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## Abstract

The behavior of the solution to a two-layer wind-driven model in a multiply connected domain with bottom topography imitating the Southern Ocean is described. The abyssal layer of the model is forced by interfacial friction, crudely simulating the effect of eddies. The analysis of the low friction regime is based on the method of characteristics. It is found that characteristics in the upper layer are closed around Antarctica, while those in the lower layer are blocked by solid boundaries. The momentum input from wind in the upper layer is balanced by lateral and interfacial friction and by interfacial pressure drag. In the lower layer the momentum input from interfacial friction and interfacial pressure drag is balanced by topographic pressure drag. Thus, the total momentum input by the wind is balanced by upper-layer lateral friction and by topographic pressure drag.

In most of the numerical experiments the circulations in the two layers appear to be decoupled. The decoupling can be explained by the JEBAR term, whose magnitude decreases as interfacial friction increases. The solution tends toward the barotropic one if the interfacial friction is large enough to render the JEBAR term to be no larger than the wind stress curl term in the potential vorticity equation. The change of regimes occurs when the value of the interfacial friction coefficient *Îº* equals *Îº*
_{0} = *H*
_{1}f_{0}(*L*
_{y}/*L*
_{x})(*A*/*H*
_{0}), where *f*
_{0} is the mean value of the Coriolis parameter; *L*
_{y} and *L*
_{x} are the meridional and zonal domain dimensions; *H*
_{0} and *H*
_{1} are the mean depths of the ocean and of the upper layer; and *A* is the amplitude of topographic perturbations. Note that *Îº*
_{0} does not depend on the strength of the wind stress.

The magnitude of the total transport is found to depend crucially on the efficiency of the momentum transfer from the upper to the lower layer, that is, on the ratio *Îº*/*Îµ,* where *Îµ* is the lateral friction coefficient. If *Îµ* and *Îº* are assumed to be proportional, the upper-layer transport and total transport vary as *Îµ*
^{âˆ’5/6}.

## Abstract

The behavior of the solution to a two-layer wind-driven model in a multiply connected domain with bottom topography imitating the Southern Ocean is described. The abyssal layer of the model is forced by interfacial friction, crudely simulating the effect of eddies. The analysis of the low friction regime is based on the method of characteristics. It is found that characteristics in the upper layer are closed around Antarctica, while those in the lower layer are blocked by solid boundaries. The momentum input from wind in the upper layer is balanced by lateral and interfacial friction and by interfacial pressure drag. In the lower layer the momentum input from interfacial friction and interfacial pressure drag is balanced by topographic pressure drag. Thus, the total momentum input by the wind is balanced by upper-layer lateral friction and by topographic pressure drag.

In most of the numerical experiments the circulations in the two layers appear to be decoupled. The decoupling can be explained by the JEBAR term, whose magnitude decreases as interfacial friction increases. The solution tends toward the barotropic one if the interfacial friction is large enough to render the JEBAR term to be no larger than the wind stress curl term in the potential vorticity equation. The change of regimes occurs when the value of the interfacial friction coefficient *Îº* equals *Îº*
_{0} = *H*
_{1}f_{0}(*L*
_{y}/*L*
_{x})(*A*/*H*
_{0}), where *f*
_{0} is the mean value of the Coriolis parameter; *L*
_{y} and *L*
_{x} are the meridional and zonal domain dimensions; *H*
_{0} and *H*
_{1} are the mean depths of the ocean and of the upper layer; and *A* is the amplitude of topographic perturbations. Note that *Îº*
_{0} does not depend on the strength of the wind stress.

The magnitude of the total transport is found to depend crucially on the efficiency of the momentum transfer from the upper to the lower layer, that is, on the ratio *Îº*/*Îµ,* where *Îµ* is the lateral friction coefficient. If *Îµ* and *Îº* are assumed to be proportional, the upper-layer transport and total transport vary as *Îµ*
^{âˆ’5/6}.

## Abstract

A linear equivalent barotropic (EB) model is applied to study the effects of the bottom topography *H* and baroclinicity on the total transport and the position of the Antarctic Circumpolar Current (ACC). The model is based on the observation of Killworth that the time mean velocity field of the FRAM Model is self-similar in the vertical.

A realistic large-scale topography HÌ„ is constructed by filtering 5-minute resolution data with an appropriate smoothing kernel. It is shown that the asymptotic behavior of the solution of the barotropic model (a particular case of the EB model) in the limit of very small bottom friction depends on subtle details of topography and basin geometry. Given the uncertainties of the smoothing procedure the authors conclude that the barotropic model is not robust with respect to possible variations of model topography.

The authors found that the EB model with a vertical profile function similar to that of Killworth reproduces the major features of the time- and depth-averaged FRAM solution, including the position and the transport of the ACC, reasonably well. The solution is robust with respect to uncertainties in HÌ„. The EB model is much improved by a parameterization of the bottom friction via near-bottom velocity, which tends to shut off the flow in the shallow regions.

## Abstract

A linear equivalent barotropic (EB) model is applied to study the effects of the bottom topography *H* and baroclinicity on the total transport and the position of the Antarctic Circumpolar Current (ACC). The model is based on the observation of Killworth that the time mean velocity field of the FRAM Model is self-similar in the vertical.

A realistic large-scale topography HÌ„ is constructed by filtering 5-minute resolution data with an appropriate smoothing kernel. It is shown that the asymptotic behavior of the solution of the barotropic model (a particular case of the EB model) in the limit of very small bottom friction depends on subtle details of topography and basin geometry. Given the uncertainties of the smoothing procedure the authors conclude that the barotropic model is not robust with respect to possible variations of model topography.

The authors found that the EB model with a vertical profile function similar to that of Killworth reproduces the major features of the time- and depth-averaged FRAM solution, including the position and the transport of the ACC, reasonably well. The solution is robust with respect to uncertainties in HÌ„. The EB model is much improved by a parameterization of the bottom friction via near-bottom velocity, which tends to shut off the flow in the shallow regions.

## Abstract

The usefulness of the concept of JEBAR, the joint effect of baroclinicity and relief, in large-scale ocean dynamics is critically analyzed. The authors address two questions. Does the JEBAR term properly characterize the joint impact of stratification and bottom topography on the ocean circulation? Do estimates of the JEBAR term from observational data allow reliable diagnostic calculations?

The authors give a negative answer to the first question. The JEBAR term need not give a true measure of the effect of bottom relief in a stratified ocean. A simple two-layer model provides examples. As to the second question, it is demonstrated that the large-scale pattern of the transport streamfunction is captured by the smoothed solution, especially with the Mellor et al. formulation of the JEBAR term. However, the calculated velocity field is very noisy and the relative errors are large.

## Abstract

The usefulness of the concept of JEBAR, the joint effect of baroclinicity and relief, in large-scale ocean dynamics is critically analyzed. The authors address two questions. Does the JEBAR term properly characterize the joint impact of stratification and bottom topography on the ocean circulation? Do estimates of the JEBAR term from observational data allow reliable diagnostic calculations?

The authors give a negative answer to the first question. The JEBAR term need not give a true measure of the effect of bottom relief in a stratified ocean. A simple two-layer model provides examples. As to the second question, it is demonstrated that the large-scale pattern of the transport streamfunction is captured by the smoothed solution, especially with the Mellor et al. formulation of the JEBAR term. However, the calculated velocity field is very noisy and the relative errors are large.