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P. H. Haynes, D. A. Poet, and E. F. Shuckburgh

Abstract

The interplay between dynamics and transport in two-dimensional flows is examined by comparing the transport and mixing in a kinematic flow in which the velocity field is imposed as a given function of time with that in an analogous dynamically consistent flow in which the advected vorticity field controls the flow evolution. In both cases the variation of the transport and mixing behavior with a parameter ϵ governing the strength of the time dependence is considered. It is shown that dynamical consistency has the effect of (i) postponing the breaking of a central transport barrier as ϵ increases and (ii) removing the property of the kinematic flow that, for a large range of ϵ, a weakly permeable central barrier persists. The first effect is associated with the development of a strong vorticity gradient and the associated jet along the central transport barrier. The second effect is associated with the fact that, in the dynamically consistent flow, the breaking of the central barrier is accompanied by a drastic change in the vorticity field and hence in the structure of the flow.

The relation between the vorticity field and transport barriers is further examined using a range of simple kinematic and dynamically consistent models. Implications for formulation of predictive models that represent the interactions between dynamics, transport, and mixing (and might be suggested as a basis for parameterizing eddies in flows that form multiple jets) are discussed.

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Keiichi Ishioka, Jitsuko Hasegawa, and Shigeo Yoden

Abstract

In a previous paper, asymmetry was found in jet profiles between eastward and westward jets, which appear spontaneously in two-dimensional β-plane decaying turbulence. That is, westward jets are narrower and more intense than eastward jets. In this paper, the dependence of the asymmetry on the order of hyperviscosity is examined. It is shown that the dependence is not as strong as expected in the previous paper. A revised theoretical scenario to explain the weak dependence is also given.

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Edwin P. Gerber and Geoffrey K. Vallis

Abstract

An idealized atmospheric general circulation model is used to investigate the factors controlling the time scale of intraseasonal (10–100 day) variability of the extratropical atmosphere. Persistence on these time scales is found in patterns of variability that characterize meridional vacillations of the extratropical jet. Depending on the degree of asymmetry in the model forcing, patterns take on similar properties to the zonal index, annular modes, and North Atlantic Oscillation. It is found that the time scale of jet meandering is distinct from the obvious internal model time scales, suggesting that interaction between synoptic eddies and the large-scale flow establish a separate, intraseasonal time scale. A mechanism is presented by which eddy heat and momentum transport couple to retard motion of the jet, slowing its meridional variation and thereby extending the persistence of zonal index and annular mode anomalies. The feedback is strong and quite sensitive to model parameters when the model forcing is zonally uniform. However, the time scale of jet variation drops and nearly all sensitivity to parameters is lost when zonal asymmetries, in the form of topography and thermal perturbations that approximate land–sea contrast, are introduced. A diagnostic on the zonal structure of the zonal index provides intuition on the physical nature of the index and annular modes and hints at why zonal asymmetries limit the eddy–mean flow interactions.

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Yuji Kitamura and Keiichi Ishioka

Abstract

Ensemble experiments of decaying shallow-water turbulence on a rotating sphere are performed to confirm the robustness of the emergence of an equatorial jet. While previous studies have reported that the equatorial jets emerging in shallow-water turbulence are always retrograde, predominance of a prograde jet, although less likely, was also found in the present ensemble experiments. Furthermore, a zonal-mean flow induced by wave–wave interactions was examined using a weak nonlinear model to investigate the acceleration mechanisms of the equatorial jet. The second-order acceleration is induced by the Rossby and mixed Rossby–gravity waves and its mechanisms can be categorized into two types. First, the local meridional wavenumber of a Rossby wave packet propagating toward the equator increases because of meridional variation of the Rossby deformation radius and/or the retrograde zonal-mean flow, resulting in a dissipation of the wave packet in the equatorial region. This mechanism always contributes to retrograde acceleration of an equatorial jet. Another mechanism is derived from the tilting of equatorial waves due to meridional shear of the zonal-mean flow. In this case, zonal-mean flow acceleration contributes to the intensification of a given basic flow.

