Dirk Olbers

The dynamical balance, transport and circulation of the Antarctic Circumpolar Current

The physical elements of the circulation of the Antarctic Circumpolar Current (ACC) are reviewed. A picture of the circulation is sketched by means of recent observations from the WOCE decade. We present and discuss the role of forcing functions (wind stress, surface buoyancy flux) in the dynamical balance of the flow and in the meridional circulation and study their relation to the ACC transport. The physics of form stress at tilted isopycnals and at the ocean bottom are elucidated as central mechanisms in the momentum balance. We explain the failure of the Sverdrup balance in the ACC circulation and highlight the role of geostrophic contours in the balance of vorticity. Emphasis is on the interrelation of the zonal momentum balance and the meridional circulation, the importance of diapycnal mixing and eddy processes. Finally, new model concepts are described: a model of the ACC transport dependence on wind stress and buoyancy flux, based on linear wave theory; and a model of the meridional overturning and the mean density structure of the Southern Ocean, based on zonally averaged dynamics and thermodynamics with eddy parametrization.

A two-dimensional model for the thermohaline circulation under an ice shelf

The production of Antarctic Bottom Water is influenced by Ice Shelf Water which is formed due to the modification of shelf water masses under huge ice shelves. The coupling of inflow conditions, thermohaline processes at the ice shelf base and the sub-ice shelf circulation is studied with a two-dimensional thermohaline circulation model which has been developed for a section perpendicular to the ice shelf edge. Different boundary conditions appropriate to the Filchner Ice Shelf regime are considered. The model results indicate that, in general, shelf water is transported toward the grounding line, where at the ice shelf base melting occurs with a maximum rate of 1.5 my−1. Accumulation of ice takes place at the end of the melting zone close to the ice shelf edge with a rate on the order of 0.1 my−1. The location of this accumulation zone determines whether or not the density increase by salt rejection causes an upper circulation cell and the separation of the modified water mass from the ice shelf base at mid-range depth. At the ice shelf edge the simulated temperature, salinity, helium and δ18O values for the temperature minimum layer are typical for Ice Shelf Water. However the sub-ice shelf circulation is highly variable as well as sensitive to changes in boundary conditions. Moderate changes in the characteristics of the inflowing water or in sea-floor topography may double the intensity of the circulation. Non-linear processes in the accumulation zone cause variabilities which can be described by an ice shelf edge oscillator influencing the entire circulation regime.

Potential Vorticity Constraints on the Dynamics and Hydrography of the Southern Ocean

Abstract Constraints on the hydrography and geostrophic velocity shear of the Southern Ocean implicit in its potential vorticity field are discussed and illustrated by diagnostic study of observed and modeled potential vorticity fields. A stress-driven, thermodynamically inactive, eddy-resolving quasigeostrophic model of the Southern Ocean suggests that, through the systematic erosion of potential vorticity gradients by geostrophic eddies, the large-scale flow equilibrates toward a state in which interior potential vorticity gradients are small. Observations of the large-scale isopycnal distribution of potential vorticity (IPV), deduced from climatological hydrographic data, reveal a much richer structure. The most striking feature of the IPV field is the presence of large, near-surface gradients of IPV (a vortocline) coinciding with the axis of the Antarctic Circumpolar Current (ACC). To the south of this front potential vorticity (PV) is large; to its north, PV has low values, and relative to those foun...

Wind-Driven Flow over Topography in a Zonal β-Plane Channel: A Quasi-geostrophic Model of the Antarctic Circumpolar Current

Abstract The paper gives a detailed account of the dynamical balance of a wind-driven zonally unbounded flow over topography. The problem is investigated with a quasi-geostrophic β-plane channel with two layers and eddy resolution. The channel has a width of 1500 km and a zonal periodicity of 4000 km. Apart from the dimensions, the model structure is similar to the one used by McWilliams et al. The experiments with this model address the problem of the relative role of transient and standing eddies as well as bottom friction and topographic form stress in the balance of a current driven by a steady surface windstress. The response of the system is investigated for different values of the friction parameter and various locations of topographic obstacles in the bottom layer of the channel. The principal momentum balance emerging from these experiments supports the concept of Munk and Palmen for the dynamics of the Antarctic Circumpolar Current, which proposes that the momentum input by windstress is transfe...

The Propagation of Internal Waves in a Geostrophic Current

Abstract The paper presents the WKB theory of internal wave propagation in a large-scale geostrophic mean flow with vertical as well as horizontal shear. As an application a mean flow with isopycnals having constant slope but arbitrary spacing is considered and the behavior of waves at turning points and critical layers is discussed. In particular, it is shown that horizontal variations of the mean flow shift the critical layer to the interior of the wave guide, i.e., away from ω02 = f2, where ω0 is the intrinsic frequency, and produces a valve effect at the critical layer which can be penetrated by a wave incident from one side while incidence from the other side results in absorption.

Interpreting Eddy Fluxes

A generalization of the transformed Eulerian and temporal residual means is presented. The new formulation uses rotational fluxes of buoyancy, and the full hierarchy of statistical density moments, to reduce the cross-isopycnal eddy flux to the physically relevant component associated with the averaged water mass properties. The resulting eddy-induced diapycnal diffusivity vanishes for adiabatic, statistically steady flow, and is related to either the growth or decay of mesoscale density variance and/or the covariance between small-scale forcing (mixing) and density fluctuations, such as that associated with the irreversible removal of density variance by dissipation. The relationship between the new formulation and previous approaches is described and is illustrated using results from an eddying channel model. The formalism is quite general and applies to all kinds of averaging and to any tracer (not just density).

