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Carsten Eden

Abstract

In the generalized temporal residual mean (TRM-G) framework, the diapycnal rotational eddy fluxes are defined such that the residual divergent diapycnal eddy flux is related to irreversible changes of buoyancy, that is, diapycnal mixing (or temporal changes of variance and higher order moments) only. Here, it is discussed that for the isopycnal eddy fluxes a similar physically meaningful property exists: rotational isopycnal eddy fluxes can be defined in TRM-G such that the residual divergent part of the flux is related to removal of mean available potential energy and transfer to eddy energy only, that is, to the classical picture of eddy activity. In two idealized eddying models, both featuring strong mesoscale eddy-driven zonal jets, large isopycnal eddy fluxes are circulating at the flanks of the jets. The residual isopycnal eddy fluxes, however, are predominantly meridional and thus downgradient, indicating vanishing anisotropic mixing of isopycnal thickness, consistent with the classical picture of eddy-driven overturning by baroclinic instability in jets. Using isotropic thickness mixing—standard in ocean models—appears therefore as sufficient in this model diagnosis.

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Carsten Eden

Abstract

Three alternative methods of averaging the general conservation equation of a fluid property in a turbulent flow in the Boussinesq approximation are compared: Lagrangian, residual, and isopycnal (or semi-Lagrangian) mean. All methods differentiate consistently but in different ways between effects of advection and irreversible changes of the average property. Because the three average properties differ, the mean transport velocities and the mean irreversible changes in the mean conservation equation differ in general.

The Lagrangian and the semi-Lagrangian (or isopycnal) mean frameworks are shown to be approximately equivalent only for weak irreversible changes, small amplitudes of the turbulent fluctuations, and particle excursion predominantly along the mean property gradient. In that case, the divergent Stokes velocity of the Lagrangian mean framework can be replaced in the Lagrangian mean conservation equation by a nondivergent, three-dimensional version of the quasi-Stokes velocity of T. J. McDougall and P. C. McIntosh, for which a closed analytical form for the streamfunction in terms of Eulerian mean quantities is given.

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Carsten Eden

Abstract

Following a suggestion by Tailleux, a consistent formulation of internal energy, the first law of thermodynamics, and the thermodynamic potentials for an ocean in Boussinesq approximation with a nonlinear equation of state is given. A modification of the pressure work in the first law is the only necessary modification from which all thermodynamic potentials and thermodynamic relations follow in a consistent way. This treatment of thermodynamics allows for a closed and explicit formulation of conservation equations for dynamic and potential reservoirs of both enthalpy and internal energy, which differentiate approximately reversible from irreversible effects on internal energy, and allows for a formulation of a closed energy cycle on which energetically consistent ocean models can be based on.

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Nils Brüggemann and Carsten Eden

Abstract

In this study, it is investigated how ageostrophic dynamics generate an energy flux toward smaller scales. Numerical simulations of baroclinic instability are used with varying dynamical conditions ranging from quasigeostrophic balance to ageostrophic flows. It turns out that dissipation at smaller scales by viscous friction is much more efficient if the flow is dominated by ageostrophic dynamics than in quasigeostrophic conditions. In the presence of ageostrophic dynamics, an energy flux toward smaller scales is observed while energy is transferred toward larger scales for quasigeostrophic dynamics. Decomposing the velocity field into its rotational and divergent components shows that only the divergent velocity component, which becomes stronger for ageostrophic flows, features a downscale flux. Variation of the dynamical conditions from ageostrophic dynamics to quasigeostrophic balanced flows shows that the forward energy flux and therefore the small-scale dissipation decreases as soon as the horizontal divergent velocity component decreases. A functional relationship between the small-scale dissipation and the local Richardson number is estimated. This functional relationship is used to obtain a global estimate of the small-scale dissipation of 0.31 ± 0.23 TW from a high-resolution realistic global ocean model. This emphasizes that an ageostrophic direct route to dissipation might be of importance in the ocean energy cycle.

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Carsten Eden and Jürgen Willebrand

Abstract

A model of the Atlantic Ocean was forced with decadal-scale time series of surface fluxes taken from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis. The bulk of the variability of the oceanic circulation is found to be related to the North Atlantic oscillation (NAO). Both realistic experiments and idealized sensitivity studies with the model show a fast (intraseasonal timescale) barotropic response and a delayed (timescale about 6–8 yr) baroclinic oceanic response to the NAO. The fast response to a high NAO constitutes a barotropic anticyclonic circulation anomaly near the subpolar front with a substantial decrease of the northward heat transport and an increase of northward heat transport in the subtropics due to changes in Ekman transport. The delayed response is an increase in subpolar heat transport due to enhanced meridional overturning and due to a spinup of the subpolar gyre. The corresponding subpolar and subtropical heat content changes could in principle act as an immediate positive feedback and a delayed negative feedback to the NAO.

