A description of numerical antarctic circumpolar currents

The three-dimensional structure of temporal mean, variance and covariance fields of the Northern Hemisphere wintertime circulation is documented by making use of twice-daily hemispheric analyses at 10 pressure levels (1000–100 mb) for 11 winters (1965–76). The Northern Hemisphere is partitioned into seven longitudinal sectors which correspond, respectively, to 1) the entrance regions of the two principal jet streams; 2) the two major oceanic storm tracks (areas with pronounced geopotential height variability in the 2.5–6 day period range); 3) the western portions of the North American and Eurasian land masses; and 4) the central part of the Asian continent. Meridional cross sections of various seasonal mean statistics averaged over meridians comprising these individual sectors are displayed. The fields presented in this manner include 1) time-averaged zonal wind and temperature; 2) temporal variance statistics of zonal and meridional wind components, temperature, and geopotential height; 3) meridional fluxes of heat, geopotential energy, westerly momentum and potential vorticity by transient eddies; and 4) poleward component of the time averaged ageostrophic flow. The hemispheric distributions of temperature statistics, meridional heat flux and mean potential vorticity in the vicinity of the tropopause (200 and 300 mb) are also shown. The structure of eddy statistics and the implied energetics in the oceanic storm tracks are in good agreement with the characteristics of developing baroclinic waves. The strongest variability in geopotential height and wind occurs at 300 mb. The geopotential height fluctuations in the 2.5–6 day period range exhibit a secondary maximum at the ground level, so that the 850 mb level corresponds to a relative minimum. Thermal variability is strongest in the middle troposphere and just above the tropopause. The primary maximum for the heat flux statistics is located at 850 mb, with a weaker secondary maximum at 200 mb. The distribution of eddy momentum flux is characterized by strong convergence of westerly momentum into the storm track axis. The western parts of the two major land masses exhibit quite distinct dynamical features in middle latitudes. The upper troposphere is characterized by equatorward heat fluxes, whereas the direction of heat transport in the lower stratosphere is poleward. The momentum fluxes in these regions are strong and poleward at the jet stream level. This configuration of heat and momentum fluxes is consistent with observed strong poleward fluxes of potential vorticity in the vicinity of the tropopause. Strong supergeostrophic winds in the eddies over the western continents are shown to induce conversion from eddy kinetic energy to eddy available potential energy in these regions. The relative importance of the mean flow forcing by the transient eddies is discussed. It is seen that the jet streams in the entrance regions are maintained by strong poleward ageostrophic flows at the tropopause level, while strong equatorward ageostrophic flows over the oceanic storm tracks act to decelerate the jets at these longitudes. The intensity of these local meridional circulations is about an order of magnitude stronger than that of the zonally averaged Ferrel cell in midlatitudes. The local forcing of the mean zonal flow by the Coriolis acceleration accompanying these time-mean ageostrophic flows is shown to be much larger than the forcing due to eddy momentum flux convergence.

The local effect of the mesoscale eddy field on the mean potential vorticity distribution of the Gulf Stream recirculation region is determined from the quasi-geostrophic eddy potential vorticity flux. This flux is calculated by finite difference of current and temperature time series from the Local Dynamics Experiment. This long-term array of moorings is the only experimental data from which the complete eddy flux can be calculated. The total eddy flux is dominated by the term due to the time variation in the thickness of isopycnal layers. This thickness flux is an order of magnitude larger than the relative vorticity flux. The total flux is statistically significant and directed 217°T to the southwest with a magnitude of 1.57 × 10−5 cm s−1. The direction of the eddy flux with respect to the mean large-scale potential vorticity gradient from hydrographic data indicates that eddies in this region tend to reduce the mean potential vorticity gradient.

