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    Schematic of internal wave mixing processes in the open ocean that are considered as part of this CPT. Tides interact with topographic features to generate high-mode internal waves (e.g., at midocean ridges) and low-mode internal waves (e.g., at tall steep ridges such as the Hawaiian Ridge). Deep currents flowing over topography can generate lee waves (e.g., in the Southern Ocean). Storms cause inertial oscillations in the mixed layer, which can generate both low- and high-mode internal waves (e.g., beneath storm tracks). In the open ocean, these internal waves can scatter off of rough topography and potentially interact with mesoscale fronts and eddies until they ultimately dissipate through wave–wave interactions. Internal waves that reach the shelf and slope can scatter or amplify as they propagate toward shallower water.

  • View in gallery

    Depth-averaged diffusivity κ from (a) the upper ocean (from MLD to 1000-m depth) and (b) the full water column, updated from Waterhouse et al. (2014). The background diffusivity map in (a) comes from the strain-based inferences of diffusivity from Argo floats, updated from Whalen et al. (2015) with observations included from 2006 to 2015. (c) Compiled observations of mixing measurements with blue and green squares and diamonds denoting microstructure measurements. Green represents full-depth profiles, while blue denotes microstructure profiles. Purple circles represent inferred diffusivity from a finescale parameterization using lowered acoustic Doppler current profiler (LADCP)/conductivity–temperature–depth (CTD) profiles [dark purple, Kunze et al. (2006); medium purple, Huussen et al. (2012)] and High Density Sounding System (HDSS) shipboard shear (light orange). Dark orange circles are diffusivities from density overturns in moored profiles.

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    (a) A snapshot of baroclinic velocity (m s−1) from a two-dimensional numerical simulation of internal tides forced by M2 (semidiurnal) tidal velocities over rough topography for parameters corresponding to the Brazil Basin (Nikurashin and Legg 2011). (b) Observational time series of internal wave breaking over tall steep topography; here, we see (top) northward velocity and (bottom) turbulent dissipation rate oscillate twice a day as the tide flows over Kaena Ridge, Hawaii (Klymak et al. 2008). (c) Global energy flux from the M2 tide into internal tides (log10 W m−2) estimated using (top) the topography resolved in the Shuttle Radar Topography Mission (SRTM) global bathymetry and elevation data at 30 arc s resolution with data voids filled (SRTM30_PLUS) bathymetry database and (bottom) a statistical representation of unresolved abyssal hill topography estimates (Melet et al. 2013b). (d) The vertical structure of dissipation from Brazil Basin observations (thick solid curve) and the Polzin (2009) [Eq. (4)] parameterization of near-field internal tide dissipation (thin solid curve), as well as associated observed values of stratification (N2) and diapycnal diffusivity (Kρ). (e) The impact of the Polzin parameterization in the GFDL CM2G coupled climate model: (top) the Indo-Pacific meridional overturning streamfunction (Sv; 1 Sv = 106 m3 s−1; averaged over the final 100 years of a 1000-yr simulation) using the Polzin (2009) parameterization and (bottom) the differences in Indo-Pacific meridional overturning streamfunction (Sv) between the simulations with the Polzin (2009) parameterization and the St. Laurent et al. (2002) parameterization as implemented by Simmons et al. (2004b) (from Melet et al. 2013a).

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    Far-field internal tide: (a) SSH amplitude (mm) of global mode-1 M2 internal tides from multisatellite altimetry (Zhao et al. 2016). The light blue color indicates regions of high mesoscale activity, which make extraction of internal tides from altimetry difficult. Modeled semidiurnal tidal fluxes and comparison to observations: (b) HYCOM-modeled semidiurnal internal tide barotropic-to-baroclinic conversion rates (background color) and vertically integrated energy flux vectors (black arrows, plotted every 768th grid point for clarity) and (c) depth-integrated semidiurnal mode-1 energy fluxes in HYCOM (red arrows) and high-resolution mooring observations to the north of Hawaii (blue arrows) (Ansong et al. 2017). Impact on thermosteric sea level of using different spatial distributions of remote internal tide energy dissipation in GFDL ESM2G climate model: (d) thermosteric sea level (m) in a reference simulation using a constant background diapycnal diffusivity for remote internal tide dissipation. Anomalies (m) of thermosteric sea level from the reference case in (d) for simulations where (e) all internal tide energy is dissipated locally, over the generation site and (f) 20% of the internal tide energy is dissipated locally and 80% is dissipated uniformly over the ocean basins with a vertical profile proportional to buoyancy squared N2 (Melet et al. 2016).

