Vladimir Ivchenko

The Dynamics of the Antarctic Circumpolar Current

Abstract The dynamics of the Antarctic Circumpolar Current (ACC) in a near-eddy-resolving model of the Southern Ocean (FRAM) are investigated. A streamwise coordinate system is used, rather than a more conventional approach of considering zonally averaged quantities. The motivation for this approach is the large deviation from a purely zonal flow made by the current. Comparisons are made with a zonal-mean analysis of the same model. It is found that the topographic form drag is the main sink of the momentum that is input by the wind. However, in contrast to a zonal-mean analysis other terms, namely, horizontal mixing, bottom friction, and advection of momentum, are no longer negligible. The total effect of transient eddies is to produce a drag on the mean flow, again in contrast to the zonally averaged case. The vertical penetration of stress is considered. A generalized formula is derived for the interfacial form stress averaged along a convoluted path and that includes nonquasigeostrophic effects. The i...

A kinetic energy budget and internal instabilities in the Fine Resolution Antarctic Model

An energy analysis of the Fine Resolution Antarctic Model (FRAM) reveals the instability processes in the model. The main source of time-mean kinetic energy is the wind stress and the main sink is transfer to mean potential energy. The wind forcing thus helps maintain the density structure. Transient motions result from internal instabilities of the flow rather than seasonal variations of the forcing. Baroclinic instability is found to be an important mechanism in FRAM. The highest values of available potential energy are found in the western boundary regions as well as in the Antarctic Circumpolar Current (ACC) region. All subregions with predominantly zonal flow are found to be baroclinically unstable. The observed deficit of eddy kinetic energy in FRAM occurs as a result of the high lateral friction, which decreases the growth rates of the most unstable waves. This high friction is required for the numerical stability of the model and can only be made smaller by using a finer horizontal resolution. A grid spacing of at least 10‐15 km would be required to resolve the most unstable waves in the southern part of the domain. Barotropic instability is also found to be important for the total domain balance. The inverse transfer (that is, transfer from eddy to mean kinetic energy) does not occur anywhere, except in very localized tight jets in the ACC. The open boundary condition at the northern edge of the model domain does not represent a significant source or sink of eddy variability. However, a large exchange between internal and external mode energies is found to occur. It is still unclear how these boundary conditions affect the dynamics of adjacent regions.

Eddies in Numerical Models of the Antarctic Circumpolar Current and Their Influence on the Mean Flow

Abstract The dynamics of the Southern Ocean have been studied using two high-resolution models, namely the Fine Resolution Antarctic Model (FRAM) and the Parallel Ocean Program (POP) model. Analysis of these models includes zonal averaging at Drake Passage latitudes, averaging along streamlines (or contours of constant sea surface height), and examining particular subregions of the flow in some detail. The subregions considered in the local analysis capture different flow regimes in the vicinity of the Crozet Plateau, the Macquarie–Ridge Complex, and Drake Passage. Many aspects of the model results are similar, for example, the magnitude of eddy kinetic energy (EKE) in the “eddy rich” regions associated with the large-scale topography. An important difference between the two models is that away from the strong topographic features the level of EKE in POP is 2–4 times greater than in FRAM, giving values close to those observed in altimeter studies. In both FRAM and POP instability analysis performed over A...

Can sea surface height be used to estimate oceanic transport variability

The relation between the sea surface height and the meridional transport across a zonal section at 26.5°N in the North Atlantic is studied by using an eddy resolving ocean state estimate simulated with the Massachusetts Institute of Technology general circulation model. It is shown that the correlation between the zonal sea surface height difference and transport can be substantially increased if the steric height contribution from the seasonal thermocline is removed. The latter explains a substantial part of sea surface height variability, but its effect on transport is weak. It is also found that the zonal steric height difference correlates well with the transport after the contribution of the seasonal thermocline has been removed. There is a similar agreement (with correlation coefficient of 0.63 for the full signal and 0.89 for the mean seasonal cycle) between the meridional transport and steric height based on observations from the Rapid Climate Change (RAPID) project.

Modeling the Antarctic Circumpolar Current: A comparison of FRAM and equivalent barotropic model results

Analyzing the FRAM simulations, Killworth (1992) noticed a strong tendency for self-similarity in the vertical structure of the velocity field of the Antarctic Circumpolar Current (ACC). By assuming the self-similarity as a hypothesis, Krupitsky et al. (1996) developed an equivalent barotropic (EB) model of the ACC capable of describing the horizontal structure of the ACC. Compared to the multi-level-primitive-equation GCM, the EB model appeared substantially simpler and therefore useful in pilot process-oriented and sensitivity studies. In the present study dynamical and kinematical comparisons of the EB and FRAM outputs are given.