Eddy Generation by Instability of a Highly Ageostrophic Front: Mean Flow Interactions and Potential Vorticity Dynamics

We examine the potential vorticity (PV) flux produced by forced Rossby waves in a two-layer quasigeostrophic model, using a perturbation analysis. Rossby waves are excited by external forcing applied to the upper layer. The southward PV flux is produced in the lower layer by the higher-order Rossby waves that are excited by nonlinear wave–wave interactions, whereas the northward PV flux is produced in the upper layer. The direction of the PV flux is consistent with that obtained by an eddy-resolving model of the wind-driven circulation in previous studies. The southward PV flux is produced in a wide parameter range comparable to the eddy-resolving model. The basic features of the PV flux remain unchanged even in the limit of weak stratification. In this limit, stratification has nearly no effect on the flow, except that it isolates the lower layer from the direct effects of external forcing. The mechanism of the southward PV flux is explained using basic features of the barotropic Rossby waves and does not depend on details of the model. Furthermore, the resonant triad interaction of Rossby waves does not affect the PV flux. Stratification weakens or strengthens the PV flux depending on the horizontal scale of the external forcing.

Toward parameterization of the eddy field near the Gulf Stream

Results from a barotropic vorticity equation model driven by symmetric, double-gyre wind forcing are described. The authors work in a regime in which the model reaches a state of turbulent equilibrium. The timeaverage of the statistically steady state exhibits a four-gyre structure, in contrast to the usual two gyres associated with symmetric double-gyre wind forcing. The four-gyre structure is found in model runs using either free-slip or superslip boundary conditions, and with either Laplacian or biharmonic mixing for the dissipation. It is shown that the vorticity budget of both the inner and outer gyres is dominated by a balance between the wind stress curl and the divergence of the eddy potential vorticity flux, with the explicit dissipation playing a much smaller role. The two inner gyres circulate in the same sense as the wind stress curl and are equilibriated, for the most part, by the eddy flux of potential vorticity. The outer gyres, on the other hand, circulate in the opposite sense to the wind stress curl and are driven by the eddy flux of potential vorticity. It is shown that the gross features of the time-averaged state can be reproduced by a parameterized model in which the divergent part of the potential vorticity flux is represented as a downgradient transfer, and a boundary condition of no normal flux of potential vorticity is applied along the model boundaries. In contrast to the eddy resolving model, the fourgyre structure in the parameterized model depends strongly on the choice of side boundary condition.

This paper is a study of the transport properties of large‐scale quasi‐geostrophic flow, when it is forced by an unstable shear of much greater horizontal scale than the scale of the resultant eddies. One of the purposes is thereby to test certain phenomenological parametrization schemes which predict the transport of potential vorticity or heat, or which predict the time‐mean state of the zonally averaged atmosphere. Models used are highly nonlinear spectral quasi‐geostrophic models, with sufficient resolution to resolve the energy‐containing scales and partially resolve an enstrophy inertial range. A scale separation is enforced between the mean and eddy flow, this being a necessary condition for transfer theories to work. An expression is derived for the rate of change of the mean flow in such cases. As a quantitative predictor of the time‐mean state of the zonal flow, baroclinic adjustment is found to work only when nonlinear wave‐wave interaction between eddies is small. In such cases, the amplitude of the eddy flow is determined by the forcing on the zonal flow, which itself equilibrates close to the critical value for linear instability. In fully nonlinear models if the zonal flow is strongly forced the mean flow can be highly supercritical. The flux of potential vorticity is found to depend strongly and monotonically on the mean shear, although no obvious simple relationship is found relating it to potential vorticity gradient. In part because potential vorticity is not a passive scalar, using phenomenological transfer coefficients is by no means straightforward. Such transfer relationships are seen to be in some ways unsatisfactory.

A model of tidal rectification in a homogeneous ocean (Part I) is extended here to include a front that separates shelf and slope waters. The front is approximated as a density discontinuity, the stratification and anchoring position of which are given, but which otherwise is coupled to the flow field. The dynamical closure is formulated through vorticity balance of the two layers and a parameterization of potential vorticity (PV) flux in terms of local tidal amplitude and the mean field. As an example of the frontal effect on the tidally rectified flow, a solution is calculated for the case of negligible interfacial stress and PV flux in the bottom boundary layer and compared with that of a homogeneous ocean. It is found that the mean along-isobath flow outside the frontal zone remains largely unchanged, but is qualitatively altered in the frontal zone. Specifically, the mean flow above the sloping front—being insulated from bottom friction—is greatly intensified by PV mixing, consistent with observed seasonal change over Georges Bank. The mean flow below the frontal interface on the other hand is weakened by enhanced frictional effect—to nearly zero at the foot of the front. The vanishing Ekman transport would strengthen the front as a barrier to offshore transport of a passive tracer.

