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D. G. Dritschel and M. E. McIntyre

Abstract

A review is given that focuses on why the sideways mixing of potential vorticity (PV) across its background gradient tends to be inhomogeneous, arguably a reason why persistent jets are commonplace in planetary atmospheres and oceans, and why such jets tend to sharpen themselves when disturbed. PV mixing often produces a sideways layering or banding of the PV distribution and therefore a corresponding number of jets, as dictated by PV inversion. There is a positive feedback in which mixing weakens the “Rossby wave elasticity” associated with the sideways PV gradients, facilitating further mixing. A partial analogy is drawn with the Phillips effect, the spontaneous layering of a stably stratified fluid, in which vertically homogeneous stirring produces vertically inhomogeneous mixing of the background buoyancy gradient. The Phillips effect has been extensively studied and has been clearly demonstrated in laboratory experiments. However, the “eddy-transport barriers” and sharp jets characteristic of extreme PV inhomogeneity, associated with strong PV mixing and strong sideways layering into Jupiter-like “PV staircases,” with sharp PV contrasts Δq barrier, say, involve two additional factors besides the Rossby wave elasticity concentrated at the barriers. The first is shear straining by the colocated eastward jets. PV inversion implies that the jets are an essential, not an incidental, part of the barrier structure. The shear straining increases the barriers’ resilience and amplifies the positive feedback. The second is the role of the accompanying radiation-stress field, which mediates the angular-momentum changes associated with PV mixing and points to a new paradigm for Jupiter, in which the radiation stress is excited not by baroclinic instability but by internal convective eddies nudging the Taylor–Proudman roots of the jets.

Some examples of the shear-straining effects for strongly nonlinear disturbances are presented, helping to explain the observed resilience of eddy-transport barriers in the Jovian and terrestrial atmospheres. The main focus is on the important case where the nonlinear disturbances are vortices with core sizes ∼LD, the Rossby (deformation) length. Then a nonlinear shear-straining mechanism that seems significant for barrier resilience is the shear-induced disruption of vortex pairs. A sufficiently strong vortex pair, with PV anomalies ±Δq vortex, such that Δq vortex ≫ Δq barrier, can of course punch through the barrier. There is a threshold for substantial penetration through the barrier, related to thresholds for vortex merging. Substantial penetration requires Δq vortex ≳ Δq barrier, with an accuracy or fuzziness of order 10% when core size ∼LD, in a shallow-water quasigeostrophic model. It is speculated that, radiation stress permitting, the barrier-penetration threshold regulates jet spacing in a staircase situation. For instance, if a staircase is already established by stirring and if the stirring is increased to produce Δq vortex values well above threshold, then the staircase steps will be widened (for given background PV gradient β) until the barriers hold firm again, with Δq barrier increased to match the new threshold. With the strongest-vortex core size ∼LD this argument predicts a jet spacing 2b = Δq barrier/βL 2 Rh (U vortex)/LD in order of magnitude, where L Rh(U vortex) = (U vortex/β)1/2, the Rhines scale based on the peak vortex velocity U vortex, when 2bL D. The resulting jet speeds U jet are of the same order as U vortex; thus also 2bL 2 Rh(U jet)/LD. Weakly inhomogeneous turbulence theory is inapplicable here because there is no scale separation between jets and vortices, both having scales ∼LD in this situation.

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John Marshall, David Ferreira, J-M. Campin, and Daniel Enderton

Abstract

Numerical experiments are described that pertain to the climate of a coupled atmosphere–ocean–ice system in the absence of land, driven by modern-day orbital and CO2 forcing. Millennial time-scale simulations yield a mean state in which ice caps reach down to 55° of latitude and both the atmosphere and ocean comprise eastward- and westward-flowing zonal jets, whose structure is set by their respective baroclinic instabilities. Despite the zonality of the ocean, it is remarkably efficient at transporting heat meridionally through the agency of Ekman transport and eddy-driven subduction. Indeed the partition of heat transport between the atmosphere and ocean is much the same as the present climate, with the ocean dominating in the Tropics and the atmosphere in the mid–high latitudes. Variability of the system is dominated by the coupling of annular modes in the atmosphere and ocean. Stochastic variability inherent to the atmospheric jets drives variability in the ocean. Zonal flows in the ocean exhibit decadal variability, which, remarkably, feeds back to the atmosphere, coloring the spectrum of annular variability. A simple stochastic model can capture the essence of the process. Finally, it is briefly reviewed how the aquaplanet can provide information about the processes that set the partition of heat transport and the climate of Earth.

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Yoshi-Yuki Hayashi, Seiya Nishizawa, Shin-ichi Takehiro, Michio Yamada, Keiichi Ishioka, and Shigeo Yoden

Abstract

Jet formation in decaying two-dimensional turbulence on a rotating sphere is reviewed from the viewpoint of Rossby waves. A series of calculations are performed to confirm the behavior of zonal mean flow generation on the parameter space of the rotation rate Ω and Froude number Fr. When the flow is nondivergent and Ω is large, intense easterly circumpolar jets tend to emerge in addition to the appearance of a banded structure of zonal mean flows with alternating flow directions. When the system allows surface elevation, circumpolar jets disappear and an equatorial easterly jet emerges with increasing Fr. The appearance of the intense easterly jets can be understood by the angular-momentum transport associated with the generation, propagation, and absorption of Rossby waves. When the flow is nondivergent, long Rossby waves tend to be absorbed near the poles. In contrast, when Fr is large, Rossby waves can hardly propagate poleward and tend to be absorbed near the equator.

