• Allen, R. A., , and N. Nakamura, 2001: A seasonal climatology of effective diffusivity in the stratosphere. J. Geophys. Res., 106 , 79177935.

    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., , J. R. Holton, , and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysical Series, Vol. 40, Academic Press, 489 pp.

    • Search Google Scholar
    • Export Citation
  • Arnold, V. I., , V. V. Kozlov, , and A. I. Neistadt, 1986: Mathematical Aspects of Classical and Celestial Mechanics. Vol. 3, Encyclopedia of Mathematical Sciencies, Springer.

    • Search Google Scholar
    • Export Citation
  • Baldwin, M. P., , P. B. Rhines, , H-P. Huang, , and M. E. McIntyre, 2007: The jet-stream conundrum. Science, 315 , 467468.

  • Banfield, D., , P. J. Gierasch, , M. Bell, , E. Ustinov, , A. P. Ingersoll, , A. R. Vasavada, , R. A. West, , and M. J. S. Belton, 1998: Jupiter’s cloud structure from Galileo imaging data. Icarus, 135 , 230250.

    • Search Google Scholar
    • Export Citation
  • Carlson, B. E., , A. A. Lacis, , and W. B. Rossow, 1994: Belt-zone variations in the Jovian cloud structure. J. Geophys. Res., 99 , 1462314658.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., , and P. G. Drazin, 1961: Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66 , 83109.

    • Search Google Scholar
    • Export Citation
  • Chen, P., , J. R. Holton, , A. O’Neill, , and R. Swinbank, 1994: Isentropic mass exchange between the tropics and extratropics in the stratosphere. J. Geophys. Res., 51 , 30063018.

    • Search Google Scholar
    • Export Citation
  • Cho, J. Y-K., , and L. Polvani, 1996: The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluids, 8 , 15311552.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., , and V. M. Gryanik, 2004: Barotropic beta-plane turbulence in a regime with strong zonal jets revisited. J. Atmos. Sci., 61 , 22832295.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., , and D. Gurarie, 2004: Scaling, spectra, and zonal jets in beta-plane turbulence. Phys. Fluids, 16 , 25922603.

  • Dowling, T. E., 1995: Dynamics of Jovian atmospheres. Annu. Rev. Fluid Mech., 27 , 293334.

  • Dritschel, D. G., , and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65 , 855874.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., , and R. K. Scott, 2008: A barotropic model of the angular momentum conserving potential vorticity staircase in spherical geometry. J. Atmos. Sci., 65 , 11051136.

    • Search Google Scholar
    • Export Citation
  • Grant, W. B., , E. V. Browell, , C. S. Long, , L. L. Stowe, , R. G. Grainger, , and A. Lambert, 1996: Use of volcanic aerosols to study the tropical stratospheric reservoir. J. Geophys. Res., 101 , 39733988.

    • Search Google Scholar
    • Export Citation
  • Haller, G., 2001: Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Phys. Fluids, 13 , 33653385.

    • Search Google Scholar
    • Export Citation
  • Haynes, P., , and E. Shuckburgh, 2000: Effective diffusivity as a diagnostic of atmospheric transport. 1. Stratosphere. J. Geophys. Res., 105 , 2277722794.

    • Search Google Scholar
    • Export Citation
  • Heimpel, M., , J. J. Aurnou, , and J. Wicht, 2005: Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model. Nature, 438 , 193196.

    • Search Google Scholar
    • Export Citation
  • Huang, H-P., , and W. A. Robinson, 1998: Two-dimensional turbulence and persistent zonal jets in a global barotropic model. J. Atmos. Sci., 55 , 611632.

    • Search Google Scholar
    • Export Citation
  • Ingersoll, A. P., , P. J. Gierasch, , D. Banfield, , and A. R. Vasavada, and the Galileo Imaging Team, 2000: Moist convection as an energy source for the large-scale motions in Jupiter’s atmosphere. Nature, 403 , 630632.

    • Search Google Scholar
    • Export Citation
  • Irwin, P. G. J., , A. L. Weir, , F. W. Taylor, , S. B. Calcutt, , and R. W. Carlson, 2001: The origin of belt/zone contrasts in the atmosphere of Jupiter and their correlation with 5-μm opacity. Icarus, 149 , 397415.

    • Search Google Scholar
    • Export Citation
  • Irwin, P. G. J., , K. Sihra, , N. Bowles, , F. W. Taylor, , and S. B. Calcutt, 2005: Methane absorption in the atmosphere of Jupiter from 1800 to 9500 cm−1 and implications for vertical cloud structure. Icarus, 176 , 255271.

    • Search Google Scholar
    • Export Citation
  • Jorba, Á, , and C. Simó, 1996: On quasi-periodic perturbations of elliptic equilibrium points. SIAM J. Math. Analy., 27 , 17041737.

  • Juckes, N. M., , and M. E. McIntyre, 1987: A high-resolution one-layer model of breaking planetary waves in the stratosphere. Nature, 328 , 590596.

    • Search Google Scholar
    • Export Citation
  • Manfroi, A. J., , and W. R. Young, 1999: Slow evolution of zonal jets on the beta plane. J. Atmos. Sci., 56 , 784800.

  • Marcus, P. S., , and C. Lee, 1998: A model for eastward and westward jets in laboratory experiments and planetary atmospheres. Phys. Fluids, 10 , 14741489.

    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., , B. Bang, , and H. Sasaki, 2005: Observational evidence of alternating zonal jets in the world ocean. Geophys. Res. Lett., 32 .L12607, doi:10.1029/2005GL022728.