Parameterization of mesoscale eddy fluxes in zonal ocean flows

Quasi-geostrophic dynamics in an eddy-resolving zonal re-entrant channel in the Southern Hemisphere have been studied for east- and westward wind forcing scenarios. The main difference is seen in the zonally averaged velocity profiles. In the case of eastward forcing, transient eddies strongly intensify the flow in the channel center into a jet, a feature totally absent in the westward forcing cases. The free jet is associated with a five times higher available potential energy compared to the westward flow. We have used these two distinctly different flow regimes to investigate possible parameterizations of the eddy fluxes in both situations. Parameterizations using a diffusion concept for the quasi-geostrophic potential vorticity (QPV) fluxes, based on earlier work by Green and Welander, have raised a number of questions concerning the transfer (or diffusion) coefficients. These coefficients must satisfy three basic integral constraints, the balances of momentum, energy and enstrophy. It is shown that the constraints related to momentum and energy conservation are associated with Pedloskys instability conditions. An analytical solution developed in this paper shows that the transfer coefficients have a theoretical upper limit in the eastward-forcing scenarios, resulting in a greater Reynolds number than a theoretically derived critical Reynolds number. A general parameterization scheme, based on the quasi-geostrophic eddy enstrophy balance, is presented, which accounts for both scenarios, a weakly baroclinic westward flow and a strongly baroclinic eastward flow. This new parameterization reproduces the main difference in the east- and westward flows; i.e., a strong jet in the eastward-forcing case and a broad smooth flow in the westward-forcing case, in agreement with the numerical results of the eddy-resolving experiments.

Eddies in numerical models of the Southern Ocean

Mesoscale eddies play a crucial role in the dynamics of the Antarctic Circumpolar Current (ACC) by facilitating horizontal redistribution and vertical penetration of the momentum, contributing to the meridional heat transport and the budgets of energy and momentum of the ACC. This chapter discusses the dynamics of the ACC based on results of numerical models that permit or resolve the mesoscale eddies. Conclusions are drawn by comparing and contrasting results from different models, including both quasi-geostrophic and primitive equation models.

Influence of Bottom Topography on Integral Constraints in Zonal Flows with Parameterized Potential Vorticity Fluxes

An integral constraint for eddy fluxes of potential vorticity (PV), corresponding to global momentum conservation, is applied to two-layer zonal quasi-geostrophic channel flow. This constraint must be satisfied for any type of parameterization of eddy PV fluxes. Bottom topography strongly influence the integral constraint compared to a flat bottom channel. An analytical solution for the mean flow solution has been found by using asymptotic expansion in a small parameter which is the ratio of the Rossby radius to the meridional extent of the channel. Applying the integral constraint to this solution, one can find restrictions for eddy PV transfer coefficients which relate the eddy fluxes of PV to the mean flow. These restrictions strongly deviate from restrictions for the channel with flat bottom topography.

Instabilities in the Agulhas Retroflection Current system: A comparative model study

The Agulhas Retroflection Current system is analyzed in two ocean general circulation models, U.K. Fine Resolution Antarctic Model (FRAM) and U.S. Parallel Ocean Program (POP). It is shown that both models have two quasizonal jets, a northerly westward flowing jet (Agulhas Current) and a more southerly eastward flowing jet (Agulhas Return Current), which act as the entrance and exits of the Retroflection region, respectively. An instability analysis has been performed on both jets, and the unstable waves are shown to be baroclinicly unstable. It is shown that this instability process is well resolved in the POP model but is poorly resolved in FRAM. An energy analysis of POP shows that both barotropic and baroclinic instability processes play a major role in the current systems, with the former process concentrated in the surface layers between the two currents, and the latter process occurring below the two currents. In FRAM a regional energy budget suggests that barotropic instability is the main mechanism by which the eddies are generated, and a meridional cross-sectional analysis shows that this occurs principally on the northern edge of the Agulhas Return Current.

Integral Constraints for Momentum and Energy in Zonal Flows with Parameterized Potential Vorticity Fluxes: Governing Parameters

Integral constraints for momentum and energy impose restrictions on parameterizations of eddy potential vorticity (PV) fluxes. The impact of these constraints is studied for a wind-forced quasigeostrophic two-layer zonal channel model with variable bottom topography. The presence of a small parameter, given by the ratio of Rossby radius to the width of the channel, makes it possible to find an analytical/asymptotic solution for the zonally and time-averaged flow, given diffusive parameterizations for the eddy PV fluxes. This solution, when substituted in the constraints, leads to nontrivial explicit restrictions on diffusivities. The system is characterized by four dimensionless governing parameters with a clear physical interpretation. The bottom form stress, the major term balancing the external force of wind stress, depends on the governing parameters and fundamentally modifies the restrictions compared to the flat bottom case. While the analytical solution bears an illustrative character, it helps to see certain nontrivial connections in the system that will be useful in the analysis of more complicated models of ocean circulation. A numerical solution supports the analytical study and confirms that the presence of topography strongly modifies the eddy fluxes.