Overturning Circulation (AMOC). The rate of water mass transformation in the Atlantic Ocean's interior shows that there is a robust buoyancy increase in the North Atlantic Deep Water (NADW, neutral density ≅ 27.6–28.15), with a diapycnal circulation of 0.5–8 Sv between 48°N and 32°S in the Atlantic Ocean. Moreover, tracers within the southward-flowing NADW may undergo a substantial diapycnal transfer, equivalent to a vertical displacement of hundreds of meters in the vertical. This result, confirmed with a zonally averaged numerical model of the AMOC, indicates that mixing can alter where tracers upwell in the Southern Ocean, ultimately affecting their global pathways and ventilation timescales. These results point to the need for a realistic mixing representation in climate models in order to understand and credibly project the ongoing climate change.

Internal waves are predominantly generated by winds, tide/topography interactions and balanced flow/topography interactions. Observations of vertical shear of horizontal velocity (u_z, v_z) from LADCP profiles conducted during GO-SHIP hydrographic surveys, as well as vessel-mounted sonars, are used to interpret these signals. Vertical directionality of intermediate-wavenumber internal waves is inferred in this study from rotary-with-depth shears. Total shear variance and vertical asymmetry ratio, i.e. the normalized difference between downward- and upward-propagating intermediate wavenumber shear variance, where Ω > 0 (< 0) indicates excess downgoing (upgoing) shear variance, are calculated for three depth ranges: 200–600 m, 600 m to 1000 mab (meters above bottom), and below 1000 mab. Globally, downgoing (clockwise-with-depth in the northern hemisphere) exceeds upgoing (counterclockwise-with-depth in the northern hemisphere) shear variance by 30% in the upper 600 m of the water column (corresponding to the globally averaged asymmetry ratio of Ω = 0.13), with a near-equal distribution below 600-m depth. Downgoing shear variance in the upper water column dominates at all latitudes. There is no statistically significant correlation between the global distribution of Ω and internal wave generation, pointing to an important role for processes that re-distribute energy within the internal wave continuum on wavelengths of Ο(100 m).

Submesoscale flows such as fronts, eddies, filaments, and instabilities with lateral dimensions between 100 m and 10 km are ubiquitous features of the ocean. They act as an intermediary between the mesoscale and small-scale turbulence and are thought to have a critical role in closing the ocean's kinetic budget by facilitating a forward energy cascade, where energy is transferred to small scales and dissipated.

The initiative uses a suite of measurements from autonomous platforms and ships combined with regional simulations to characterize the submesoscale flows in the western Pacific Ocean between Luzon and Mariana Island arcs &$151; the ARCTERX region.

Program goals are to characterize the strength and spectral properties of the turbulent cascade of kinetic energy on the submesoscales in the ARCTERX study region and understand the processes that control energy transfers across scales and their seasonal variability.

Use of an ocean parameter and state estimation framework — such as the Estimating the Circulation and Climate of the Ocean (ECCO) framework — could provide an opportunity to learn about the spatial distribution of the diapycnal diffusivity parameter (k_ρ) that observations alone cannot due to gaps in coverage. However, we show that the inclusion of misfits to observed physical variables — such as in situ temperature, salinity, and pressure — currently accounted for in ECCO is not sufficient, as k_ρ from ECCO does not agree closely with any observationally derived product. These observationally derived k_ρ products were inferred from microstructure measurements, derived from Argo and conductivity–temperature–depth (CTD) data using a strain-based parameterization of fine-scale hydrographic structure, or calculated from climatological and seafloor data using a parameterization of tidal mixing. The k_ρ products are in close agreement with one another but have both measurement and structural uncertainties, whereas tracers can have relatively small measurement uncertainties. With the ultimate goal being to jointly improve the ECCO state estimate and representation of k_ρ in ECCO, we investigate whether adjustments in k_ρ due to inclusion of misfits to a tracer — dissolved oxygen concentrations from an annual climatology — would be similar to those due to inclusion of misfits to observationally derived k_ρ products. We do this by performing sensitivity analyses with ECCO. We compare multiple adjoint sensitivity calculations: one configuration uses misfits to observationally derived k_ρ, and the other uses misfits to observed dissolved oxygen concentrations. We show that adjoint sensitivities of dissolved oxygen concentration misfits to the state estimate's control space typically direct k_ρ to improve relative to the observationally derived values. These results suggest that the inclusion of oxygen in ECCO's misfits will improve k_ρ in ECCO, particularly in (sub)tropical regions.