    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., , O. V. Melnichenko, , P. P. Niiler, , and H. Sasaki, 2008: Stationary mesoscale jet-like features in the ocean. Geophys. Res. Lett, 35 .L08603, doi:10.1029/2008GL033267.

    • Search Google Scholar
    • Export Citation
  • Minschwaner, K., and Coauthors, 1996: Bulk properties of isentropic mixing into the tropics in the lower stratosphere. J. Geophys. Res., 101 , 94339440.

    • Search Google Scholar
    • Export Citation
  • Mote, P. W., , T. J. Dunkerton, , M. E. McIntyre, , E. A. Ray, , P. H. Haynes, , and J. M. Russell III, 1998: Vertical velocity, vertical diffusion, and dilution by midlatitude air in the tropical lower stratosphere. J. Geophys. Res., 103 , 86518666.

    • Search Google Scholar
    • Export Citation
  • Nozawa, T., , and S. Yoden, 1997: Formation of zonal bands structure in forced two-dimensional turbulence on a rotating sphere. Phys. Fluids, 9 , 20812093.

    • Search Google Scholar
    • Export Citation
  • Peltier, W. K., , and G. R. Stunhe, 2002: The upscale turbulent cascade: Shear layers, cyclones, and gas giant bands. Meteorology at the Millennium, R. P. Pierce, Ed., Academic Press, 43–61.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1996: A “tropical pipe” model of stratospheric transport. J. Geophys. Res., 101 , 39573972.

  • Porco, C. C., and Coauthors, 2003: Cassini imaging of Jupiter’s atmosphere, satellites, and rings. Science, 299 , 15411547.

  • Read, P. L., , P. J. Gierasch, , B. J. Conrath, , A. Simon-Miller, , T. Fouchet, , and Y. H. Yamazaki, 2006: Mapping potential-vorticity dynamics on Jupiter. I: Zonal-mean circulation from Cassini and Voyager 1 data. Quart. J. Roy. Meteor. Soc., 132 , 15771603.

    • Search Google Scholar
    • Export Citation
  • Read, P. L., , Y. H. Yamazaki, , S. R. Lewis, , P. D. Williams, , R. Wordsworth, , K. Miki-Yamazaki, , J. Sommeria, , and H. Didelle, 2007: Dynamics of convectively driven banded jets in the laboratory. J. Atmos. Sci., 64 , 40314052.

    • Search Google Scholar
    • Export Citation
  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69 , 417443.

  • Richards, K. J., , N. A. Maximenko, , F. O. Bryan, , and H. Sasaki, 2006: Zonal jets in the Pacific Ocean. Geophys. Res. Lett., 33 .L03605, doi:10.1029/2005GL024645.

    • Search Google Scholar
    • Export Citation
  • Rypina, I. I., , M. G. Brown, , F. J. Beron-Vera, , H. Koçak, , M. J. Olascoaga, , and I. A. Udovydchenkov, 2007a: On the Lagrangian dynamics of atmospheric zonal jets and the permeability of the stratospheric polar vortex. J. Atmos. Sci., 64 , 35953610.

    • Search Google Scholar
    • Export Citation
  • Rypina, I. I., , M. G. Brown, , F. J. Beron-Vera, , H. Koçak, , M. J. Olascoaga, , and I. A. Udovydchenkov, 2007b: Robust transport barriers resulting from strong Kolmogorov–Arnold–Moser stability. Phys. Rev. Lett., 98 .104102, doi:10.1103/PhysRevLett.98.104102.

    • Search Google Scholar
    • Export Citation
  • Scott, R. K., , and L. M. Polvani, 2007: Forced–dissipative shallow-water turbulence on the sphere and the atmospheric circulation of the giant planets. J. Atmos. Sci., 64 , 31583176.

    • Search Google Scholar
    • Export Citation
  • Sevryuk, M. B., 2007: Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman’s method. Discrete Contin. Dyn. Syst., 18 , 569595.

    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 2007: Transport in the middle atmosphere. J. Meteor. Soc. Japan, 85B , 165191.

  • Showman, A. P., , and I. de Pater, 2005: Dynamical implications of Jupiter’s tropospheric ammonia abundance. Icarus, 174 , 192204.

  • Simon-Miller, A. A., , D. Banfield, , and P. J. Gierasch, 2001: Color and the vertical structure in Jupiter’s belts, zones, and weather systems. Icarus, 154 , 459474.

    • Search Google Scholar
    • Export Citation
  • Trepte, C. R., , and M. H. Hitchman, 1992: Tropical stratospheric circulation deduced from satellite aerosol data. Nature, 355 , 626628.

    • Search Google Scholar
    • Export Citation
  • Trepte, C. R., , R. E. Veiga, , and M. P. McCormick, 1993: The poleward dispersal of Mount Pinatubo volcanic aerosol. J. Geophys. Res., 98 , 1856318574.

    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., , and M. E. Maltrud, 1993: Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr., 23 , 13461362.

    • Search Google Scholar
    • Export Citation
  • Vasavada, A. R., , and A. P. Showman, 2005: Jovian atmospheric dynamics: An update after Galileo and Cassini. Rep. Prog. Phys., 68 , 19351996.

    • Search Google Scholar
    • Export Citation
  • Waugh, D. W., 1996: Seasonal variation of isentropic transport out of the tropical stratosphere. J. Geophys. Res., 101 , 40074023.