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R. K. Scott and L. M. Polvani

Abstract

Although possibly the simplest model for the atmospheres of the giant planets, the turbulent forced-dissipative shallow-water system in spherical geometry has not, to date, been investigated; the present study aims to fill this gap. Unlike the freely decaying shallow-water system described by Cho and Polvani, equilibrium states in the forced-dissipative system are highly dependent on details of the forcing and the dissipation. For instance, it is found that for a given equilibrated energy level, the steadiness of zonal jets depends crucially on the balance between forcing and dissipation.

With long (up to 100 000 days) high-resolution (T170) calculations, the dependence of the equilibrium states on Rossby number Ro and Rossby deformation radius LD is explored, for the case when the dissipation takes the form of hypodiffusion (acting predominantly at large scales) and the random forcing at small scales is δ correlated in time. When LD is large compared to the planetary radius, zonal jets are verified to scale closely with the Rhines scale over a wide range of Ro; furthermore, the jets at the equator are found to be both prograde and retrograde with approximately equal likelihood. As LD is decreased, the equatorial jets become increasingly and consistently retrograde, in agreement with the freely decaying turbulence results. Also, the regime recently discussed by Theiss, where zonal jets are confined to low latitudes, is illustrated to emerge robustly in the limit of small LD. Finally, specific calculations with parameter values typical of the giant planets are presented, confirming many of the earlier results obtained in the freely decaying case.

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Yohai Kaspi and Glenn R. Flierl

Abstract

In this paper it is proposed that baroclinic instability of even a weak shear may play an important role in the generation and stability of the strong zonal jets observed in the atmospheres of the giant planets. The atmosphere is modeled as a two-layer structure, where the upper layer is a standard quasigeostrophic layer on a β plane and the lower layer is parameterized to represent a deep interior convective columnar structure using a negative β plane as in Ingersoll and Pollard. Linear stability theory predicts that the high wavenumber perturbations will be the dominant unstable modes for a small vertical wind shear like that inferred from observations. Here a nonlinear analytical model is developed that is truncated to one growing mode that exhibits a multiple jet meridional structure, driven by the nonlinear interaction between the eddies. In the weakly supercritical limit, this model agrees with previous weakly nonlinear theory, but it can be explored beyond this limit allowing the multiple jet–induced zonal flow to be stronger than the eddy field. Calculations with a fully nonlinear pseudospectral model produce stable meridional multijet structures when beginning from a random potential vorticity perturbation field. The instability removes energy from the background weak baroclinic shear and generates turbulent eddies that undergo an inverse energy cascade and form multijet zonal winds. The jets are the dominant feature in the instantaneous upper-layer flow, with the eddies being relatively weak. The jets scale with the Rhines length, but are strong enough to violate the barotropic stability criterion. It is shown that the basic physical mechanism for the generation and stability of the jets in the full numerical model is similar to that of the truncated model.

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Adam P. Showman

Abstract

To test the hypothesis that the zonal jets on Jupiter and Saturn result from energy injected by thunderstorms into the cloud layer, forced-dissipative numerical simulations of the shallow-water equations in spherical geometry are presented. The forcing consists of sporadic, isolated circular mass pulses intended to represent thunderstorms; the damping, representing radiation, removes mass evenly from the layer. These results show that the deformation radius provides strong control over the behavior. At deformation radii <2000 km (0.03 Jupiter radii), the simulations produce broad jets near the equator, but regions poleward of 15°–30° latitude instead become dominated by vortices. However, simulations at deformation radii >4000 km (0.06 Jupiter radii) become dominated by barotropically stable zonal jets with only weak vortices. The lack of midlatitude jets at a small deformation radii results from the suppression of the beta effect by column stretching; this effect has been previously documented in the quasigeostrophic system but never before in the full shallow-water system. In agreement with decaying shallow-water turbulence simulations, but in disagreement with Jupiter and Saturn, the equatorial flows in these forced simulations are always westward. In analogy with purely two-dimensional turbulence, the size of the coherent structures (jets and vortices) depends on the relative strengths of forcing and damping; stronger damping removes energy faster as it cascades upscale, leading to smaller vortices and more closely spaced jets in the equilibrated state. Forcing and damping parameters relevant to Jupiter produce flows with speeds up to 50–200 m s−1 and a predominance of anticyclones over cyclones, both in agreement with observations. However, the dominance of vortices over jets at deformation radii thought to be relevant to Jupiter (1000–3000 km) suggests that either the actual deformation radius is larger than previously believed or that three-dimensional effects, not included in the shallow-water equations, alter the dynamics in a fundamental manner.