Ocean density increases with increasing depth, supporting internal waves below the ocean surface. These internal waves are generated near the surface by varying wind forcing such as passing storms and near the bottom by interactions of currents (including tidal) with rough bathymetry (such as seamounts and ridges). They can travel for long distances in both the vertical and the horizontal. When they break, they play important roles in mixing temperature, salinity, and other water properties. Deep Argo is an observing system designed to measure temperature and salinity profiles from the surface to the bottom of the ocean. One model of Deep Argo float serendipitously observes internal wave signals as variations in descent rate data, which it collects primarily for navigation purposes, from the surface to the seafloor. These observations reveal patterns in the magnitudes of these internal wave signals, with stronger internal wave activity near continental rises and mid-ocean ridges and lower levels over smoother abyssal plains. Also, regions with strong deep flows, such as the Samoan Passage through which bottom water is funneled into the North Pacific, or the region south of the Campbell Plateau through which the Antarctic Circumpolar Current flows, exhibit stronger deep internal wave signatures.

The abyssal Southwest Pacific Basin has warmed significantly between 1992–2017, consistent with warming along the bottom limb of the meridional overturning circulation seen throughout the global oceans. Here we present a framework for assessing the abyssal heat budget that includes the time-dependent unsteady effects of decadal warming and direct and indirect estimates of diapycnal mixing from microscale temperature measurements and finescale parameterizations. The unsteady terms estimated from the decadalwarming rate are shown to be within a factor of 3 of the steady state terms in the abyssal heat budget for the coldest portion of the water column and therefore, cannot be ignored. We show that a reduction in the lateral heat flux for the coldest temperature classes compensated by an increase in warmer waters advected into the basin has important implications for the heat balance and diffusive heat fluxes in the basin. Finally, vertical diffusive heat fluxes are estimated in different ways: using the newly available CTD-mounted microscale temperature measurements, a finescale strain parameterization, and a vertical kinetic energy parameterization from data along the P06 transect along 32.5°S. The unsteady-state abyssal heat budget for the basin shows closure within error estimates, demonstrating that (i) unsteady terms have become consequential for the heat balance in the isotherms closest to the ocean bottom and (ii) direct and indirect estimates from full depth GO-SHIP hydrographic transects averaged over similarly large spatial and temporal scales can capture the basin-averaged abyssal mixing needed to close the deep overturning circulation.

The large scale circulation of the ocean is primarily driven by density differences. As dense, heavy water sinks, it fills the deep ocean basins and aids in pushing water around the globe, cycling around the world over many centuries. A key location where this happens is around Antarctica. The ice and cold winds cool the water, making it denser. This cooled water sinks, displacing the deep water and pushing it northwards. As Antarctica warms, this water carries the extra heat into the rest of the world, causing the deep ocean to rapidly warm. In the Southwest Pacific Basin, we find that this bottom intensified warming has caused a significant reduction in the stratification of the deepest layer over the past three decades. This change can disrupt the global ocean conveyor belt, impacting the transport of heat, carbon dioxide, nutrients, and other dissolved matter around the world.

This chapter gives an overview of recent advances in in situ observations of ocean mixing. It starts by providing a brief history of measuring ocean mixing. It then describes adaptations of traditional measurements and methods to autonomous platforms, including profiling floats and autonomous underwater vehicles. For each approach, the method is described as well as its limitations. Evidence for successful application of each method is provided.

The rate of turbulent kinetic energy dissipation and diapycnal diffusivity are estimated along 10 hydrographic sections across the Indian Ocean from a depth of 500 m to the seabed. Six sections were occupied twice. On the meridional section, which is nominally along 95°E, spatial patterns were observed to persist throughout the three occupations. Since the variability in diffusivity exceeds the variability in the vertical gradients of temperature and salinity, we conclude that the diffusive diapycnal fluxes vary mostly with diffusivity. In high latitudes, diapycnal diffusion of both temperature and salinity contribute almost equally to density diffusion, particularly across isopycnals just above the salinity maximum, while mainly temperature contributes in other latitudes. The known zonal difference in turbulence is reproduced. Diffusivity from the seabed to 4000 m above the seabed has an exponential profile with a mode value of 4 x 10^-4 m²s^-1 at 1000 m above the seabed and is positively correlated with topographic roughness as reported previously. It is found that the diffusivity also correlates with wind power injected through the surface at near-inertial frequencies 10–80 days before the observations. These correlations were used to interpolate the observation-based turbulence quantities to the entire Indian Ocean. Although the dissipation averaged along selected neutral-density surfaces is less than the dissipation needed to explain the meridional overturning circulation evaluated across 32°S latitude, this may be explained by effects not captured by the ship-based observations and parameterization. These effects likely include unobserved high-mixing events, near bottom processes (e.g. hydraulic jumps), and deep equatorial jets.