  • Williams, G. P., 1978: Planetary circulations. I. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci., 35 , 13991426.

    • Search Google Scholar
    • Export Citation
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    (left) Zonal velocity and (right) potential vorticity in a PV staircase zonal flow. The zonal velocity structure shown corresponds to the finite LD case, Eq. (4), with LD = b/2 = 2000 km, roughly approximating midlatitude conditions on Jupiter. In this figure the ideal PV jumps have smooth transition regions with tanh dependence on y locally.

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    Instantaneous zonally averaged (left) zonal velocity and (middle) potential vorticity, and (right) the potential vorticity after a 1-yr simulation of the quasigeostrophic equations (1)(2) using as the initial state a perturbation to the PV staircase flow of Fig. 1.

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    (a) Zonally averaged zonal velocity u(y) at t = 1 yr. (b) Initial positions [x(0), y(0)] of color-coded passive tracers. (c) Positions [x(τ), y(τ)] of color-coded passive tracers at t = τ = 1 yr. (d) Finite-time Lyapunov exponent (FTLE) field as a function of initial position computed using a 1-yr integration time interval. The time-dependent velocity field whose final state is shown in Fig. 2 was used to construct (a), (c), and (d).

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    (left) Zonally averaged zonal wind speed as a function of latitude on Jupiter at the cloud top level as inferred from images taken in December 2000 by the Cassini spacecraft (Porco et al. 2003). Gray and white zonal bands indicate belts and zones, respectively. (right) Near-instantaneous visible band image of Jupiter constructed from images taken by Cassini in December 2000. Note that many features of Jupiter’s weather layer that are not seen in this image may be revealed by radiative transfer analyses outside of the visible band of the electromagnetic spectrum. NASA image PIA07782 (PIA images are available at NASA’s planetary photojournal Web site, http://photojournal.jpl.nasa.gov).

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    Meridional distribution of zonally averaged (left) zonal wind u0(y), (center) potential vorticity q0(y), and (right) potential vorticity gradient q0(y) in Jupiter’s weather layer based on Cassini data. Both unsmoothed and smoothed wind profiles are plotted; the smoothed wind profile was used to compute q0(y) and q0(y). Solid and dashed horizontal lines are drawn at the latitudes of the cores of westward and eastward jets, respectively. Note that large positive values of q0(y) coincide with the cores of eastward jets. A spherical planet (rather than a β-plane, which is used elsewhere in this paper) was assumed to compute the q0(y) and q0(y) structures shown.

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    Seven-year (1992–98) monthly average of zonally averaged zonal wind and potential vorticity on the 460 K isentropic surface based on the ERA-40 reanalysis product. Contours show zonal winds (m s−1). Solid and dashed contours represent eastward and westward flow, respectively. Colors indicate Ertel’s potential vorticity.

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Zonal Jets as Transport Barriers in Planetary Atmospheres

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  • 1 Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
  • | 2 Departments of Computer Science and Mathematics, University of Miami, Coral Gables, Florida
  • | 3 Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
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Abstract

The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter’s midlatitude weather layer and in the earth’s summer hemisphere subtropical stratosphere.

* Current affiliation: Woods Hole Oceanographic Institution, Woods Hole, Massachusetts.

Corresponding author address: F. J. Beron-Vera, RSMAS/AMP, University of Miami, 4600 Rickenbacker Cswy., Miami, FL 33149. Email: fberon@rsmas.miami.edu

Abstract

The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter’s midlatitude weather layer and in the earth’s summer hemisphere subtropical stratosphere.

* Current affiliation: Woods Hole Oceanographic Institution, Woods Hole, Massachusetts.

Corresponding author address: F. J. Beron-Vera, RSMAS/AMP, University of Miami, 4600 Rickenbacker Cswy., Miami, FL 33149. Email: fberon@rsmas.miami.edu

1. Introduction

In Rypina et al. (2007a), it was argued that the transport barrier near the core of the austral polar night jet can be explained by a mechanism different from the potential vorticity (PV) barrier mechanism (Juckes and McIntyre 1987). The new barrier mechanism, which was subsequently referred to as strong KAM stability (Rypina et al. 2007b), follows from an argument that does not make use of dynamical constraints on the streamfunction. This necessitates that dynamical constraints be considered separately. Interestingly, decoupling of the dynamical constraints from the barrier mechanism leads to the possibility that transport barriers in PV-conserving flows may occur at locations that do not coincide with PV barriers. Rypina et al. (2007a) predicted that barriers of this type should be present in close proximity to the cores of westward zonal jets in planetary atmospheres. In this paper, we demonstrate that transport barriers of this type are present in a numerically simulated PV-conserving flow. We also argue that barriers of the type described are present in Jupiter’s midlatitude weather layer and in the earth’s summer hemisphere subtropical stratosphere.

In the following section, passive tracer transport in a numerically simulated perturbed PV staircase flow is investigated. It is shown that robust meridional transport barriers in close proximity to the cores of both eastward and westward zonal jets are present. The surprise is that westward jets, at which the background PV gradient vanishes, act as transport barriers. Essential elements of the strong Kolmogorov–Arnold–Moser (KAM) stability argument are reviewed to explain this behavior. In section 3, we discuss the relevance of transport barriers of the strong KAM stability type to the interpretation of 1) Jupiter’s midlatitude weather layer belt-zone structure, and 2) the earth’s summer hemisphere subtropical stratosphere. In the final section, we briefly discuss our results.