The sensitivity of the equilibrated state of a dry high-resolution quasigeostrophic β-plane channel model, coupled to both a simplified model of the atmospheric boundary layer and an interactive static stability, to changes in forcings is investigated. An earlier study with the same model found that with standard parameter values, the potential vorticity in the center of the channel just above the atmospheric boundary layer was homogenized. The new experiments show that this result is robust does not vary strongly with variations in forcing over a wide range of forcing parameters. This is so even though the meridional temperature gradients and static stability are generally sensitive to the forcing; that is, the changes in these cooperate to keep the meridional potential vorticity gradient zero. The potential vorticity gradients at higher levels are also robust although nonzero. The homogenization in the lower troposphere does disappear if the differential diabatic heating is decreased sufficiently or if the tropopause level is lowered sufficiently. The model results are also used to assess proposed parameterizations of eddy effects. Stone's parameterization of the meridional eddy heat flux is most successful at reproducing the model's results for most of the experiments. However, no parameterizations of the eddy heat flux captured the results of the experiments in which the diabatic heating timescale was varied. In these experiments, changes in the eddy heat fluxes kept the tropospheric temperature structure essentially unchanged even though the timescale changed from 5 to 80 days.

Large-scale atmospheric flows are often analyzed in the context of a quasigeostrophic (QG) model, which is characterized by conservation of quasigeostrophic potential vorticity (PV). Some of the subtle properties and limitations of a system may be best appreciated in terms of its intrinsic symmetry properties. For example, Nakamura (1993) points out that if the zonal mean flow and potential vorticity gradient in a QG system are vertically antisymmetric at one time, they remain antisymmetric for all time. It follows that the important barotropic governor mechanism (James 1987) cannot take place in such a situation, albeit a rather unrealistic one. Other symmetry properties have been noted and will be commented on shortly. Here we report yet another more general symmetry property of a QG system that has an implication for the constraint to baroclinic wave life cycle.

Extremely persistent, equivalent barotropic zonal jets are observed in statistically steady quasigeostrophic two-layer beta-plane turbulence. Flows are forced by an imposed unstable vertical shear, horizontally uniform over domains several tens of Rossby radii wide. Damping is by surface drag, small-scale mixing, and for some runs, radiative relaxation. When dissipation is weak, zonal jets emerge with a meridional scale related to beta and the equilibrated eddy energy level as suggested by Rhines. Spinup behavior suggests a priori prediction of this level will be difficult. The scale of energy conversion also cannot be determined a priori, and while upscale energy transfer is important, (reverse) energy cascading ranges of any significant extent do not occur. Time scales considerably longer than those simply related to model parameters are prominent. The choices of doubly periodic boundary conditions and spatially homogeneous forcing and dissipation emphasize that the low-frequency behavior is due to internal dynamics. When the domain size is an integral multiple of the jet scale, jets evolve rather independently of each other, meandering on relatively long time scales. Jet interactions are predominantly pairwise when the implicit quantization is violated. Eddy fluxes occur in intermittent bursts asymmetric about jet axes, producing momentum flux convergences to maintain the jets against surface drag. Heat fluxes are everywhere downgradient, reaching local maxima in jet cores. Potential vorticity homogenization is not seen in these forced-dissipative equilibria. Zonally averaged potential vorticity gradients are bounded away from zero when forcing is strong, and zero crossings occur only in the lower layer at weak forcing (when they may be anticipated from the form of the forcing). The relation between potential vorticity fluxes and their gradients is determined by details of the dissipation rather than by any general principle. As seen earlier with a “one-dimensional” model, baroclinic adjustment parameterizations are inappropriate in wide domains.