The turbulent energy dissipation rate in the ocean can be measured by using rapidly sampling microstructure shear probes, or by applying a finescale parametrization to coarser resolution density and/or shear profiles. The two techniques require measurements that are on different spatiotemporal scales and generate dissipation rate estimates that also differ in spatiotemporal scale. Since the distribution of the measured energy dissipation rate is closer to lognormal than normal and fluctuates with the strength of the turbulence, averaging the two approaches on equivalent spatiotemporal scales is critical for accurately comparing the two methods. Here, microstructure data from the 1997 Brazil Basin Tracer Release Experiment (BBTRE) is used to demonstrate that comparing averages of the dissipation rate on different spatiotemporal scales can generate spurious discrepancies of up to a factor of O10 in regions of strong turbulence and smaller biases of up to a factor of 2 in the presence of weaker turbulence.

Generated at large horizontal scales by winds, near‐inertial waves (NIWs) are inefficient at radiating energy without a shift to smaller wavelengths. The lateral scales of NIWs can be reduced by gradients in the Coriolis parameter (β‐refraction) or in the vertical vorticity (ζ‐refraction) or by strain. Here we present ship‐based surveys of NIWs in a dipole vortex in the Iceland Basin that show, for the first time, direct evidence of ζ‐refraction. Differences in NIW phase across the dipole were observed to grow in time, generating a lateral wavelength that shrank at a rate consistent with ζ‐refraction, reaching ~40 km in 1.5 days. Two days later, a NIW beam with an ~13 km horizontal and ~200 m vertical wavelength was detected at depth radiating energy downward and toward the dipole's anticyclone. Strain, while significant in strength in the dipole, had little direct effect on the NIWs.

Turbulent mixing from breaking oceanic internal waves drives a vertical transport of water, heat and other climatically important tracers in the ocean, thereby playing an important role in shaping the circulation and distributions of heat and carbon within the climate system. However, linking internal wave-driven mixing to its impacts on climate poses a formidable challenge, since it requires understanding of the complex life cycle of internal waves — including generation, propagation and breaking into turbulence — and knowledge of the spatio-temporal variability of these processes in the diverse, rapidly evolving oceanic environment. In this Review, we trace the energy pathways from tides, winds and geostrophic currents to internal wave mixing, connecting this mixing with the global climate system. Additionally, we discuss avenues for future work, including understanding energy transfer processes within the internal wave field, how internal waves can be modified by background currents and how internal wave mixing is integrated within the global climate system.

Vertical mixing is often regarded as the Achilles' heel of ocean models. In particular, few models include a comprehensive and energy‐constrained parameterization of mixing by internal ocean tides. Here, we present an energy‐conserving mixing scheme which accounts for the local breaking of high‐mode internal tides and the distant dissipation of low‐mode internal tides. The scheme relies on four static two‐dimensional maps of internal tide dissipation, constructed using mode‐by‐mode Lagrangian tracking of energy beams from sources to sinks. Each map is associated with a distinct dissipative process and a corresponding vertical structure. Applied to an observational climatology of stratification, the scheme produces a global three‐dimensional map of dissipation which compares well with available microstructure observations and with upper‐ocean finestructure mixing estimates. This relative agreement, both in magnitude and spatial structure across ocean basins, suggests that internal tides underpin most of observed dissipation in the ocean interior at the global scale. The proposed parameterization is therefore expected to improve understanding, mapping, and modeling of ocean mixing.

Oceanic mesoscale structures such as eddies and fronts can alter the propagation, breaking and subsequent turbulent mixing of wind-generated internal waves. However, it has been difficult to ascertain whether these processes affect the global-scale patterns, timing and magnitude of turbulent mixing, thereby powering the global oceanic overturning circulation and driving the transport of heat and dissolved gases. Here we present global evidence demonstrating that mesoscale features can significantly enhance turbulent mixing due to wind-generated internal waves. Using internal wave-driven mixing estimates calculated from Argo profiling floats between 30° and 45°N, we find that both the amplitude of the seasonal cycle of turbulent mixing and the response to increases in the wind energy flux are larger to a depth of at least 2,000 m in the presence of a strong and temporally uniform field of mesoscale eddy kinetic energy. Mixing is especially strong within energetic anticyclonic mesoscale features compared to cyclonic features, indicating that local modification of wind-driven internal waves is probably one mechanism contributing to the elevated mixing observed in energetic mesoscale environments.

