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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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Nils Brüggemann and Carsten Eden

Abstract

In this study, the authors discuss two different parameterizations for the effect of mixed layer eddies, one based on ageostrophic linear stability analysis (ALS) and the other one based on a scaling of the potential energy release by eddies (PER). Both parameterizations contradict each other in two aspects. First, they predict different functional relationships between the magnitude of the eddy fluxes and the Richardson number (Ri) related to the background state. Second, they also predict different vertical structure functions for the horizontal eddy fluxes. Numerical simulations for two different configurations and for a large range of different background conditions are used to evaluate the parameterizations. It turns out that PER is better suited to capture the Ri dependency of the magnitude of the eddy fluxes. On the other hand, the vertical structure of the meridional eddy fluxes predicted by ALS is more accurate than that of PER, while the vertical structure of the vertical eddy fluxes is well predicted by both parameterizations. Therefore, this study suggests the use of the magnitude of PER and the vertical structure functions of ALS for an improved parameterization of mixed layer eddy fluxes.

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Nils Brüggemann, Carsten Eden, and Dirk Olbers

Abstract

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 Δpi, the zonal pressure difference Δpb of the boundary layer, and the zonal velocity uδ at the interface between the two regions. Here Δpi is parameterized using a frictionless vorticity balance, Δpb by the difference of the mean pressure in the interior and western boundary, and uδ 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.

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Nils Brüggemann and Caroline A. Katsman

Abstract

In this study, we explore the downward branch of the Atlantic meridional overturning circulation (AMOC) from a perspective in depth space (Eulerian downwelling) as well as from a perspective in density space (diapycnal downwelling). Using an idealized model, we focus on the role of eddying marginal seas, where dense water is formed by deep convection due to an intense surface heat loss. We assess where diapycnal mass fluxes take place, investigate the pathways of dense water masses, and elucidate the role of eddies. We find that there are fundamental differences between the Eulerian and diapycnal downwelling: the strong Eulerian near-boundary downwelling is not associated with substantial diapycnal downwelling; the latter takes place in the interior and elsewhere in the boundary current. We show that the diapycnal downwelling appears to be more appropriate to describe the pathways of water masses. In our model, dense water masses are exported along two routes: those formed in the upper part of the boundary current are exported directly; those formed in the interior move toward the boundary along isopycnals due to eddy stirring and are then exported. This study thus reveals a complex three-dimensional view of the overturning in a marginal sea, with possible implications for our understanding of the AMOC.

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Manita Chouksey, Carsten Eden, and Nils Brüggemann

Abstract

We aim to diagnose internal gravity waves emitted from balanced flow and investigate their role in the downscale transfer of energy. We use an idealized numerical model to simulate a range of baroclinically unstable flows to mimic dynamical regimes ranging from ageostrophic to quasigeostrophic flows. Wavelike signals present in the simulated flows, seen for instance in the vertical velocity, can be related to gravity wave activity identified by frequency and frequency–wavenumber spectra. To explicitly assign the energy contributions to the balanced and unbalanced (gravity) modes, we perform linear and nonlinear modal decomposition to decompose the full state variable into its balanced and unbalanced counterparts. The linear decomposition shows a reasonable separation of the slow and fast modes but is no longer valid when applied to a nonlinear system. To account for the nonlinearity in our system, we apply the normal mode initialization technique proposed by Machenhauer in 1977. Further, we assess the strength of the gravity wave activity and dissipation related to the decomposed modes for different dynamical regimes. We find that gravity wave emission becomes increasingly stronger going from quasigeostrophic to ageostrophic regime. The kinetic energy tied to the unbalanced mode scales close to Ro2 (or Ri−1), with Ro and Ri being the Rossby and Richardson numbers, respectively. Furthermore, internal gravity waves dissipate predominantly through small-scale dissipation, which emphasizes their role in the downscale energy transfer.

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