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R. Lee Panetta

Abstract

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.

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R. Lee Panetta
and
Isaac M. Held

Abstract

Statistically steady states of a two-layer quasi-geostrophic model truncated to retain only the zonal mean flow and one nonzero zonal wavenumber, but with high meridional resolution, are described. The model is forced by imposing a time-mean unstable meridional temperature gradient, assuming that deviations from the time-mean are doubly periodic. A comparison is made with a more conventional channel model with the same zonal truncation, in which the flow is forced by radiative relaxation to an unstable temperature gradient. It is shown that the statistics of the channel model approach those of the doubly periodic model as the width of the unstable region in the former is increased. Implications for parameterization theories are discussed.

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Isaac M. Held
,
R. Lee Panetta
, and
Raymond T. Pierrehumbert

Abstract

The structure of stationary Rossby waves in the presence of a mean westerly zonal flow with vertical shear is examined. There is typically only one stationary vertical mode, the external mode, trapped within the troposphere. For more than one tropospheric mode to exist, we find that vertical shears must be smaller than those usually observed in extratropical latitudes. The vertical structure, horizontal wavenumber and group velocity of the external mode, and the projection onto this mode of topographic and thermal forcing are studied with continuous models (a linear shear profile as well as more realistic basic states), and a finite-differenced model with resolution and upper boundary condition similar to that used in GCMs. We point out that the rigid-lid upper boundary condition need not create artificial stationary resonances, as the artificial stationary vertical modes that are created are often horizontally evanescent.

The results are presented in a form which allows one to design the equivalent barotropic model that captures the external mode's contribution to the stationary wave field. It is found, in particular, that the wind blowing over the topography in such a barotropic model should generally be larger than the surface wind but smaller than the wind at the equivalent barotropic level. Also, the group velocity of the stationary external mode in realistic vertical shear is found to be considerably greater than that of the stationary Rossby wave in the equivalent barotropic model.

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Isaac M. Held
,
Raymond T. Pierrehumbert
, and
R. Lee Panetta

Abstract

External Rossby waves in vertical shear can be destabilized by thermal damping. They can also be destabilized by damping of potential vorticity if this damping is larger in the lower than in the upper troposphere. Results are described in detail for Charney's model. Implications for the effects of diabatic heating and mixing due to smaller scale transients on equivalent barotropic stationary or quasi-stationary long waves are discussed. It is painted out that energy or potential enstrophy budgets may indicate that transients are damping the long waves while, in fact, their presence is destabilizing these waves.

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R. Lee Panetta
,
Isaac M. Held
, and
Raymond T. Pierrehumbert

Abstract

In order to clarify the extent to which the two-layer model can successfully simulate the remote tropospheric response to localized stationary forcing, the structure of stationary Rossby waves in the two-layer model is compared with that in continuous models. One finds a close correspondence when the two-layer flow is supercritical in the sense of the Phillips' criterion, except for the possibility of upstream propagation in the two-layer model when the lower-layer wind is small. When the two-layer flow is subcritical, the stationary waves can be very seriously distorted. The manner in which neutral modes are spatially or temporally destabilized by damping in the two-layer model is contrasted with similar results for Charney's model.

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John M. Wallace
,
R. Lee Panetta
, and
Jerry Estberg

Abstract

A 35-year record of monthly mean zonal wind data for the equatorial stratosphere is represented in terms of a vector (radius and phase angle) in a two-dimensional phase space defined by the normalized expansion coefficients of the two leading empirical orthogonal functions (E0Fs) of the vertical structure. The tip of the vector completes one nearly circular loop during each cycle of the quasi-biennial oscillation (QBO). Hence, its position and rate of progress along the orbit of the point provide a measure of the instantaneous amplitude and rate of phase progression of the QBO. Although the phase of the QBO bears little if any relation to calendar month, the rate of phase progression is strongly modulated by the first and second harmonics of the annual cycle, with a primary maximum in April/May, in agreement with previous studies based on the descent rates of easterly and westerly regimes.

A simple linear prediction model is developed for the rate of phase progression, based on the phase of the QBO and the phase of the annual cycle. The model is capable of hindcasting the phase of the QBO to within a specified degree of accuracy approximately 50% longer than a default scheme based on the mean observed rate of phase progression of the QBO (1 cycle per 28.1 months). If the seasonal dependence is ignored, the prediction equation corresponds to the “circle map,” for which an extensive literature exists in dynamical systems theory.

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