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    Internal lee waves: (a) observations from DIMES showing (left) turbulent dissipation rates (logarithmic scales from 10−10 to 10−7 W kg−1) for the Phoenix Ridge (circles in right inset) and (right) average height above bottom profiles of turbulent kinetic energy dissipation [see details in St. Laurent et al. (2012)]. (b) Power conversion into lee waves [Nikurashin and Ferrari (2011) used in Melet et al. (2014)],(c) consequences of parameterized lee-wave mixing on the global ocean meridional overturning circulation [Sv; averaged over the final 100 years of 1000-yr simulations, from Melet et al. (2014)], and (d) global map of depth-integrated dissipation due to parameterized topographic wave drag inserted inline into global 1/25° HYCOM simulation, from Trossman et al. (2016).

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    Near-inertial internal waves: (a) observational example from Alford et al. (2012) showing a (top) 2-yr record of wind work and (bottom) near-inertial kinetic energy in the northeastern Pacific. (b) One estimate of global power input (shading) and low-mode NIW energy fluxes (arrows; Simmons and Alford 2012). (c) Impact of near-inertial waves on annual-mean precipitation in ocean climate models: (top) the mean precipitation (mm day−1) from an experiment where the NI flux is set to 0.34 TW and (bottom) the same experiment, but with a doubling of the NI flux to 0.68 TW. The total tropical precipitation in the two experiments differs by less than 1%. An increase in near-inertial energy flux within observational uncertainties ameliorates the double ITCZs in the Atlantic and Pacific Oceans and creates the South Pacific convergence zone, three significant improvements for climate simulations of tropical precipitation.

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Climate Process Team on Internal Wave–Driven Ocean Mixing

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  • 1 Scripps Institution of Oceanography, La Jolla, California
  • | 2 Applied Physics Laboratory, University of Washington, Seattle, Washington
  • | 3 Scripps Institution of Oceanography, La Jolla, California
  • | 4 Goddard Earth Sciences Technology and Research, Greenbelt, and Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, Maryland
  • | 5 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
  • | 6 University of Alaska Fairbanks, Fairbanks, Alaska
  • | 7 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
  • | 8 Scripps Institution of Oceanography, La Jolla, California
  • | 9 Oregon State University, Corvallis, Oregon
  • | 10 National Center for Atmospheric Research,* Boulder, Colorado
  • | 11 Oregon State University, Corvallis, Oregon
  • | 12 Massachusetts Institute of Technology, Cambridge, Massachusetts
  • | 13 Scripps Institution of Oceanography, La Jolla, California
  • | 14 Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey, and Mercator Ocean, Ramonville St. Agne, France
  • | 15 Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey
  • | 16 National Center for Atmospheric Research,* Boulder, Colorado
  • | 17 Northwest Research Associates, Seattle, Washington
  • | 18 University of Victoria, Victoria, British Columbia, Canada
  • | 19 Niels Bohr Institute, Copenhagen, Denmark
  • | 20 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
  • | 21 NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey
  • | 22 Scripps Institution of Oceanography, La Jolla, California
  • | 23 National Center for Atmospheric Research,* Boulder, Colorado
  • | 24 Center for Ocean-Atmospheric Prediction Studies, Florida State University, Tallahassee, Florida
  • | 25 The University of Southern Mississippi, Hattiesburg, Mississippi, and Division of Marine Science, John C. Stennis Space Center, Hancock County, Mississippi
  • | 26 National Center for Atmospheric Research,* Boulder, Colorado
  • | 27 Scripps Institution of Oceanography, La Jolla, California
  • | 28 Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, Michigan
  • | 29 Scripps Institution of Oceanography, La Jolla, California
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Abstract

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 spatiotemporal 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 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (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.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

CURRENT AFFILIATIONS: Musgrave—Woods Hole Oceanographic Intitution, Woods Hole, Massachusetts; Melet—Mercator Ocean, Ramonville Saint-Agne, France

CORRESPONDING AUTHOR: Jennifer A. MacKinnon, jmackinnon@ucsd.edu

Abstract

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 spatiotemporal 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 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (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.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

CURRENT AFFILIATIONS: Musgrave—Woods Hole Oceanographic Intitution, Woods Hole, Massachusetts; Melet—Mercator Ocean, Ramonville Saint-Agne, France

CORRESPONDING AUTHOR: Jennifer A. MacKinnon, jmackinnon@ucsd.edu

The study summarizes recent advances in our understanding of internal wave–driven turbulent mixing in the ocean interior and introduces new parameterizations for global climate ocean models and their climate impacts.

Ocean turbulence influences the transport of heat, freshwater, dissolved gases such as CO2, pollutants, and other tracers. It is central to understanding ocean energetics and reducing uncertainties in global circulation and simulations from climate models. The dissipation of turbulent energy in stratified water results in irreversible diapycnal (across density surfaces) mixing. Recent work has shown that the spatial and temporal inhomogeneity in diapycnal mixing may play a critical role in a variety of climate phenomena. Hence, a quantitative understanding of the physics that drive the distribution of diapycnal mixing in the ocean interior is fundamental to understanding the ocean’s role in climate.

