ALBERT

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 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.

Description: 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.

Description: 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.

Description: This thesis aims to provide a better understanding of the role of ageostrophic processes in ocean dynamics by analyzing three different case studies - the large-scale circulation, the mixing of eddies in the upper ocean and the ability of ageostrophic dynamics to feature a direct route to dissipation. Furthermore, it examines to which extent parameterizations can yield adequate simplifications of the more complex ageostrophic phenomena. The first case study concerns zonally averaged models of the large-scale meridional overturning circulation. Ageostrophic processes need to be considered here to correctly describe the dynamics in western boundary currents, while the interior ocean can be described by a geostrophic balance. Both, interior geostrophic and ageostrophic dynamics in the western boundary current need to be considered for the zonally averaged flow. It is illustrated that many zonally averaged models which do not consider both regimes show dynamical inconsistencies in comparison with zonally resolved models. A new parameterization for the zonally averaged flow is developed, in which both dynamical regimes are directly represented and which does not suffer from those inconsistencies. Zonally resolved models show good agreement with the new zonally averaged model, demonstrating that the new parameterization is dynamically consistent. The second case study deals with the mixing of eddies in the upper ocean. Since the stratification is often weak within the mixed layer, ageostrophic processes are likely to occur here. Two parameterizations for the eddy mixing are compared, which especially take ageostrophic dynamics into account. The first is based on linear stability analysis while the second is based on a scaling of the potential energy release. Numerical simulations for a wide range of dynamical conditions are used to diagnose the ability of these parameterizations to predict the mixing effect of the eddies. It turns out that the mean difference between both parameterizations and the diagnosed eddy fluxes is less than a factor of two. While the parameterization based on linear stability analysis performs slightly better in an equilibrated forced-dissipative flow scenario, the parameterization based on the scaling of the potential energy release performs better in a scenario of a re-stratifying density front. In addition it is found that the vertical structure of the eddy fluxes is better described by the former in both scenarios. The third case study investigates the role of ageostrophic dynamics for kinetic energy dissipation. Numerical simulations for a wide range of different dynamical conditions characterized by their Richardson number are used to diagnose the energy flux in wavenumber space. It is found that quasi-geostrophic dynamics feature an upscale kinetic energy flux while kinetic energy is transferred towards smaller scales for ageostrophic dynamics. Horizontal divergent velocities evolving under ageostrophic conditions can be identified to be responsible for the downscale flux. An important consequence is that the small-scale dissipation is larger in the presence of ageostrophic dynamics. To quantify the effect of ageostrophic dynamics on the small-scale dissipation, its dependency on the Richardson number is investigated and a power law relating the energy dissipation with the Richardson number is estimated.

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 Delta p(i), the zonal pressure difference Delta p(b) of the boundary layer, and the zonal velocity us at the interface between the two regions. Here Delta p(i) is parameterized using a frictionless vorticity balance, Delta p(b), by the difference of the mean pressure in the interior and western boundary, and u(delta) 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: 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.