2. Transport barriers in a perturbed PV staircase flow

In this section, we consider passive tracer transport in a perturbed PV staircase flow. We assume quasigeostrophic dynamics in a one-layer reduced-gravity setting and make use of a local Cartesian coordinate system (x, y) in which x and y increase to the east and north, respectively, and the constant β is the local y derivative of the Coriolis parameter. The zonal and meridional components of the velocity field are u = −∂ψ/∂y and υ = ∂ψ/∂x, respectively, where ψ (x, y, t) is the streamfunction. The flow is constrained to satisfy
i1520-0469-65-10-3316-e1
where
i1520-0469-65-10-3316-e2
is the quasigeostrophic potential vorticity and LD is the deformation radius. Recent theoretical, numerical, and experimental work, including extensions involving spherical geometry, shallow-water dynamics, and inclusion of weak forcing and dissipation, has shown that flows satisfying (1)(2) with periodic boundary conditions in x tend to evolve toward a state of the form
i1520-0469-65-10-3316-e3
where ψ1 is a small perturbation to ψ0 (Cho and Polvani 1996; Danilov and Gryanik 2004; Danilov and Gurarie 2004; Dritschel and McIntyre 2008; Huang and Robinson 1998; Manfroi and Young 1999; Nozawa and Yoden 1997; Peltier and Stunhe 2002; Read et al. 2007; Rhines 1975; Scott and Polvani 2007; Vallis and Maltrud 1993; Williams 1978). The background zonal flow is characterized by an approximately piecewise constant PV distribution that has been appropriately described as a PV staircase (Baldwin et al. 2007; Dritschel and McIntyre 2008; Dunkerton and Scott 2008). The corresponding zonal velocity profile u0(y) = −0/dy is periodic in y. Taking the period to be 2b, the jump in q0(y) at each step is 2, and the zonal flow is the periodic extension of
i1520-0469-65-10-3316-e4
consisting of a periodic sequence of alternating narrow eastward and broad westward zonal jets with q0(y) piecewise constant between adjacent eastward jets, as illustrated in Fig. 1. Note that at the center of each constant q0 band lies a westward jet. In the limit LD/b → ∞, (4) reduces to
i1520-0469-65-10-3316-e5
whose qualitative features are identical to those of the finite LD/b case. The flows (4) and (5) are normalized so that the integral of u0(y) over y vanishes. The Rhines scale U/β, where U is a characteristic velocity, is an approximate measure of the separation between adjacent eastward jets. Corresponding to (5) this separation is exactly 2b = 23Umax/β, where Umax is the wind speed at the core of one of the eastward jets.

Before presenting numerical simulations of passive tracer transport in a perturbed PV staircase flow, we describe predictions based on two different arguments of the expected locations of transport barriers in this flow. First, the PV barrier argument (Dritschel and McIntyre 2008) leads to the expectation that transport barriers should be present only near the cores of the eastward jets. The basic elements of the PV barrier argument were used originally by Juckes and McIntyre (1987) to explain the mechanism by which the eastward jet at the perimeter of the austral stratospheric polar vortex, sometimes referred to as the austral polar night jet, during the late winter and early spring serves to trap ozone-depleted air inside the polar vortex. The essential elements of the argument are that at eastward jets the large gradient of q0(y) is associated with a large Rossby wave restoring force (“Rossby wave elasticity”) that inhibits meridional exchange of fluid at larger scales and that shear u0(y) = du0/dy acts to inhibit meridional exchange at smaller scales. [However, note that in Rypina et al. (2007a) it is argued that increasing meridional shear acts, on average, to increase meridional exchange.]

An alternative argument, based on the strong KAM stability mechanism (Rypina et al. 2007a, b), leads to the expectation that transport barriers should be present near the cores of both eastward and westward jets in a PV staircase flow. The argument leading to this expectation will now be reviewed. The Lagrangian (particle trajectory) equations of motion,
i1520-0469-65-10-3316-e6
constitute a nonautonomous one-degree-of-freedom Hamiltonian system with (x, y) the canonically conjugate coordinate–momentum pair and ψ(x, y, t) the Hamiltonian. This allows results from studies of integrable and nonintegrable Hamiltonian systems to be applied. In the background steady flow, with ψ = ψ0 (y), Eqs. (6) are integrable and the motion is describable using a transformed Hamiltonian H0(I), where (I, θ) are action–angle variables. Each trajectory lies on a torus that is labeled by its I value. Motion is 2π periodic in θ with angular frequency ω(I) = H0(I). According to each of many variants of the Kolmogorov–Arnold–Moser theorem (Arnold et al. 1986), many of the unperturbed tori survive in the perturbed system (3), albeit in a slightly distorted form, provided certain conditions are met. Surviving tori cannot be traversed and serve as transport barriers. [For reasons described in Rypina et al. (2007a), the process known as Arnold diffusion does not occur in the systems under study.] Torus destruction is caused by the excitation and overlapping of resonances. Each resonance has a characteristic width Δω. Nondegenerate ω′(I) ≠ 0 resonance widths are proportional to |ω′(I)|1/2. Degenerate ω′(I) = 0 resonance widths do not vanish but are generally narrower than nondegenerate resonance widths. [Quantitative estimates of both degenerate and nondegenerate resonance widths are given in Rypina et al. (2007b); for our purposes it suffices to note the general trend.] For most moderate strength perturbations to the background, small resonance widths near degenerate tori lead to nonoverlapping resonances and thus unbroken tori that serve as transport barriers. This constitutes the strong KAM stability barrier argument. In our model (3), the connection between (x, y) and (I, θ) is particularly simple: I = −Ry/2π, θ = 2πx/R, where R is the distance around the planet along a constant latitude circle at the latitude at which β is defined. The period of motion 2π/ω is R/u0(y), so ω(I) = 2πR−1u0(−I/R). At the cores of both eastward and westward jets u0(y) = 0, so ω′(I) = 0 at these locations: the strong KAM stability argument predicts that robust meridional transport barriers should be present. Barriers of this type may be broken if the transient perturbation ψ1 (x, y, t) strongly excites a low-order resonance with the frequency ω = 2πu0(y)/R of the background flow near the core of the jet. Three final issues are noteworthy. First, because the strong KAM stability argument is a kinematic argument [based on (6) alone], dynamical consistency—that is, consistency between (1)(3) and (4) or (5)—and flow stability must be considered separately. Second, our emphasis on jets is unnecessarily restrictive inasmuch as the strong KAM stability argument holds at all locations where u0(y) = 0. Third, the stated results of KAM theory assume that ψ1(x, y, t) can be expressed as a multiperiodic (generically quasiperiodic) function of t (Jorba and Simó 1996; Sevryuk 2007).