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Cegeon J. Chan, R. Alan Plumb, and Ivana Cerovecki

Abstract

The authors investigate the dynamics of zonal jets in a semihemisphere zonally reentrant ocean model. The forcings imposed in the model are an idealized atmospheric wind stress and relaxation to a latitudinal temperature profile held constant in time. While there are striking similarities to the observed atmospheric annular modes, where the leading mode of variability is associated with the primary zonal jet’s meridional undulation, secondary (weaker) jets emerge and systematically migrate equatorward.

The model output suggests the following mechanism for the equatorward migration: while the eddy momentum fluxes sustain the jets, the eddy heat fluxes have a poleward bias causing an anomalous residual circulation with poleward (equatorward) flow on the poleward (equatorward) flanks. By conservation of mass, there must be a rising residual flow at the jet. From the thermodynamics equation, the greatest cooling occurs at the jet core, thus creating a tendency to reduce the baroclinicity on the poleward flank, while enhancing it on the equatorward flank. Consequently, the baroclinic zone shifts, perpetuating the jet migration.

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Peter L. Read, Yasuhiro H. Yamazaki, Stephen R. Lewis, Paul D. Williams, Robin Wordsworth, Kuniko Miki-Yamazaki, Joël Sommeria, and Henri Didelle

Abstract

The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

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Shin Takehiro, Michio Yamada, and Yoshi-Yuki Hayashi

Abstract

A series of numerical experiments on two-dimensional decaying turbulence is performed for a barotropic fluid on a rotating sphere. Numerical calculations have confirmed two important asymptotic features: emergence of the banded structure of zonal flows and their extreme latitudinal inhomogeneities in which kinetic energy is accumulated into the easterly circumpolar jets. The banded structure of zonal flows is established relatively early on in the initial stage. Later, after extended periods of time integration, only the circumpolar jets are intensified gradually, while there is no further evolution in the banded structure in the low and midlatitudes. Wave activity flux analysis illustrates that the initial vortices in the low and midlatitudes propagate poleward as Rossby waves and converge to produce easterly circumpolar flows. In association with this convergence, accumulation of the mean zonal component of kinetic energy proceeds. The tendency for the accumulation becomes strong as the rotation rate is increased, and nearly all of the kinetic energy is concentrated to the circumpolar flows in cases of rapid rotation.

A theoretical model is constructed under the assumption that a circumpolar jet emerges around the latitude where the local Rhines scale is equal to the distance from the Pole, and that initial vortices at the lower latitudes contribute to the generation of the jets. The model describes the mean zonal component of kinetic energy and the averaged speed and width of the circumpolar jets as functions of the rotation rate, which agree satisfactorily with the numerical results.

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Thomas Jung and Peter B. Rhines

Abstract

Some effects of Greenland on the Northern Hemisphere wintertime circulation are discussed. Inviscid pressure drag on Greenland’s slopes, calculated from reanalysis data, is related to circulation patterns. Greenland lies north of the core of the tropospheric westerly winds. Yet strong standing waves, which extend well into the stratosphere, produce a trough/ridge system with jet stream lying close to Greenland, mean Icelandic low in its wake, and storm track that interacts strongly with its topography. In the lower troposphere, dynamic height anomalies associated with strongly easterly pressure drag on the atmosphere are quite localized in space and relatively short-lived compared to upper levels, yet they involve a hemispheric-scale dislocation of the stratospheric polar vortex. It is a two-scale problem, however; the high-pass time-filtered part of the height field, responsible for 73% of the pressure drag, is quite different, and expresses propagating cyclonic development in the Atlantic storm track. Eliassen–Palm flux (EP flux) analysis shows that the atmospheric response is (counterintuitively) an acceleration of the westerly winds. The hemispheric influence is consistent with the model results of Junge et al. suggesting that Greenland affects the stationary waves in winter.

This discussion shows that Greenland is not a simple “stirring rod” in the westerly circulation, yet involvement of Greenland’s topography with the shape, form, and intensity of the storm track is strong. Interaction of traveling storms, the jet stream, and the orographic wake frequently leads to increase of the lateral scale such that cyclonic system expands to the size of Greenland itself (∼2500 km). Using the global ECMWF general circulation model, the authors explore the effect of model resolution on these circulations. Statistically, in two case studies, and in higher-resolution global models at TL255 to TL799 resolution, intense tip jet, hydraulic downslope jet, and gravity wave radiation appear in strong flow events, in accord with the work of Doyle and Shapiro. Three-dimensional particle trajectories and vorticity maps show the nature and intensity of the summit-gap flow. Cyclonic systems in the lee of Greenland are strongly affected by the downslope jet. Penetration of the Arctic Basin by cyclonic systems arises from this source region, and the amplitude of the pressure drag is enhanced at high resolution. At the higher resolutions, storm-track analysis verifies the splitting of the storm track by Greenland with a substantial minority of storms moving northward through Baffin Bay. Finally, analysis of 20 winters of 40-yr ECMWF Re-Analysis (ERA-40) reforecasts shows little evidence that negative pressure-drag events are followed by anomalously large forecast errors over Europe, throughout the forecast. Forecast skill for the pressure drag is surprisingly good, with a correlation of 0.65 at 144 h.