Thermohaline and Wind Forcing of a Circumpolar Channel with Blocked Geostrophic Contours

The Antarctic Circumpolar Current is governed by unique dynamics. Because the latitude belt of Drake Passage is not zonally bounded by continents, the Sverdrup theory does not apply to the Antarctic Circumpolar Current. However, most of the geostrophic contours are blocked at Drake Passage, which provides an important dynamic constraint for the vorticity equation of the depth averaged flow. This study addresses the effects of thermohaline and wind forcing on the large-scale transport of a circumpolar current with blocked geostrophic contours. Various numerical experiments with three different idealized model geometries were conducted. Based on the results and theoretical arguments, the authors promote an indirect wind effect on the circumpolar current: while the direct effects of the wind in driving the circumpolar current through a vertical transfer of the applied wind stress are of minor importance, the wind does substantially influence the circumpolar current transport through its effects on the density field. This indirect wind effect is discussed in two steps. First, at the latitudes of the circumpolar current and longitudes where the geostrophic contours are blocked, the meridional gradient of the mass transport streamfunction is to leading order balanced by the meridional gradient of the baroclinic potential energy. This balance implies that the total transport is to leading order baroclinic and that the deep transport is small. For this statement, some theoretical arguments are offered. Second, a simplified analytical model is used to obtain the distribution of the baroclinic potential energy. Assuming an advective‐diffusive balance for the densities in the deep downwelling northern branch of the Deacon cell, this model reproduces the qualitative dependence of the circumpolar current transport on the imposed wind and thermohaline forcing as well as on the turbulent diffusivities.

Comments on “On the Obscurantist Physics of ‘Form Drag’ in Theorizing about the Circumpolar Current*

In recent years the interest in the dynamical balance of the Antarctic Circumpolar Current (ACC) has seen a renaissance in oceanographic research. Various papers deal with the barotropic circulation in channels with simple topography—these are largely analytical solutions (e.g., Johnson and Bryden 1989; Krupitsky and Cane 1994; Wang and Huang 1995; Olbers and Volker 1996)—and a few numerical solutions have appeared, noteworthy eddy-resolving quasigeostrophic channel circulations (McWilliams et al. 1978; Wolff et al. 1991; Olbers 1993; Marshall et al. 1993) and the FRAM experiment (FRAM Group 1991). Apart from subtleties due to the different ingredients in these models the investigations have verified the early proposal of Munk and Palmen (1951) on the importance of the pressure force on the submarine topography—the bottom form stress—in the balance of the zonal momentum. In fact, the concept of a ‘‘canonical’’ balance may be formulated: The flux of momentum imparted by the surface wind stress is carried—via the interfacial form stress mechanism—by standing and transient eddies to the depth where the flow is blocked by topography and the bottom form stress acts to transfer the momentum to the earth. To many oceanographers this dynamical concept of the ACC, however, still appears mysterious since the conventional tools of oceanographic science—for example, the Ekman and geostrophic transports and the Sverdrup balance—seem not to pertain to this canonical concept, which, moreover, seems to be insuffient to determine the zonal transport of the circumpolar flow. Warren et al. (1996, hereafter WLR) express their in-

The annual cycle of the global ocean circulation as determined by 4D VAR data assimilation

Abstract A method is presented that allows the estimation of a consistent oceanic circulation from hydrographic data using a coarse-resolution ocean model. The major difference to previous attempts to solve this well known problem in a global context lies in the application of a time dependent model that is optimized for a cyclo-stationary solution, i.e. the annual cycle is included and the interannual variability is minimized. Furthermore it is shown, that integral constraints on the large scale fluxes are important, when our goal is to get beyond the reproduction of the temperature and salinity measurements and is targeted at a realistic flow field. In order to estimate both the initial temperature and salinity fields as well as the surface forcing a new procedure is developed which is based on the adjoint technique. A sequence of sub-problems is constructed in which either the initial model state or the forcing fields are used as control variables. The corresponding cost functions are minimized iteratively by a gradient descent algorithm while each sub-problem involves several years of model integration per iteration. In this paper we report on two assimilation experiments. The first experiment, which uses temperature and salinity data only, fits the observations well. However, it was not very successful in reproducing our knowledge about the circulation and the transports. In the second experiment we gathered more a-priori knowledge in appropriate constraints and also utilize the sea surface height data from the TOPEX/Poseidon mission. Compared to assimilation attempts using stationary models our results clearly profit from taking into account the annual cycle as well as from optimizing the forcing. The remaining model-data misfit stays within the range of the expected errors and the retrieved forcing is, in general, consistent with prior estimates. Thus the model finally provides a reasonable seasonal cycle of the oceans heat as well as freshwater transport that is consistent with prior estimates. Most of the remaining discrepancies can be attributed to the coarse spatial resolution, while the large timestep obviously is not a problem.

Disqualifying Two Candidates for the Energy Balance of Oceanic Internal Waves

Abstract It is shown that spreading of tidal energy across the wave continuum and bottom scattering play no role in the spectral energetics of ocean internal waves.