We now describe a set of numerical experiments that were performed to investigate passive tracer transport in a perturbed PV staircase flow. The streamfunctions on which our tracer transport simulations are based were constructed by numerically solving (1)(2) using as an initial state a perturbation to the background PV staircase (4). Before presenting the results, it is appropriate to make two comments about what we expect to learn from these simulations. First, these simulations provide a test of the assertion that the decomposition (1)(4) is dynamically consistent. Second, given a positive outcome of the first test, these simulations test whether westward zonal jets, across which there is no PV barrier, serve as robust meridional transport barriers. The quasigeostrophic equation pair (1)(2) was solved numerically using a standard pseudospectral technique on a 2562 grid in the [0, 8b) × [−4b, 4b) computational domain. Periodic boundary conditions in ψ were applied in both x and y directions. The Arakawa representation of the advective terms, which are often written as a Jacobian, was used. The solution was marched forward in time using a second-order Adams–Bashforth scheme with a dimensionless time step βbΔt = 0.002. To control the spurious amplification of high wavenumber modes, we applied a weak exponential cutoff filter and included a small amount of hyperviscosity. Two types of initial perturbation to the background PV staircase were used in our simulations. The first type of perturbation consisted of a superposition of periodic displacements of PV contours with random phases uniformly distributed on [0, 2π). The second type of perturbation was a doubly periodic perturbation to the streamfunction consisting of a sum of a product of Fourier modes with random phases. In all of our simulations the separation between adjacent eastward jets 2b was taken to be 8000 km and β = 3.442 × 10−9 km−1 s−1 was used. The simulations shown correspond to LD = b/2. In anticipation of our discussion of Jupiter in the following section, these parameters were chosen to approximately reproduce conditions on Jupiter. Note, however, that in our simulations the period in x is 32 000 km, approximately one-tenth the midlatitude distance around Jupiter on a line of constant latitude. Many 1-yr model simulations were run. For some parameter values 10-yr model simulations were performed. For the parameter values given, the change in both energy and enstrophy throughout the duration of the simulations performed was less than 1%, giving us confidence in the accuracy of the simulations. Both types of initial perturbation gave similar results.

Figure 2 shows plots of instantaneous, at t = τ = 1 yr, zonally averaged zonal velocity u(y, τ), zonally averaged potential vorticity q(y, τ), and potential vorticity q(x, y, τ). Comparison of Figs. 1 and 2 provides strong support for the dynamical consistency of the decomposition (3)(4), but these plots provide no insight into whether transport barriers are present. To address the latter question we have used the year-long records of computed velocity fields to: 1) follow the evolution of distributions of passive tracers, which evolve according to (6); and 2) compute finite-time Lyapunov exponents (FTLEs) (see, e.g., Haller 2001). Typical results are shown in Fig. 3. As shown in the figure, the initial positions of the passive tracers fell on the lines ±2y/b = {1, 3, 5, 7}, which lie midway between the unperturbed eastward and westward jets. It is seen that after a 1-yr integration the regions between jets are well mixed but that there is no meridional transport across the cores of the zonal jets. It should be emphasized that in this and other simulations tracer particles spread meridionally to fill the domains shown in about two weeks. Throughout the remainder of the 1-yr integration, no additional meridional tracer spreading occurs. With this in mind, Fig. 3 clearly shows that both eastward and westward zonal jets act as meridional transport barriers, consistent with the strong KAM stability argument. Calculation of FTLE provides an additional test of the correctness of the strong KAM stability argument. Lyapunov exponents are a measure of the rate of divergence of neighboring trajectories. According to the strong KAM stability argument, the transport barriers at the cores of zonal jets coincide with generally thin bands of KAM invariant tori on which Lyapunov exponents are zero. Finite time estimates of Lyapunov exponents will not be identically zero on KAM invariant tori, but these structures should be readily identifiable as thin bands of low FTLE estimates. This is precisely what is seen in Fig. 3; both westward and eastward jets are identifiable as thin bands of low FTLE estimates, consistent with the strong KAM stability argument. Typical computed values of FTLE in units of 10−3βb, shown in Fig. 3, are 2 at the cores of the westward jets, 7 at the cores of the eastward jets, and 17 in the well-mixed regions.