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Lars Czeschel and Carsten Eden

Abstract

In a series of large-eddy simulations with different forcing, we study the generation of internal gravity waves at the base of the surface mixed layer. If turbulent eddies act as obstacles and undulate the base of the mixed layer, horizontal velocities associated with inertial oscillations and Ekman dynamics can move the obstacles relative to the stratified interior, exciting internal gravity waves similar to lee waves. We find strong evidence that the “obstacle mechanism” is able to excite large parts of the internal wave spectrum, including near inertial waves. The high-frequency part of the excited wave spectrum is filtered by the increased stratification in the transition layer between the mixed layer and lower stratified interior, but a substantial part of the wave spectrum is able to overcome this barrier, hence contributing to interior mixing. The magnitude of the downward-radiated energy below the transition layer depends on the source of turbulence, but we show that the obstacle mechanism, especially under destabilizing heat fluxes, has the potential to contribute considerably to the internal wave energy in the interior ocean.

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Dirk Olbers and Carsten Eden

Abstract

A new type of ocean general circulation model with simplified physics is described and tested for various simple wind-driven circulation problems. The model consists of the vorticity balance of the depth-averaged flow and a hierarchy of equations for “vertical moments” of density and baroclinic velocity. The first vertical density moment is the (vertically integrated) potential energy, which is used to describe the predominant link between the barotropic and the baroclinic oceanic flow in the presence of sloping topography. Tendency equations for the vertical moments of density and baroclinic velocity and an appropriate truncation of the coupled hierarchy of moments are derived that, together with the barotropic vorticity balance, yield a closed set of equations describing the barotropic–baroclinic interaction (BARBI) model of the oceanic circulation. Idealized companion experiments with a numerical implementation of the BARBI model and a primitive equation model indicate that wave propagation properties and baroclinic adjustments are correctly represented in BARBI in midlatitudes as well as in equatorial latitudes. Furthermore, a set of experiments with a realistic application to the Atlantic/Southern Ocean system reproduces important aspects that have been previously reported by studies of gyre circulations and circumpolar currents using full primitive equation models.

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M. Jochum and Carsten Eden

Abstract

Coupled GCM simulations are analyzed to quantify the dynamic effect of Southern Ocean (SO) winds on transports in the ocean. It is found that the closure for skew diffusivity in the non-eddy-resolving ocean model does not allow for a realistic eddy saturation of the zonal transports in the SO in response to the wind changes and that eddy compensation of the meridional transports in the SO is underestimated too. Despite this underestimated eddy compensation in the SO, however, and in contrast to previous suggestions, the Atlantic meridional overturning circulation (AMOC) strength is almost insensitive to SO winds. In the limit of weak SO winds the AMOC waters upwell not in the SO but rather in the tropical Indo-Pacific. Through their effect on sea ice, weaker SO winds also lead to less production of Antarctic Bottom Water and therefore a deeper and stronger AMOC.

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Carsten Eden and Dirk Olbers

Abstract

The recently proposed Internal Wave Dissipation, Energy and Mixing (IDEMIX) model, describing the propagation and dissipation of internal gravity waves in the ocean, is extended. Compartments describing the energy contained in the internal tides and the near-inertial waves at low, vertical wavenumber are added to a compartment of the wave continuum at higher wavenumbers. Conservation equations for each compartment are derived based on integrated versions of the radiative transfer equation of weakly interacting waves. The compartments interact with each other by the scattering of tidal energy to the wave continuum by triad wave–wave interactions, which are strongly enhanced equatorward of 28° due to parametric subharmonic instability of the tide and by scattering to the continuum of both tidal and near-inertial wave energy over rough topography and at continental margins. Global numerical simulations of the resulting model using observed stratification, forcing functions, and bottom topography yield good agreement with available observations.

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Dirk Olbers and Carsten Eden

Abstract

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 energy density variables in physical space. A further simplification results in a single partial differential equation 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, the wave energy is forced by wind-driven near-inertial motions and baroclinic tides, radiating waves from the respective boundary layers at the surface and the bottom into the ocean interior. The model predicts plausible magnitudes and three-dimensional structures of internal wave energy, dissipation rates, and diapycnal 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.

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