Description: Two surface waves can interact to produce an internal gravity wave by nonlinear resonant coupling. The process has been called spontaneous creation (SC) because it operates without internal waves being initially present. Previous studies have shown that the generated internal waves have high frequency close to the local Brunt–Väisälä frequency and wavelengths that are much larger than those of the participating surface waves, and that the spectral transfer rate of energy to the internal wave field is small compared to other generation processes. The aim of the present analysis is to provide a global map of the energy transfer into the internal wave field by surface–internal wave interaction, which is found to be about 10 23 TW in total, based on a realistic wind-sea spectrum (depending on wind speed), mixed layer depths, and stratification below the mixed layer takenfrom a state-of-the-art numericalocean model.Unlikepreviouscalculationsof the spectral transfer rate based on a vertical mode decomposition, the authors use an analytical framework that directly derives the energy flux of generated internal waves radiating downward from the mixed layer base. Since the radiated waves are of high frequency, they are trapped and dissipated in the upper ocean. The radiative flux thus feeds only a small portion of the water column, unlike in cases of wind-driven near-inertial waves that spread over the entire ocean depth before dissipating. The authors also give an estimate of the interior dis- sipation and implied vertical diffusivities due to this process. In an extended appendix, they review the modal description of the SC interaction process, completed by the corresponding counterpart, the modulation in- teraction process (MI), where a preexisting internal wave is modulated by a surface wave and interacts with another one. MI establishes a damping of the internal wave field, thus acting against SC. The authors show that SC overcomes MI for wind speeds exceeding about 10m/s.

Description: Small-scale turbulent mixing affects large-scale ocean processes such as the global overturning circulation but remains unresolvedin ocean models. Since the breaking of internal gravity waves is a major source of this mixing, consistent parameterizations take internal wave energetics into account. The model Internal Wave Dissipation,EnergyandMixing(IDEMIX)predictstheinternalwaveenergy,dissipationrates,anddiapycnal diffusivities based on a simplification of the spectral radiation balance of the wave field and can be used as a mixing module in global numerical simulations. In this study, it is evaluated against finestructure estimates of turbulent dissipation rates derived from Argo float observations. In addition, a novel method to compute internal gravity wave energy from finescale strain information alone is presented and applied. IDEMIX well reproducesthe magnitudeandthelarge-scalevariations ofthe Argo-derived dissipationrateandenergylevel estimates. Deficiencies arise with respect to the detailed vertical structure or the spatial extent of mixing hot spots. This points toward the need to improve the forcing functions in IDEMIX, both by implementing additionalphysicaldetailandbybetterconstrainingtheprocessesalreadyincludedinthemodel.Aprominent example is the energy transfer from the mesoscale eddies to the internal gravity waves, which is identified as an essential contributor to turbulent mixing in idealized simulations but needs to be better understood through the help of numerical, analytical, and observational studies in order to be represented realistically in ocean models.

Description: An energetically consistent model for the diapycnal diffusivity induced by breaking of internal gravity waves is proposed and tested in local and global settings. The model [Internal Wave Dissipation, Energy and Mixing (IDEMIX)] is based on the spectral radiation balance of the wave field, reduced by integration over the wavenumber space, which yields a set of balances for energydensity variables in physical space. A further simplification results in a single partial differentialequation for the total energy density of the wave field. The flux of energy to high vertical wavenumbers is parameterized by a functional derived from the wave–wave scattering integral of resonant wave triad interactions, which also forms the basis for estimates of dissipation rates and related diffusivities of ADCP and hydrography fine-structure data. In the current version of IDEMIX,thewaveenergyisforcedbywind-drivennear-inertialmotionsandbaroclinictides,radiatingwaves from the respectiveboundarylayers at the surfaceand the bottom into the ocean interior. The model predicts plausible magnitudes and three-dimensional structures of internal wave energy, dissipation rates, and dia- pycnal diffusivities in rough agreement to observational estimates. IDEMIX is ready for use as a mixing module in ocean circulation models and can be extended with more spectral components.

Description: Simple idealized layered models and primitive equation models show that the meridional gradient of the zonally averaged pressure has no direct relation with the meridional flow. This demonstrates a contradiction in an often-used parameterization in zonally averaged models. The failure of this parameterization reflects the inconsistency between the model of Stommel and Arons and the box model of Stommel, as previously pointed out by Straub. A new closure is proposed. The ocean is divided in two dynamically different regimes: a narrow western boundary layer and an interior ocean; zonally averaged quantities over these regions are considered. In the averaged equations three unknowns appear: the interior zonal pressure difference Dpi, the zonal pressure difference Dpb of the boundary layer, and the zonal velocity ud at the interface between the two regions. Here Dpi is parameterized using a frictionless vorticity balance, Dpb by the difference of the mean pressure in the interior and western boundary, and ud by the mean zonal velocity of the western boundary layer. Zonally resolved models, a layer model, and a primitive equation model validate the new parameterization by comparing with the respective zonally averaged counterparts. It turns out that the zonally averaged models reproduce well the buoyancy distribution and the meridional flow in the zonally resolved model versions with respect to the mean and time changes.

Description: Possibilities to construct a realistic quasi-global ocean model in Boussinesq approximation with a closed energy cycle are explored in this study. In such a model, the energy related to the mean variables would interact with all parameterizedforms of energy withoutany spuriousenergy sources or sinks. This means that the energy available for interior mixing in the ocean would be only controlled by external energy input from the atmosphere and the tidal system and by internal exchanges. In the current implementation of such a consistent model, however, numerical biases and sources due to the nonlinear equation of state violate energyconservation,resultinginanoverallresidualuptoseveralpercent.Inthree(approximately)consistent model versions with different scenarios of mesoscale eddy dissipation, the parameterized internal wave field providesbetween2and3TWforinteriormixingfromthetotalexternalenergyinputofabout4TW,suchthat a transfer between 0.3 and 0.4 TW into mean potential energy contributes to drive the large-scale circulation in the model. In contrast, the wind work on the mean circulation contributes by about 1.8 TW to the large- scale circulation in all model versions. It is shown that the consistent model versions are more energetic than standard and inconsistent model versions and in better agreement with hydrographic observations.

Description: The generation of internal gravity waves from an initially geostrophically balanced flow is diagnosed in nonhydrostatic numerical simulations of shear instabilities for varied dynamical regimes. A nonlinear decomposition method up to third order in the Rossby number (Ro) is used as the diagnostic tool for a consistent separation of the balanced and unbalanced motions in the presence of their nonlinear coupling. Wave emission is investigated in an Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable modes are used to initialize the flow in different simulations. Gravity wave emission is in general very weak over a range of values for Ro. At sufficiently high Ro, however, when the condition for symmetric instability is satisfied with negative values of local potential vorticity, significant wave emission is detected even at the lowest order. This is related to the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves. Thus, gravity waves are excited from the instability of the balanced mode to lowest order only if the condition of symmetric instability is satisfied and ageostrophic unstable modes obtain finite growth rates.