We have performed many numerical experiments based on PV staircase flows of the type described here. These simulations support the conclusion that both eastward zonal jets (where ∂q/∂y is very large) and westward zonal jets (where ∂q/∂y is very small) act as robust meridional transport barriers. This conclusion is not sensitive to the choice of parameter values or details of the initial perturbation. Two general trends are noteworthy. First, for a small perturbation the width of the barrier region near westward jets is greater than the width of the barrier region near eastward jets. This behavior is consistent with the strong KAM stability argument: |ω′(I)| is small over a larger y domain near westward jets than near eastward jets. Second, as the perturbation strength increases, transport barriers near westward jets generally break before eastward jet barriers break. In our simulations the westward jet barriers broke when the initial rms meridional PV contour displacement exceeded approximately b/4, while the eastward jet barriers broke when the initial rms displacement was approximately twice this value. Possible explanations for the somewhat more robust nature of the eastward jets are: 1) the PV barrier mechanism and the strong KAM stability barrier mechanism act in tandem to strengthen the barriers near eastward jets, and 2) we have performed a linear theory Rossby wave analysis of PV staircase flows that reveals that Rossby wave critical layers are precluded at the eastward jets (see also Dunkerton and Scott 2008), which suggest that the eastward jet barriers may be more robust.

3. Observational evidence from planetary atmospheres

In the previous section it was demonstrated that transport barriers may exist in a PV-conserving flow at locations that do not coincide with PV barriers. In this section, we discuss observational evidence that suggests the existence of transport barriers in the absence of PV barriers. We consider two examples: 1) Jupiter’s weather layer, and 2) the earth’s stratosphere. In both cases, conclusions drawn should be regarded as tentative inasmuch as we do not treat either system in enough depth to make a definitive statement. In spite of our incomplete treatment of these topics, we feel that it is important to point out that, consistent with the theoretical and numerical results presented in the previous section, there is observational evidence in planetary atmospheres that suggests the existence of transport barriers in the absence of PV barriers that can be explained by the strong KAM stability mechanism. Both examples considered are, in our view, sufficiently important that the connection between the observations discussed and the strong KAM stability barrier mechanism is worthy of a much more thorough investigation.

It is natural to focus on flows consisting of a sequence of alternating eastward and westward zonal jets because many of the arguments used in the previous section are then applicable. In particular, for this class of flows, meridional transport barriers of the strong KAM stability type are predicted to occur at the latitudes where u0(y) = 0. Furthermore, in alternating zonal jet flows one may anticipate that eastward and westward jets are associated with large and small background PV gradients, respectively. Note, however, that for the purpose of identifying transport barriers in the absence of PV barriers it is not necessary that the background PV distribution in the flows considered be that of an idealized PV staircase. This point is discussed in more detail below. The following simple scaling argument shows why an alternating zonal jet flow is well developed in Jupiter’s weather layer but is only marginally identifiable in the earth’s stratosphere. These systems are then discussed in turn.

Recall that in a PV staircase flow the separation between adjacent eastward jets is 2b = 23Umax/β. We shall assume that this estimate approximately holds for general midlatitude multiple zonal jet mean flow patterns. Let r denote planetary radius and Ω planetary rotation rate. Then β ∼ Ω/r, and the number of eastward (or westward) jets one expects to observe in each hemisphere at midlatitudes (whose extent in latitude is taken here to be half the equator to pole distance) is approximately njetπ/4 r/(23Umaxr) ∼ 1/4 Ω/(Umaxr).

In Jupiter’s weather layer Umax ∼ 50 m s−1, r ∼ 7 |m˜ 104 km, and Ω ∼ 2π/10 h giving njet ∼ 5, in good agreement with Fig. 4, as described below. In the earth’s stratosphere Umax ∼ 50 m s−1, r ∼ 6.4 |m˜ 103 km, and Ω ∼ 2π/24 h, giving njet ∼ 1.

Thus, conditions for the formation of a multiple zonal jet mean-flow pattern are only marginally satisfied in the earth’s stratosphere. In the earth’s troposphere Umax is smaller, suggesting more favorable conditions, but mountain ranges and thermal exchange processes between the atmosphere and irregularly shaped oceans and continents constitute significant hindrances to the formation of zonal flows. Conditions are favorable in the earth’s oceans (Umax ∼ 0.5 m s−1, corresponding to njet ∼ 8), but there the presence of lateral boundaries dictates that zonal jets be embedded in recirculation gyres (Maximenko et al. 2005, 2008; Richards et al. 2006).

a. Jupiter’s weather layer

The most striking feature of Jupiter’s weather layer circulation (Porco et al. 2003; Vasavada and Showman 2005) is that it is organized in a sequence of alternating eastward and westward zonal jets whose meridional excursion is very small. Figure 4 shows zonally averaged zonal wind speed on Jupiter at the cloud top level as a function of latitude. Regions with dark and light shading in this figure are referred to as belts and zones, respectively. Belts and zones correspond to regions in which the background motion is cyclonic [u0(y) < 0] and anticyclonic [u0(y) > 0], respectively. The boundaries between adjacent belts and zones coincide with the cores of the zonal jets. At these boundaries u0(y) = 0. Belts and zones have different radiative transfer properties (analyses are not limited to the visible band of the electromagnetic spectrum), which is attributed to differences in chemical composition (Banfield et al. 1998; Carlson et al. 1994; Irwin et al. 2005; Irwin et al. 2001; Simon-Miller et al. 2001). Assuming that the weather layer flow is approximately two-dimensional and that chemical species are long-lived, one may infer from the observation that adjacent belts and zones have different chemical constituents and that there is very little fluid exchange between adjacent belts and zones, implying that both eastward and westward zonal jets act as robust meridional transport barriers.