Diapycnal mixing is very difficult to accurately parameterize in numerical ocean models for two reasons. The first one is due to the discrete representation of tracer advection in directions that are not perfectly aligned with isopycnals, which can result in numerically induced mixing from truncation errors that is larger than observed diapycnal mixing (Griffies et al. 2000; Ilıcak et al. 2012). The second reason is related to the intermittency of turbulence, which is generated by complex and chaotic motions that span a large space–time range. Furthermore, this mixing is driven by a wide range of processes with distinct governing physics that create a rich global geography [see MacKinnon et al. (2013c) for a review]. The difficulty is also related to the relatively sparse direct sampling of ocean mixing, whereby sophisticated ship-based measurements are generally required to accurately characterize ocean mixing processes. Nonetheless, we have sufficient evidence from theory, process models, laboratory experiments, and field measurements to conclude that away from ocean boundaries (atmosphere, ice, or the solid ocean bottom), diapycnal mixing is largely related to the breaking of internal gravity waves, which have a complex dynamical underpinning and associated geography. Consequently, in 2010, a Climate Process Team (CPT), funded by the National Science Foundation (NSF) and the National Atmospheric and Oceanic Administration (NOAA), was convened to consolidate knowledge on internal wave–driven turbulent mixing in the ocean, develop new and more accurate parameterizations suitable for global ocean models, and consider the consequences for global circulation and climate. Here, we report on the major findings and products from this CPT.

Ocean internal gravity waves propagate through the stratified interior of the ocean. They are generated by a variety of mechanisms, with the most important being tidal flow over topography, wind variations at the sea surface, and flow of ocean currents and eddies over topography leading to lee waves (see schematic in Fig. 1). As waves propagate horizontally and vertically away from their generation sites, they interact with each other, producing an internal gravity wave continuum consisting of energy in many frequencies and wavenumbers. The waves with high vertical wavenumbers (small vertical scales) are more likely to break, leading to turbulent mixing. The distribution of diapycnal mixing therefore depends on the entire chain of processes shown in Fig. 1.

Fig. 1.
Fig. 1.

Schematic of internal wave mixing processes in the open ocean that are considered as part of this CPT. Tides interact with topographic features to generate high-mode internal waves (e.g., at midocean ridges) and low-mode internal waves (e.g., at tall steep ridges such as the Hawaiian Ridge). Deep currents flowing over topography can generate lee waves (e.g., in the Southern Ocean). Storms cause inertial oscillations in the mixed layer, which can generate both low- and high-mode internal waves (e.g., beneath storm tracks). In the open ocean, these internal waves can scatter off of rough topography and potentially interact with mesoscale fronts and eddies until they ultimately dissipate through wave–wave interactions. Internal waves that reach the shelf and slope can scatter or amplify as they propagate toward shallower water.

Citation: Bulletin of the American Meteorological Society 98, 11; 10.1175/BAMS-D-16-0030.1

A brief history of vertical mixing parameterizations used by ocean models.

Ocean models often approximate diapycnal mixing processes through vertical Fickian diffusion, which takes the mathematical form
e1
where ψ is the tracer concentration, z is the geopotential vertical coordinate, and κ is the diapycnal diffusivity (dimensions of L2T–1, where L is length and T is time). Through the 1990s, global models routinely used space–time constant vertical diffusivities. A notable exception was Bryan and Lewis (1979), who prescribed a horizontally uniform diffusivity that increased with depth, reflecting the observed larger vertical mixing in the deep ocean and reduced mixing in the pycnocline. By the mid-1990s, ocean climate models began to separate diapycnal mixing into surface boundary layer and interior processes. In and near the surface boundary layer, mixing is controlled by a balance between buoyancy input (e.g., heat and freshwater fluxes) and mechanical forcing (e.g., wind) that establish the surface boundary layer and fluxes through it. Climate models of this era used boundary layer schemes such as Gaspar et al. (1990) and Large et al. (1994). In the stably stratified ocean interior, both shear-driven mixing (Pacanowski and Philander 1981; Large et al. 1994) and double-diffusive processes (Large et al. 1994) were parameterized. Gravitational instabilities giving rise to vertical convection were accounted for through a large vertical diffusivity (Large et al. 1994; Klinger et al. 1996) or a convective adjustment scheme (Rahmstorf 1993).