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Semion Sukoriansky, Nadejda Dikovskaya, and Boris Galperin

Abstract

The notion of the cascade arrest in a β-plane turbulence in the context of continuously forced flows is revised in this paper using both theoretical analysis and numerical simulations. It is demonstrated that the upscale energy propagation cannot be stopped by a β effect and can only be absorbed by friction. A fundamental dimensional parameter in flows with a β effect, the Rhines scale, LR, has traditionally been associated with the cascade arrest or with the scale that separates turbulence and Rossby wave–dominated spectral ranges. It is shown that rather than being a measure of the inverse cascade arrest, LR is a characteristic of different processes in different flow regimes. In unsteady flows, LR can be identified with the moving energy front propagating toward the decreasing wavenumbers. When large-scale energy sink is present, β-plane turbulence may attain several steady-state regimes. Two of these regimes are highlighted: friction-dominated and zonostrophic. In the former, LR does not have any particular significance, while in the latter, the Rhines scale nearly coincides with the characteristic length associated with the large-scale friction. Spectral analysis in the frequency domain demonstrates that Rossby waves coexist with turbulence on scales smaller than LR thus indicating that the Rhines scale cannot be viewed as a crossover between turbulence and Rossby wave ranges.

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Francis Codron

Abstract

In a zonally symmetric climatology with a single eddy-driven jet, such as prevails in the Southern Hemisphere summer, the midlatitude variability is dominated by fluctuations of the jet around its mean position, as described by the Southern Hemisphere annular mode (SAM). To study whether this result holds for a zonally asymmetric climatology, the observed variability of the Southern Hemisphere winter is analyzed. The mean state in this case is characterized by relatively weak stationary waves; yet there exist significant zonal variations in the mean strength and meridional structure of the subtropical jet stream.

As in summer, the winter SAM signature is annular in shape and the corresponding wind anomalies are dipolar; but it is associated with two different behaviors of the eddy-driven jet in different longitudinal ranges. Over the Indian Ocean, the SAM is associated primarily with a latitudinal shift of the jet around its mean position. Over the Pacific sector, it is instead characterized by a seesaw in the wind speed between two distinct latitudes, corresponding to the positions of the midlatitude and subtropical jets. Composites of eddy forcing and baroclinicity over both sectors appear consistent with the two different behaviors. As in the zonal-mean case, high-frequency eddies both force and maintain the low-frequency wind anomalies associated with the SAM. The positive feedback by eddies is, however, not local: changes in the eddy forcing are influenced most strongly by zonal wind anomalies located upstream.

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I. G. Watterson

Abstract

Both high-latitude (HLM) and low-latitude modes (LLM) of variability of zonal wind in the Southern Hemisphere have been identified. Through an analysis of a simulation for 1871–2200 by the CSIRO Mark 3 climate model, the extent to which these might both be described as “annular modes,” based on their statistical patterns, physical mechanisms, and usefulness in climate study, is assessed. The modes are determined as EOF1 and EOF2 of vertically integrated zonal and monthly mean zonal wind, for 1871–1970. These match well those from ECMWF Re-Analysis (ERA) data and also from the earlier Mark 2 model. The mode index time series relate to largely annular patterns of local wind and surface pressure anomalies [with HLM giving the familiar southern annular mode (SAM)], and other simulated quantities. While modes calculated from 90° sectors are only moderately correlated (mostly in the polar region) for HLM, the link increases with time scale. There is little such relationship for LLM. A momentum equation analysis using daily data confirms that both zonal modes are driven by eddies, but only HLM features a positive eddy–mean flow feedback. Variation in feedback and surface damping through the seasonal cycle relate well to that in index autocorrelation, with the HLM being more persistent in summer. Stratospheric winds feature a long-lived component that tends to lead the HLM. The HLM drives sea surface temperature anomalies that persist for months, and coupling with the ocean increases variability on longer time scales. The annular variability in the warmer climate of the twenty-second century is barely changed, but the mean climate change in the far south projects strongly on the HLM. The LLM features some statistical annularity and may have some uses. However, only the HLM can be considered to be a physically based mode—the zonal-wind equivalent to the one southern annular mode.

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