Figure 5 shows u0(y), q0(y), and q0(y) in Jupiter’s weather layer. The same data are shown (but are plotted differently) in Read et al. (2006). The question of whether a PV staircase is a useful approximate model of Jupiter’s weather layer has been considered by many authors (Dowling 1995; Marcus and Lee 1998; Peltier and Stunhe 2002; Read et al. 2006). For our purposes the answer to this question is not critical. Our focus is on identifying transport barriers that cannot be explained by the PV barrier mechanism. Figure 5 shows that, while all eastward jets are associated with large meridional PV gradients, most of the westward jets are associated with small meridional PV gradients. (Here and above, we are using the term westward jet somewhat loosely to include minima of u0(y), even when u0 > 0 at the minimum.) In other words, most of the transport barriers near the cores of the westward jets cannot be explained by the PV barrier mechanism. But all of the belt–zone boundaries—the apparent meridional transport barriers—coincide with latitudes at which u0(y) = 0, consistent with the strong KAM stability barrier mechanism. Thus, all of the apparent transport barriers can be explained by the strong KAM stability barrier mechanism. Note, however, that there is no apparent barrier on the equator, where u0(y) = 0. This is probably due to a combination of anomalous equatorial dynamics (Heimpel et al. 2005) and the manner by which chemical constituents are pumped into the near-equatorial weather layer.

Some caveats relating to our interpretation of observations from Jupiter should be emphasized, however. First, we have assumed that the weather layer flow is nearly two-dimensional and horizontally nondivergent, being only weakly forced by convection. Although these assumptions are generally accepted (see, e.g., Vasavada and Showman 2005), it should be noted that our explanation of the apparent transport barrier rests on their validity. A second assumption that we have made is that chemical species in Jupiter’s weather layer are long-lived. Another possible explanation of the apparent transport barriers between adjacent belts and zones is that chemical species are short-lived, being continuously pumped into the weather layer by convective overturning (Ingersoll et al. 2000; Showman and de Pater 2005). We cannot rule out this possibility. Our argument shows, however, that the apparent lack of fluid exchange between adjacent belts and zones can be explained using dynamical arguments assuming shallow-water dynamics.

b. The earth’s stratosphere

The simple scaling argument given above predicts that conditions for the formation of a stable alternating multiple jet zonal-mean flow pattern are only marginally satisfied in the earth’s stratosphere. In qualitative agreement with this prediction, in each hemisphere there is one readily identifiable eastward zonal jet and one westward jet, and the appearance of these jets is seasonal (see, e.g., Andrews et al. 1987). The stronger jets are the high-latitude eastward polar night jets that appear in the winter hemisphere. (The austral polar night jet is particularly strong, persisting throughout most of the stratosphere during the austral fall, winter, and spring.) The westward jets are present in the subtropics throughout most of the stratosphere during the summer months in each hemisphere. The eastward polar night jets, especially in the Southern Hemisphere, act as transport barriers and are associated with strong PV gradients. Because the focus in the present study is on identifying transport barriers in the absence of PV barriers, these jets are not of interest here. In contrast, the summer hemisphere westward subtropical jets are very much of interest because these are not associated with strong PV gradients. The properties just described are illustrated in Fig. 6. That figure shows a 7-yr (1992–98) monthly average of zonally averaged potential vorticity (in color) and zonal wind (as contours) on the 460 K isentropic surface (which lies in the lower stratosphere) based on the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) product. Both the eastward polar night jets and the westward subtropical jets are readily identifiable. As we have noted, the eastward winter hemisphere polar night jets are associated with strong meridional PV gradients, whereas the westward subtropical jets are associated with nearly homogenous PV distributions. The westward subtropical jets have the dynamical properties that we seek—zonal jets in the absence of strong PV gradients. We note also that, consistent with arguments made originally by Charney and Drazin (1961), Rossby wave perturbations to the background in these regions are weak. From the standpoint of applicability of the strong KAM stability argument, weak perturbations are advantageous.

We turn our attention now to the question of whether the cores of these jets serve as robust meridional transport barriers. Studies of stratospheric transport based on effective diffusivity have been carried out by Allen and Nakamura (2001) and Haynes and Shuckburgh (2000). The effective diffusivity is large (small) in regions where fluid is well (poorly) mixed. Fluid in the vicinity of a transport barrier is poorly mixed; these regions are thus characterized by a small effective diffusivity. Both stratospheric effective diffusivity analyses reveal that the westward subtropical jet in the summer hemisphere coincides with a region of anomalously low effective diffusivity; see Plates 1 and 4 in Allen and Nakamura (2001) and 1 through 4 in Haynes and Shuckburgh (2000). This suggests that these westward jets act as meridional transport barriers. Previous work by Waugh (1996) and Chen et al. (1994) had focused on this “subtropical barrier.” Indeed, this barrier comprises a critical element of the “tropical pipe” model (Plumb 1996) of stratospheric transport. Observational evidence that suggests the presence of subtropical transport barriers is presented in Grant et al. (1996), Mote et al. (1998), Minschwaner et al. (1996), Trepte and Hitchman (1992) and Trepte et al. (1993). Shepherd (2007) provides a recent review of stratospheric transport, including a discussion of subtropical transport barriers.

