A Wave Amplitude Transition in a Quasi-Linear Model with Radiative Forcing and Surface Drag

This paper introduces the concept of potential momentum, which is a nonlocal measure of the thermal structure that has momentum units. Physically, it may be interpreted as the zonal momentum that the flow would realize through an adiabatic redistribution of mass that made the isentropic thickness uniform poleward of a reference latitude. At the surface, a poleward temperature gradient is equivalent to an easterly reservoir of potential momentum. Potential momentum gives a global picture of the thermal field that also takes into account the meridional structure. When the mean flow is redefined in terms of the total momentum (the standard zonal momentum plus this newly defined potential momentum), the mean-flow response to the eddy forcing can be formulated locally. This allows one to relate in equilibrium the eddy absorption and the restoration of the mean flow. Using the concept of potential momentum, vertical propagation can be related to thermal forcing by means of an equation analogous to the relation between meridional propagation and surface friction. Based on these ideas, it is argued that the time-mean eddy propagation is largely constrained by the strength and structure of the forcing. The new formalism is applied to a forced–dissipative two-layer model to study the dependence of meridional and vertical propagation and of the global circulation on changes in the diabatic and frictional forcing time scales. It is found that baroclinic adjustment, in the form of a fixed potential vorticity (PV) gradient, is a good approximation because the intensity of the circulation only depends weakly on the forcing time scale. Another remarkable result is that, owing to the robustness of this PV gradient, thermal homogenization is always enhanced with stronger friction.

A β-plane multilevel quasigeostrophic channel model with interactive static stability and a simplified parameterization of atmospheric boundary layer physics is used to study the role of different boundary layer processes in eddy equilibration and their relative effect in maintaining the strong boundary layer potential vorticity (PV) gradient. The model results show that vertical thermal diffusion, along with the surface heat exchange, is primarily responsible for limiting PV homogenization by baroclinic eddies in the boundary layer. Under fixed SST boundary conditions, these two processes act as the source of the mean flow baroclinicity in the lower levels and result in stronger eddy heat fluxes. Reducing surface friction alone does not result in efficient elimination of the boundary layer PV gradient, but the equilibrium state temperature gradient is still largely influenced by surface friction and its response to changes in surface friction is not monotonic. In the regime of strong surface friction, with reduced poleward eddy heat flux, a strong temperature gradient is still retained. When the surface friction is sufficiently weak along with the stronger zonal wind, the critical level at the center of the jet drops below the surface. As a result, in the lower levels, the eddy heat flux forcing on the mean flow moves away from the center of the jet and the equilibrium state varies only slightly with the strength of the vertical momentum diffusion in the boundary layer.

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.

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.

Medium-scale waves (zonal wavenumbers 4-7) frequently dominate Southern Hemisphere summer circulation patterns. Randel and Stanford have studied the dynamics of these features, demonstrating that the medium-scale waves result from baroclinic excitation and exhibit well-defined life cycles. This study details the evolution of the medium-scale waves during a particular life cycle. The specific case chosen exhibits a high degree of zonal symmetry, prompting study based upon zonally averaged diagnostics. An analysis of the medium-scale wave energetics reveals a well-defined life cycle of baroclinic growth, maturity, and barotropic decay. Eliassen-Palm flux diagrams detail the daily wave structure and its interaction with the zonally-averaged flow.

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.

A description of numerical antarctic circumpolar currents

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.

This paper proposes and discusses mechanisms whereby mean flows and jets are produced by differential rotation and by topographic effects. It is shown that, in general, a mean gradient of potential vorticity not only inhibits the cascade of energy to large scales but directly produces anisotropic structures. Scalings for this are examined on the β plane using ideas from classical phenomenology. The scalings are naturally anisotropic and predict the formation of zonal flows directly through a turbulent cascade. Numerical simulations and two-point closure calculations qualitatively confirm the predictions. Also, simulations of barotropic flow on the β plane can produce zonal jet structures of exceptional persistence over many eddy turnover times. Unsteady flow over topography generally produces a mean flow with a correlation between streamfunction and topography, with anticyclonic motion over humps. If the topography is shallow (or the flow sufficiently energetic) the mean streamfunction will be of...

Throughout the latter part of January and most of February 1989 a large-scale intense blocking event occurred over the northeast Pacific Ocean. During its lifetime the block exhibited two distinct spatial configurations corresponding to Omega and dipole shapes, respectively. A time series of scatter diagrams of 5-day-averaged 500-mb geostrophic streamfunction versus potential vorticity (ψ vs q) is computed. It is suggested that both the Omega and dipole forms may correspond to free modes. It is shown that immediately prior to the block formation there is a rapid steepening of the q(ψ) scatter diagrams associated with a strong increase in net vorticity being advected out of the block region. A suggestion is made that this analysis may be useful in identifying flow configurations that are capable of initiating blocks. It is possible to separate the geostrophic streamfunction into a product of horizontal and vertical components. The vertical structure problem is solved analytically using a constant lapse rate approximation for the background atmosphere, and a constant value for the gradient of the mean flow potential vorticity with respect to the geostrophic streamfunction. It is shown that as the block develops, the contribution of the gravest, quasi-barotropic mode dramatically increases and forms the dominant mode. Immediately prior to the formation of the dipole configuration, a small increase in baroclinicity was observed near the block interior. It is suggested that this event could be evidence of eddy forcing similar to that proposed for the maintenance of North Atlantic dipole blocks.