Recent advances in our understanding of internal-wave driven turbulent mixing in the ocean interior are summarized. New parameterizations for global climate ocean models, and their climate impacts, are introduced.

Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatio-temporal patterns of mixing are largely driven by the geography of generation, propagation and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last five years and under the auspices of US CLIVAR, a NSF- and NOAA-supported Climate Process Team has been engaged in developing, implementing and testing dynamics-based parameterizations for internal-wave driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here we review recent progress, describe the tools developed, and discuss future directions.

Air–Sea Interactions in the Northern Indian Ocean (ASIRI) is an international research effort (2013–17) aimed at understanding and quantifying coupled atmosphere–ocean dynamics of the Bay of Bengal (BoB) with relevance to Indian Ocean monsoons. Working collaboratively, more than 20 research institutions are acquiring field observations coupled with operational and high-resolution models to address scientific issues that have stymied the monsoon predictability. ASIRI combines new and mature observational technologies to resolve submesoscale to regional-scale currents and hydrophysical fields. These data reveal BoB’s sharp frontal features, submesoscale variability, low-salinity lenses and filaments, and shallow mixed layers, with relatively weak turbulent mixing. Observed physical features include energetic high-frequency internal waves in the southern BoB, energetic mesoscale and submesoscale features including an intrathermocline eddy in the central BoB, and a high-resolution view of the exchange along the periphery of Sri Lanka, which includes the 100-km-wide East India Coastal Current (EICC) carrying low-salinity water out of the BoB and an adjacent, broad northward flow (~300 km wide) that carries high-salinity water into BoB during the northeast monsoon. Atmospheric boundary layer (ABL) observations during the decaying phase of the Madden–Julian oscillation (MJO) permit the study of multiscale atmospheric processes associated with non-MJO phenomena and their impacts on the marine boundary layer. Underway analyses that integrate observations and numerical simulations shed light on how air–sea interactions control the ABL and upper-ocean processes.

Upper-ocean turbulent heat fluxes in the Bay of Bengal and the Arctic Ocean drive regional monsoons and sea ice melt, respectively, important issues of societal interest. In both cases, accurate prediction of these heat transports depends on proper representation of the small-scale structure of vertical stratification, which in turn is created by a host of complex submesoscale processes. Though half a world apart and having dramatically different temperatures, there are surprising similarities between the two: both have (1) very fresh surface layers that are largely decoupled from the ocean below by a sharp halocline barrier, (2) evidence of interleaving lateral and vertical gradients that set upper-ocean stratification, and (3) vertical turbulent heat fluxes within the upper ocean that respond sensitively to these structures. However, there are clear differences in each ocean’s horizontal scales of variability, suggesting that despite similar background states, the sharpening and evolution of mesoscale gradients at convergence zones plays out quite differently. Here, we conduct a qualitative and statistical comparison of these two seas, with the goal of bringing to light fundamental underlying dynamics that will hopefully improve the accuracy of forecast models in both parts of the world.

The effects of a parameterized linear internal wave drag on the semidiurnal barotropic and baroclinic energetics of a realistically forced, three-dimensional global ocean model are analyzed. Although the main purpose of the parameterization is to improve the surface tides, it also influences the internal tides. The relatively coarse resolution of the model of ~8 km only permits the generation and propagation of the first three vertical modes. Hence, this wave drag parameterization represents the energy conversion to and the subsequent breaking of the unresolved high modes. The total tidal energy input and the spatial distribution of the barotropic energy loss agree with the Ocean Topography Experiment (TOPEX)/Poseidon (TPXO) tidal inversion model. The wave drag overestimates the high-mode conversion at ocean ridges as measured against regional high-resolution models. The wave drag also damps the low-mode internal tides as they propagate away from their generation sites. Hence, it can be considered a scattering parameterization, causing more than 50% of the deep-water dissipation of the internal tides. In the near field, most of the baroclinic dissipation is attributed to viscous and numerical dissipation. The far-field decay of the simulated internal tides is in agreement with satellite altimetry and falls within the broad range of Argo-inferred dissipation rates. In the simulation, about 12% of the semidiurnal internal tide energy generated in deep water reaches the continental margins.