High-resolution simulations of β-channel, zonal-jet, baroclinic turbulence with a three-dimensional quasigeostrophic (QG) model including surface potential vorticity (PV) are analyzed with emphasis on the competing role of interior and surface PV (associated with isopycnal outcropping). Two distinct regimes are considered: a Phillips case, where the PV gradient changes sign twice in the interior, and a Charney case, where the PV gradient changes sign in the interior and at the surface. The Phillips case is typical of the simplified turbulence test beds that have been widely used to investigate the effect of ocean eddies on ocean tracer distribution and fluxes. The Charney case shares many similarities with recent high-resolution primitive equation simulations. The main difference between the two regimes is indeed an energization of submesoscale turbulence near the surface. The energy cycle is analyzed in the (k, z) plane, where k is the horizontal wavenumber. In the two regimes, the large-scale buoyancy forcing is the primary source of mechanical energy. It sustains an energy cycle in which baroclinic instability converts more available potential energy (APE) to kinetic energy (KE) than the APE directly injected by the forcing. This is due to a conversion of KE to APE at the scale of arrest. All the KE is dissipated at the bottom at large scales, in the limit of infinite resolution and despite the submesoscales energizing in the Charney case. The eddy PV flux is largest at the scale of arrest in both cases. The eddy diffusivity is very smooth but highly nonuniform. The eddy-induced circulation acts to flatten the mean isopycnals in both cases.

The dependence of the temperature and wind distribution of the zonal mean flow in the extratropical troposphere on the gradient of pontential vorticity along isentropes is examined. The extratropics here refer to the region outside the Hadley circulation. Of particular interest is whether the distribution of temperature and wind corresponding to a constant potential vorticity (PV) along isentropes resembles the observed, and the implications of PV homogenization along isentropes for the role of the tropics. With the assumption that PV is homogenized along isentropes, it is found that the temperature distribution in the extratropical troposphere may be determined by a linear, first-order partial differential equation. When the observed surface temperature distribution and tropical lapse rate are used as the boundary conditions, the solution of the equation is close to the observed temperature distribution except in the upper troposphere adjacent to the Hadley circulation, where the troposphere with no PV gradient is considerably colder. Consequently, the jet is also stronger. It is also found that the meridional distribution of the balanced zonal wind is very sensitive to the meridional distribution of the tropopause temperature. The result may suggest that the requirement of the global momentum balance has no practical role in determining the extratropical temperature distribution. The authors further investigated the sensitivity of the extratropical troposphere with constant PV along isentropes to changes in conditions at the tropical boundary (the edge of the Hadley circulation). It is found that the temperature and wind distributions in the extratropical troposphere are sensitive to the vertical distribution of PV at the tropical boundary. With a surface distribution of temperature that decreases linearly with latitude, the jet maximum occurs at the tropical boundary and moves with it. The overall pattern of wind distribution is not sensitive to the change of the position of the tropical boundary. Finally, the temperature and wind distributions of an extratropical troposphere with a finite PV gradient are calculated. It is found that the larger the isentropic PV gradient, the warmer the troposphere and the weaker the jet.

A 10-yr climatology (1986–95) was performed using ECMWF gridded analyses on isentropic surfaces to identify regions where the lower-tropospheric meridional potential vorticity (PV) gradient changes sign across Africa and Australia during their respective summer seasons. While an African sign reversal has been documented, no similar study has been performed for the Australian region, which also has desert on the poleward side of open ocean. In each hemisphere, a northward decrease of PV is sufficient to produce a sign reversal. It was found that PV decreases northward in the lower troposphere across northern Australia, with the maximum reversal on the 315-K surface. It had comparable magnitude but smaller zonal extent (∼3000 km) than that on the 320-K surface in Africa (∼5000 km). In each region the sign reversal was associated with cyclonic PV anomalies on the equatorward side and anticyclonic anomalies on the poleward side. OLR was used as a proxy for deep convective heating in order to evaluate...

Dynamical model of mesoscales in z-coordinates