In the deep ocean, a prognostic parameterization for internal tide–driven mixing was introduced by St. Laurent et al. (2002), who combined an estimate of internal tide generation over rough topography with an empirical vertical decay scale for the enhanced turbulence (see the section on “Near-field tidal mixing”). State-of-the-art ocean climate simulations prior to the CPT, as represented by the Geophysical Fluid Dynamics Laboratory (GFDL) and National Center for Atmospheric Research (NCAR) phase 5 of the Coupled Model Intercomparison Project (CMIP5) simulations (Dunne et al. 2012; Danabasoglu et al. 2012), included a version of Eq. (3) (see the section on “Near-field tidal mixing”), along with parameterizations of mixing in the surface (Large et al. 1994) and bottom boundary layers and/or overflows (Legg et al. 2006; Danabasoglu et al. 2010) and mixing from resolved shear (Large et al. 1994; Jackson et al. 2008). These parameterizations produced spatially and temporally varying diapycnal diffusivities, with bottom enhancement and stratification dependence. However, these simulations did not include an energetically consistent representation of internal tide breaking away from the generation site, explicit representation of mixing from internal waves generated by winds and subinertial flows, nor spatial and temporal variability in the dissipation vertical profile. The work described here has revolved around developing and testing energetically consistent, spatially and temporally variable mixing parameterizations. The resulting parameterizations are based upon internal gravity wave dynamics and the patterns of wave generation, propagation, and dissipation.

Overall strategy and philosophy of the CPT approach.

As with previous CPTs, we have found that parameterizations are most productively developed when there is a broad base of knowledge that is in a state of readiness to be consolidated, implemented, and tested. Much of the basic research described here was published or nearing completion at the time this project started, allowing for a focused effort on parameterization development, model implementation, and global model testing. A key CPT component was the inclusion of four dedicated postdoctoral scholars, who formed “the glue” to bridge the expertise of different principal investigators, promoting projects at the intersection of theory and models, observations, and simulations, while gaining valuable broad training and networking.

One of the important tenets of the CPT is the consistent use of energy, power, and the turbulent kinetic energy (KE) dissipation rate ε (dimensions of L2T−3), rather than diapycnal diffusivity, as the currency of turbulent mixing; ε describes the rate at which turbulence dissipates mechanical energy at the smallest scales. It is typically related to a diapycnal diffusivity through a dimensionless mixing efficiency Г, following Osborn (1980):
e2
where N2 is the squared buoyancy frequency. Equation (2) shows that keeping the diffusivity fixed in a world with changing stratification implies changes in energy dissipation in ways that are not always consistent with the physical processes supplying energy for dissipation. We can overcome this problem by formulating parameterizations directly in terms of ε. This approach also has the advantage of providing a transparent connection to dynamical processes driving mixing, since the downscale energy cascade can be directly linked to constraints of total power available for turbulence and other facets of ocean energetics (e.g., St. Laurent and Simmons 2006; Ferrari and Wunsch 2009). The topic of an appropriate value for mixing efficiency has had a resurgence of interest in recent years. Some theoretical and numerical studies suggest that a mixing efficiency that is systematically lower in areas of low ocean stratification might bias the type of global mixing estimates presented here and require modifications to model parameterizations (Mashayek et al. 2013; Venayagamoorthy and Koseff 2016; Salehipour et al. 2016). A careful evaluation of mixing efficiency was not part of the CPT work, and a thorough discussion is beyond the scope of this paper. Interested readers are instead referred to recent reviews such as Peltier and Caulfield (2003) and Gregg et al. (2018).

GLOBAL PATTERNS AND CONSTRAINTS.

Many of the early parameterizations described in the section titled “A brief history of vertical mixing parameterizations used by ocean models” were motivated by individual process experiments or observational studies. At the same time, the novel observations, theories, and model results that fundamentally drive the field forward frequently arise unexpectedly from programs funded by many agencies. For example, the long-range propagation of coherent internal tides was discovered in both the Acoustic Thermometry of Ocean Climate (ATOC; Dushaw et al. 1995) and satellite altimeter (Ray and Mitchum 1996) datasets fortuitously; neither mission was set up with a focus on internal tides.

Another factor contributing to the readiness of this CPT was the increased use of new techniques to infer mixing rates indirectly from a wide variety of data sources, allowing the rich patterns like those in Fig. 2 to emerge. There are now enough direct microstructure and indirect estimates of turbulent dissipation rates and diapycnal diffusivities to examine depth and geographical patterns, temporal variability, and global budgets (Waterhouse et al. 2014). These patterns in turn have inspired new insights on the underlying dynamics driving and energetically supplying small-scale turbulence and provided valuable constraints on modeled turbulent mixing rates. Compilation of both direct microstructure measurements and indirect estimates of turbulence is discussed in the section titled “Tools and techniques.” Here, we briefly describe recent results related to global patterns and statistics.