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

It is well-known that when Rossby waves are stationary in the belt of mid-latitude westerlies, resonance conditions occur allowing the atmospheric response to external perturbations to begreatly enhanced. The concept lies at the heart of the interaction of planetary flows withtopographic mountain chains. In contrast, early studies of the atmospheric response to thermalforcing, focussed on the off resonance response. Now available, many GCM studies dealingwith the atmospheric response to prescribed SST have revealed a great variety of responses, the difficulty of extracting the signal at planetary scale being compounded by the overwhelmingactivity of transient eddies at the synoptic scale. Given the long lasting influence of large scaleSST anomalies, climate predictability may be expected to improve if one can identify feedbacksbetween the large scale climate anomalies and the SST distribution. We propose a simple theorythat explores the physics of this atmospheric response to SST and may suggest ways to analyzedata from the more complex GCM. We neglect all interactions between the transient eddiesand the large scale waves that would go beyond Fickian mixing laws although there is evidencethat the transient eddies by themselves take part in the maintenance of the low frequencyvariability. Because the observed perturbations are small, a linear theory is appropriate. Usinga 2-level model of the atmosphere, a resonance condition occurs when the Rossby waves arestationary against the vertically averaged mean zonal flow. The resonance is sharp when eddydissipation through surface friction is small. In a small wavenumber window controlled by thevertical structure of the mean flow, the response is equivalent barotropic and baroclinic elsewhere.Only in this window is the familiar response of high SLP downstream of warm SST recovered.For certain combination of thermal damping and surface drag, the atmospheric response is amplifiedto produce a positive feedback on the SST. When the atmospheric model is coupled to a oneand a half level oceanmodel with a zonally periodic geometry appropriate to the SouthernOceans, a linear instability appears. The application of this process of thermal resonance to the Antarcticcircumpolar wave is discussed. We find that under realistic values of the mean state, an unstablecoupled wave emerges in a narrow wavenumber window which coincides with the near resonanceconditions found previously in the atmospheric model. This instability provides a powerful scaleselective mechanism for the perturbations. The thermal forcing is primarily responsible for amplificationof the SST while the powerful Antarctic circumpolar current is primarily responsible foradvecting the anomalies around the globe and setting the period.

Baroclinic adjustment and turbulent diffusion are two popular paradigms used to describe the eddy–mean flow closure in the two-layer model, with very different implications for the criticality of the system. Baroclinic adjustment postulates the existence of preferred equilibrium states, while the turbulent diffusion framework predicts smooth variations of the mean state with the forcing. This study investigates the relevance of each paradigm over a wide range of the parameter space, including very strong changes in the diabatic forcing. The results confirm the weak sensitivity of the criticality against changes in the forcing noted by baroclinic adjustment studies but do not support the existence of preferred equilibrium states. The weak sensitivity of the mean state when the forcing is varied is consistent with the steepness of the diffusive closure predicted by homogeneous turbulence theories. These turbulent predictions have been tested locally against observed empirical diffusivities, extending a previous study by Pavan and Held. The results suggest that a local closure works well, even at low criticalities when the eddy momentum fluxes are important, provided that the criticality is generalized to include the effect of the meridional curvature potential vorticity (PV) gradient. When friction is weak, the development of this curvature may be important for halting the cascade and making the flow more linear. A remarkable difference from previous homogeneous results is that the empirical closure does not appear to steepen at low criticality. This may be due to the use of a generalized criticality or to the distinction between a local and domain-averaged closure.

The response of the Kuroshio Extension (KE) to large-scale Rossby waves remotely excited by wind stress changes associated with the 1970s climate regime shift is studied using a high-resolution regional ocean model. Two ensemble simulations are conducted: The control run uses monthly climatological forcing while, in the second ensemble, anomalous forcing is imposed at the model eastern boundary around 165°E derived from a hindcast of decadal changes in subsurface temperature and salinity using a coarser-resolution model of the Pacific basin. Near the KE, ocean adjustment deviates strongly from the linear Rossby wave dynamics. Most notably, the eastward acceleration of the KE is much narrower in meridional extent than that associated with the incoming Rossby waves imposed on the eastern boundary. This KE acceleration is associated with an enhanced potential vorticity (PV) gradient across the front that is consistent with the inertial western boundary layer theory: the arrival of the Rossby waves at the western boundary causes the eastward current to accelerate, leading to enhanced advection of low (high) PV water of subtropical (subarctic) origin along the western boundary layer. The meridional dipole of PV anomalies results in a pair of anomalous recirculations with a narrow eastward jet in between. A three-layer quasigeostrophic model is used to demonstrate this inertial adjustment mechanism. Finally, transient eddy activity increases significantly and the eddy momentum transport acts to strengthen the mean flow response. The result that ocean physical response to broad-scale atmospheric forcing is large near the KE front has important implications for fisheries research.

Gravity Wave Instability and Turbulence