O cean turbulence influences the transport of heat, freshwater, dissolved gases such as CO 2 , 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. 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.

Two global ocean models ranging in horizontal resolution from 1/12° to 1/48° are used to study the space and time scales of sea surface height (SSH) signals associated with internal gravity waves (IGWs). Frequency‐horizontal wavenumber SSH spectral densities are computed over seven regions of the world ocean from two simulations of the HYbrid Coordinate Ocean Model (HYCOM) and three simulations of the Massachusetts Institute of Technology general circulation model (MITgcm). High wavenumber, high‐frequency SSH variance follows the predicted IGW linear dispersion curves. The realism of high‐frequency motions (> 0.87  cpd) in the models is tested through comparison of the frequency spectral density of dynamic height variance computed from the highest‐resolution runs of each model (1/25° HYCOM and 1/48° MITgcm) with dynamic height variance frequency spectral density computed from nine in situ profiling instruments. These high‐frequency motions are of particular interest because of their contributions to the small‐scale SSH variability that will be observed on a global scale in the upcoming Surface Water and Ocean Topography (SWOT) satellite altimetry mission. The variance at supertidal frequencies can be comparable to the tidal and low‐frequency variance for high wavenumbers (length scales smaller than ∼50 km), especially in the higher‐resolution simulations. In the highest‐resolution simulations, the high‐frequency variance can be greater than the low‐frequency variance at these scales.

In recent years, high-resolution ("eddying") global three-dimensional ocean general circulation models have begun to include astronomical tidal forcing alongside atmospheric forcing. Such models can carry an internal tide field with a realistic amount of nonstationarity, and an internal gravity wave continuum spectrum that compares more closely with observations as model resolution increases. Global internal tide and gravity wave models are important for understanding the three-dimensional geography of ocean mixing, for operational oceanography, and for simulating and interpreting satellite altimeter observations. Here we describe the most important technical details behind such models, including atmospheric forcing, bathymetry, astronomical tidal forcing, self-attraction and loading, quadratic bottom boundary layer drag, parameterized topographic internal wave drag, shallow-water tidal equations, and a brief summary of the theory of linear internal gravity waves. We focus on simulations run with two models, the HYbrid Coordinate Ocean Model (HYCOM) and the Massachusetts Institute of Technology general circulation model (MITgcm). We compare the modeled internal tides and internal gravity wave continuum to satellite altimeter observations, moored observational records, and the predictions of the Garrett-Munk (1975) internal gravity wave continuum spectrum. We briefly examine specific topics of interest, such as tidal energetics, internal tide nonstationarity, and the role of nonlinearities in generating the modeled internal gravity wave continuum. We also describe our first attempts at using a Kalman filter to improve the accuracy of tides embedded within a general circulation model. We discuss the challenges and opportunities of modeling stationary internal tides, non-stationary internal tides, and the internal gravity wave continuum spectrum for satellite altimetry and other applications. Introductionhis book chapter is about global modeling of oceanic internal tides and the oceanic internal gravity wave continuum. The chapter focuses on hydrodynamical modeling, rather than empirical modeling, of such motions. Due to the operational oceanography theme of the book in which this chapter resides, we focus on high-spatial-resolution numerical models run over relatively short time scales-i.e., simulations that could form the dynamical backbone of operational models-rather than on lower-resolution models run over decades or centuries for climate forecasting purposes. In this introductory section, after defining internal gravity waves and internal tides, we discuss the motivation for, requirements for, and history of global modeling of internal tides and the internal gravity wave continuum. A subsequent section focuses on the technical details underlying such models, such as atmospheric forcing, bathymetry, astronomical tidal forcing, self-attraction and loading, quadratic bottom boundary layer drag, parameterized topographic internal wave drag, shallow-water tidal equations, and a brief synopsis of internal wave theor...

A global high-resolution ocean circulation model forced by atmospheric fields and the M 2 tidal constituent is used to explore plausible scenarios for the damping of low-mode internal tides. The plausibility of different damping scenarios is tested by comparing the modeled barotropic tides with TPXO8, a highly accurate satellite-altimetry-constrained tide model, and by comparing the modeled coherent baroclinic tide amplitudes against along-track altimetry. Five scenarios are tested: (1) a topographic internal wave drag, argued here to represent the breaking of unresolved high vertical modes, applied to the bottom flow (default configuration), (2) a wave drag applied to the barotropic flow, (3) absence of wave drag, (4) a substantial increase in quadratic bottom friction along the continental shelves (with wave drag turned off), and (5) application of wave drag to the barotropic flow at the same time that quadratic bottom friction is substantially increased along the shelves. Of the scenarios tested here, the default configuration (1) yields the most accurate tides. In all other scenarios (2-5), the lack of damping on open ocean baroclinic motions yields baroclinic tides that are too energetic and travel too far from their sources, despite the presence of a vigorous mesoscale eddy field which can scatter and decohere internal tides in the model. The barotropic tides are also less accurate in the absence of an open ocean damping on barotropic motions, that is, in scenarios (3) and (4). The results presented here suggest that low-mode internal tides experience substantial damping in the open ocean.

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.