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Walter A. Robinson

Abstract

Interactions between stationary planetary waves are investigated in the context of severely truncated quasi-geostrophic dynamics in a midlatitude beta-channel. Such interactions are solely a consequence of dissipation and are mediated by waves with smaller meridional scales. Linear numerical experiments with wave 1 and 2 basic states indicate that wave 1 is amplified in a wave 2 basic state, while the behaviour of a wave 2 disturbance in a wave 1 basic state is sensitive to the relative phases of the waves. At some phases, wave 2 is confined below the region of law wave 1 amplitudes.

The dynamics of these interactions are diagnosed using the potential enstrophy budgets of the waves. These budgets are more sensitive to the wave-wave interactions than are the amplitudes of the waves themselves. Nonlinear experiments show behavior that is a combination of the linear results with an amplification of wave 1 and a strong dependence on the relative phases of waves 1 and 2 in the stratosphere.

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Walter A. Robinson

Abstract

A three-dimensional, severely truncated, quasi-geostrophic model in a beta channel is used to explore the dynamics of the observed anticorrelation between the amplitudes of planetary waves 1 and 2 in the Northern Hemisphere winter stratosphere. The model, which includes interactions among eight horizontal modes, generates realistic wave 1–wave 2 vacillations when westward traveling wave 1 interacts with stationary waves 1 and 2. It is found that while wave 1 oscillates in response to wave–mean flow interactions, the oscillations in the amplitude of wave 2 are driven primarily by wave–wave interactions. Experiments with a barotropic model revel that the timing of the strongest wave–wave interactions is determined by the wave 1 interaction with the mean flow.

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Walter A. Robinson

Abstract

The response of linear planetary wave 2 to changes in the isentropic zonally symmetric distribution of potential vorticity (PV) is investigated numerically. Wave 2 is sensitive to the width and position of a region where the meridional derivative of PV is weak, denoted the “surf zone”, in the middle stratosphere. A narrow surf zone leads to an amplification of wave 2, and confines some of its Eliassen-Palm wave activity in high latitudes. For wider surf zones the wave activity is concentrated near the associated critical surface, and the amplitude of the wave decreases. Large changes in the wave amplitude and in the distribution of its activity are associated with the subtle changes in the zonal winds produced by modest modifications in the distribution of PV.

Basic states that include regions of reversed meridional gradients of PV lead to wave overreflection and strong poleward focusing of wave activity. The amplitude of wave 2 is enhanced in the presence of negative gradients, with large responses occurring for eastward traveling waves.

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Walter A. Robinson

Abstract

Mechanisms of low-frequency variability are examined in an extended run of a two-level nonlinear global model with a single isolated mountain. The presence of the mountain modifies the low-frequency behavior, compared with that in a zonally homogeneous model, in two ways. First, slow variations in the zonally averaged circulation, the zonal index, are manifest as variability in the train of stationary waves generated by the orography. Second, trains of low-frequency Rossby waves are modified by their propagation through the model's zonally asymmetric time-mean flow. These eddies become meridionally elongated at the jet entrance and zonally elongated at its exit, allowing them to extract energy barotropically from the mean flow in the jet exit.

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Walter A. Robinson

Abstract

Fluctuations in the global angular momentum of a two-layer zonally homogeneous global model of the atmosphere are dominated by very low frequencies, periods longer than 100 days. This variability is confined to the tropics, where it is associated with variations of approximately ±5 m s−1 in the zonal winds. Lagged correlations suggest that the variations in angular momentum are a response to variability in the zonally averaged eddy flux of vorticity in the tropics.

A zonally symmetric model is constructed to determine the response to an impulsive rearrangement of vorticity across the tropics. The response of the angular momentum in the zonally symmetric model, in convolution with the tropical eddy flux of vorticity derived from the full model, provides a successful model of the variations in angular momentum in the full model.

The relevance of the results to James and James' finding ultralow-frequency variability in a five-layer model and to the possibility of ultralow-frequency variability in the atmosphere is discussed.

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Walter A. Robinson

Abstract

A wave-1 minor warming is simulated in a mechanistic, global, primitive equation model. The modification of the zonal flow by the rearrangement of potential vorticity on a middle stratospheric isentrope is compared in a fully nonlinear model and in a model with only one wave and the zonal flow (a quasi-linear model). The permanent rearrangement of potential vorticity during the wave episode is more intense and more localized meridionally in the fully nonlinear model, which is able to capture the process of planetary wave breaking in some detail.

Additional experiments reveal that the differences between the quasi-linear and nonlinear models persist for a broad range of wave amplitudes, and that the quasi-linear model can qualitatively reproduce the modification of the zonal flow by the wave when the diffusive dissipation of the wave is enhanced. These results are discussed in the context of the theory of barotropic Rossby waves in shear flows, and in comparison with recent numerical simulations of the middle atmosphere.

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Walter A. Robinson

Abstract

Zonally averaged flows in general circulation models exhibit strong sensitivity to the strength of the surface friction, subgrid-scale diffusion, and gravity wave drag. A commonly observed effect is that the midlatitude jets shift poleward as the drag on the zonal wind is decreased. In the present two-level primitive equation model the jet moves poleward with decreasing surface friction and with increasing subgrid-scale diffusion. The barotropic component of the jet shows much greater sensitivity than does the baroclinic component. Experiments using different values of friction for the eddies and for the zonal means reveal that the jet latitude is primarily controlled by the drag on the zonal means.

The shift in the latitude of the jet is derived from the altered equilibrium response of the zonal wind to forcing by eddies when the friction is changed and the change in meridional structure of the eddy momentum fluxes in response to the modified zonal wind. The latter effect is also displayed by linear baroclinic modes.

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Walter A. Robinson

Abstract

The quasi-geostrophic form of the Eliassen-Palm flux is calculated for steady linear planetary wave 1 in a realistic zonal flow with dissipation. This flux shows a region of divergence in the polar stratosphere that is similar to that found in time averages of observations. Comparison with the full primitive equation form of the Eliassen-Palm flux indicates that in the model this divergent region is spurious and results from the overestimation of the momentum flux divergence when it is calculated from geostrophic winds. An approximate expression for the Eliassen-Paim flux in terms of balanced winds is suggested as an alternative to the quasi-geostrophic form.

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Walter A. Robinson

Abstract

We examine the dynamics of low-frequency variability in a simple global model with zonally homogeneous boundary conditions. Low-frequency structure comprises trains of nearly equivalent barotropic Rossby waves with weak eastward phase velocities and strong eastward group velocities. These low-frequency eddies are strongly coupled to synoptic activity. The flux of vorticity by synoptic waves acts both to reinforce the low-frequency eddies and to retard their eastward propagation.

Mechanistic experiments with an imposed forcing show that the synoptic-scale vorticity fluxes are organized by the low-frequency flow. The behavior is generally similar to that found in previous studies of blocks; the present work shows that strong mutual interactions between the low and synoptic frequencies also characterize less dramatic, low-frequency flows.

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