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Friederike Pollmann

Abstract

A key ingredient of energetically consistent ocean models is the parameterized link between small-scale turbulent mixing, an important energy source of large-scale ocean dynamics, and internal gravity wave energetics. Theory suggests that this link depends on the wave field’s spectral characteristics, but because of the paucity of suitable observations, its parameterization typically relies on a model spectrum [Garrett–Munk (GM)] with constant parameters. Building on the so-called “finestructure method,” internal gravity wave spectra are derived from vertical strain profiles obtained from Argo floats to provide a global estimate of the spatial and temporal variability of the GM model’s spectral parameters. For spectral slopes and wavenumber scales, the highest variability and the strongest deviation from the model’s canonical parameters are observed in the North Atlantic, the northwest Pacific, and the Southern Ocean. Internal wave energy levels in the upper ocean are well represented by the GM model value equatorward of approximately 50°, while they are up to two orders of magnitude lower poleward of this latitude. The use of variable spectral parameters in the energy level calculation hides the seasonal cycle in the northwest Pacific that was previously observed for constant parameters. The global estimates of how the GM model’s spectral parameters vary in space and time are hence expected to add relevant detail to various studies on oceanic internal gravity waves, deepening the understanding of their energetics and improving parameterizations of the mixing they induce.

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Friederike Pollmann, Fabien Roquet, and Gurvan Madec

Abstract

Large-scale overturning cells in the ocean typically combine an essentially horizontal surface branch and an interior branch below, where the circulation spans both horizontal and vertical scales. The aim of this study is to analyze the impact of this asymmetry between the two branches by “folding” a one-dimensional thermohaline loop, such that its lower part remains vertical while its upper part is folded down into the horizontal plane. It is found that both the transitory response and the distribution of thermohaline properties are modified significantly when the loop is folded. In some cases, velocity oscillations are induced during the spinup that were not seen in the unfolded case. This is because a circular loop allows for compensations between the density torques produced above and below the heat forcing level, while such compensations are not possible in the folded loop because of the horizontal direction of the surface circulation. Furthermore, the dynamical effects associated with nonlinearities of the equation of state are significantly altered by the folding. Cabbeling tends to decelerate the flow in the folded loop, instead of accelerating it as in the circular case, and can also act to dampen velocity oscillations. Thermobaricity also alters the loop circulation, although comparatively less.

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Carsten Eden, Friederike Pollmann, and Dirk Olbers

Abstract

Spectral energy transfers by internal gravity wave–wave interactions for given empirical energy spectra are evaluated numerically from the kinetic equation that is derived from the assumption of weak interactions. Wave spectrum parameters, such as bandwidth, spectral slope, and Coriolis frequency f, are varied, as is the spectral resolution. In agreement with previous studies, we find in all cases a forward energy cascade toward smaller vertical and horizontal wavelengths. Energy sinks due to the transfers are predominantly at frequencies between 2f and 3f. While the mechanism of the energy transfer differs partly from findings of previous studies, a parameterization for internal wave dissipation—which is used in the fine structure parameterization to estimate dissipation and mixing rates from observations—agrees well with the numerical evaluation of the energy transfers. We also find a dependency of the energy transfers on the spectral slope, offering the possibility to decrease the bias of the fine structure parameterization by improving the knowledge about the spatial variations of this (and other) spectral parameter.

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Friederike Pollmann, Carsten Eden, and Dirk Olbers

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Small-scale turbulent mixing affects large-scale ocean processes such as the global overturning circulation but remains unresolved in 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, Energy and Mixing (IDEMIX) predicts the internal wave energy, dissipation rates, and diapycnal 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 reproduces the magnitude and the large-scale variations of the Argo-derived dissipation rate and energy level 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 additional physical detail and by better constraining the processes already included in the model. A prominent 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.

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Dirk Olbers, Friederike Pollmann, and Carsten Eden

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Barotropic tidal oscillations over seafloor topography generate baroclinic tides that may be damped in turn via nonlinear triad interactions with internal gravity waves, fueling the ambient wave field. We derive the kinetic equations for this tidal damping and the energy transfer to the ambient wave field and compute damping times and energy transfer rates for the M2 tide and a Garrett–Munk-like ambient wave field. We show that parametric subharmonic instability (PSI) interactions are important, where the tide interacts resonantly with two background waves, each of half the tidal frequency. PSI is restricted to the latitude belt 28.8°N/S and yields under typical conditions damping times of about 20 days for tides with low vertical wavenumber. Damping times decrease with equivalent mode number j roughly as 1/j 2. Outside the critical latitudes PSI is not possible, and damping times are from one to two orders of magnitude larger. The energy transfer to the ambient wave field is concentrated at half the tidal frequency ω at all latitudes within the critical latitude belt. Outside, the transfer is much smaller and peaks at ω + f and N. An estimation of the tidal spectral transfer on the global scale is hampered by insufficient knowledge of the baroclinic energy distribution over the vertical modes. Using results from a numerical circulation model with tidal forcing, we find an energy transfer from the tide to the ambient wave field of typically 0.3 TW, about half of what is currently proposed for the conversion of barotropic to baroclinic energy.

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Carsten Eden, Friederike Pollmann, and Dirk Olbers

Abstract

Energy transfers by internal gravity wave–wave interactions in spectral space are diagnosed from numerical model simulations initialized with realizations of the Garrett–Munk spectrum in physical space and compared with the predictions of the so-called scattering integral or kinetic equation. Averaging the random phase of the initialization, the energy transfers by wave–wave interactions in the model agree well with the predictions of the kinetic equation for certain ranges of frequency and wavenumbers. This validation allows now, in principle, the use of the energy transfers predicted by the kinetic equation to design a global spectral energy budget for internal gravity waves in the ocean where divergences of energy transports in physical and spectral space balance forcing, dissipation, the energy transfers by the wave–wave interactions, or the rate of change of the spectral wave energy. First global estimates show indeed accumulation of the wave energy in a range of latitude ϕ consistent with tidal waves at frequency ω T propagating toward the latitudinal window where 2 < ω T/f(ϕ) < 3, as predicted by the kinetic equation.

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