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Yasuko Hio and Shigeo Yoden

Abstract

Weakly nonlinear aspects of a barotropically unstable polar vortex in a forced–dissipative system with a zonally asymmetric surface topography are investigated in order to obtain a deeper understanding of rather periodic variations of the winter circumpolar vortex in the Southern Hemisphere stratosphere that are characterized by the wave–wave interaction between the stationary planetary wave of zonal wavenumber 1 (denoted as Wave 1) and the eastward traveling Wave 2 as studied by Hio and Yoden in 2004. The authors use a spherical barotropic model with a forcing of zonally symmetric jet, dissipation, and sinusoidal surface topography. A parameter sweep experiment is performed by changing the amplitude of the surface topography, which forces the stationary Wave 1, and the width of the prescribed zonally symmetric jet, which controls the barotropic instability, to generate the traveling Wave 2. Several types of solutions from a time-independent solution to a nonperiodic irregular solution are obtained for the combination of these external parameters, but the predominant solution obtained in a wide parameter space is periodic.

Details of the wave–wave interactions are described for the transition from a quasiperiodic vacillation to a periodic solution as the increase of the amplitude of topography. Phase relationships are locked at the transition, and variations of zonal-mean zonal flow and topographically forced Wave 1 synchronize with periodic progression of Wave 2 in the periodic solution. A diagnosis with a low-order “empirical mode expansion” of the vorticity equation gives a limited number of dominant nonlinear triad interactions among the zonal-mean, Wave-1, and Wave-2 components around the transition point.

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Michael J. Ring and R. Alan Plumb

Abstract

Previous studies using simplified general circulation models have shown that “annular modes” arise as the dominant mode of variability. A simple GCM is used here to explore to what extent these modes are also the preferred response of the system to generic forcing.

A number of trials are conducted under which the model is subjected to an artificial, zonally symmetric angular momentum forcing, and the climatologies of these trials are compared to that of the control. The forcing location is varied among the several trials. It is found that the changes in the model’s climatology are generally annular mode–like, as long as the imposed forcing projects strongly upon the annular modes of the unforced model.

The role of changes to the eddy–zonal flow feedback versus the action of direct forcing is also considered through the use of a zonally symmetric version of the model. It is found that the direct responses to forcing are insufficient to capture either the strength or the structure of the annular mode responses. Instead, the changes in eddy fluxes are needed to produce the correct responses.

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P. B. Rhines

Abstract

This paper describes qualitative features of the generation of jetlike concentrated circulations, wakes, and blocks by simple mountainlike orography, both from idealized laboratory experiments and shallow-water numerical simulations on a sphere. The experiments are unstratified with barotropic lee Rossby waves, and jets induced by mountain orography. A persistent pattern of lee jet formation and lee cyclogenesis owes its origins to arrested topographic Rossby waves above the mountain and potential vorticity (PV) advection through them. The wake jet occurs on the equatorward, eastern flank of the topography. A strong upstream blocking of the westerly flow occurs in a Lighthill mode of long Rossby wave propagation, which depends on βa 2/U, the ratio of Rossby wave speed based on the scale of the mountain, to zonal advection speed, U (β is the meridional potential vorticity gradient, f is the Coriolis frequency, and a is the diameter of the mountain). Mountains wider (north–south) than the east–west length scale of stationary Rossby waves will tend to block the oncoming westerly flow. These blocks are essentially β plumes, which are illustrated by their linear Green function. For large βa 2/U, upwind blocking is strong; the mountain wake can be unstable, filling the fluid with transient Rossby waves as in the numerical simulations of Polvani et al. For small values, βa 2/U ≪ 1 classic lee Rossby waves with large wavelength compared to the mountain diameter are the dominant process. The mountain height, δh, relative to the mean fluid depth, H, affects these transitions as well. Simple lee Rossby waves occur only for such small heights, δh/h/f, that the f/h contours are not greatly distorted by the mountain. Nongeostrophic dynamics are seen in inertial waves generated by geostrophic shear, and ducted by it, and also in a texture of finescale, inadvertent convection. Weakly damped circulations induced in a shallow-water numerical model on a sphere by a lone mountain in an initially simple westerly wind are also described. Here, with βa 2/U ∼1, potential vorticity stirring and transient Rossby waves dominate, and drive zonal flow acceleration. Low-latitude critical layers, when present, exert strong control on the high-latitude waves, and with no restorative damping of the mean zonal flow, they migrate poleward toward the source of waves. While these experiments with homogeneous fluid are very simplified, the baroclinic atmosphere and ocean have many tall or equivalent barotropic eddy structures owing to the barotropization process of geostrophic turbulence.

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