The evidence that we have pointed out strongly suggests that: 1) the stratospheric subtropical barrier is a robust meridional transport barrier that coincides with the core of a westward jet; 2) the associated meridional PV gradient is very small, so this barrier cannot be explained by the PV barrier mechanism; and 3) because u0(y) = 0 at this barrier, the barrier is predicted by the strong KAM stability barrier mechanism. To test these tentative conclusions more rigorously, a study based on realistic synoptic winds that track both potential vorticity and tracer distributions should be conducted.

4. Summary and discussion

In the first part of this paper, we presented numerical simulations of passive tracer transport in a perturbed PV staircase flow and showed that both eastward and westward jets in this flow act as meridional transport barriers. The surprise is that westward jets, where the background PV gradient vanishes, act as transport barriers. This behavior was explained as being a consequence of the strong KAM stability barrier mechanism.

We then briefly discussed the applicability of the strong KAM stability mechanism to explaining observations of Jupiter’s weather layer and the earth’s subtropical stratosphere. In both of these systems westward jets are present that appear to act as robust meridional transport barriers in the absence of a background meridional PV barrier. These barriers are predicted by the strong KAM stability mechanism. In both cases the evidence presented should be regarded as suggestive. More thorough investigations of both problems are recommended.

The principal weakness of our explanation of the apparent lack of fluid exchange between adjacent belts and zones in Jupiter’s midlatitude weather layer is that we cannot exclude the possibility that the observed chemical composition differences in adjacent belts and zones are caused by a combination of strong convective overturning and short-lived chemical species. In spite of this caveat, it is important to emphasize that we have shown that maintenance of the apparent chemical composition differences between adjacent belts and zones can be explained using a dynamical argument (as opposed to a chemistry-based argument) in which the weather layer flow is only weakly convectively forced.

The principal weaknesses in our discussion of the earth’s subtropical stratospheric transport barrier were that all of the properties noted were based on averaged winds rather than synoptic winds and that tracer transport and potential vorticity distributions were not estimated in a way that was guaranteed to be self-consistent. It should not be difficult to overcome these shortcomings using model-based synoptic winds.

Acknowledgments

We thank T. Dowling and R. Morales-Juberias for providing the data used to construct Figs. 4 and 5. Comments on the manuscript by anonymous reviewers and by T. Shepherd, T. Özgökmen, and J. Willemsen are sincerely appreciated. The ECMWF ERA-40 data used in this study were obtained from the ECMWF data server. Support for this work was provided by the U.S. National Science Foundation under Grants CMG0417425 and OCE0648284.

REFERENCES

  • Allen, R. A., , and N. Nakamura, 2001: A seasonal climatology of effective diffusivity in the stratosphere. J. Geophys. Res., 106 , 79177935.

    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., , J. R. Holton, , and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysical Series, Vol. 40, Academic Press, 489 pp.

    • Search Google Scholar
    • Export Citation
  • Arnold, V. I., , V. V. Kozlov, , and A. I. Neistadt, 1986: Mathematical Aspects of Classical and Celestial Mechanics. Vol. 3, Encyclopedia of Mathematical Sciencies, Springer.

    • Search Google Scholar
    • Export Citation
  • Baldwin, M. P., , P. B. Rhines, , H-P. Huang, , and M. E. McIntyre, 2007: The jet-stream conundrum. Science, 315 , 467468.

  • Banfield, D., , P. J. Gierasch, , M. Bell, , E. Ustinov, , A. P. Ingersoll, , A. R. Vasavada, , R. A. West, , and M. J. S. Belton, 1998: Jupiter’s cloud structure from Galileo imaging data. Icarus, 135 , 230250.

    • Search Google Scholar
    • Export Citation
  • Carlson, B. E., , A. A. Lacis, , and W. B. Rossow, 1994: Belt-zone variations in the Jovian cloud structure. J. Geophys. Res., 99 , 1462314658.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., , and P. G. Drazin, 1961: Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66 , 83109.

    • Search Google Scholar
    • Export Citation
  • Chen, P., , J. R. Holton, , A. O’Neill, , and R. Swinbank, 1994: Isentropic mass exchange between the tropics and extratropics in the stratosphere. J. Geophys. Res., 51 , 30063018.

    • Search Google Scholar
    • Export Citation
  • Cho, J. Y-K., , and L. Polvani, 1996: The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluids, 8 , 15311552.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., , and V. M. Gryanik, 2004: Barotropic beta-plane turbulence in a regime with strong zonal jets revisited. J. Atmos. Sci., 61 , 22832295.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., , and D. Gurarie, 2004: Scaling, spectra, and zonal jets in beta-plane turbulence. Phys. Fluids, 16 , 25922603.

  • Dowling, T. E., 1995: Dynamics of Jovian atmospheres. Annu. Rev. Fluid Mech., 27 , 293334.

  • Dritschel, D. G., , and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65 , 855874.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., , and R. K. Scott, 2008: A barotropic model of the angular momentum conserving potential vorticity staircase in spherical geometry. J. Atmos. Sci., 65 , 11051136.

    • Search Google Scholar
    • Export Citation
  • Grant, W. B., , E. V. Browell, , C. S. Long, , L. L. Stowe, , R. G. Grainger, , and A. Lambert, 1996: Use of volcanic aerosols to study the tropical stratospheric reservoir. J. Geophys. Res., 101 , 39733988.

    • Search Google Scholar
    • Export Citation
  • Haller, G., 2001: Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Phys. Fluids, 13 , 33653385.

    • Search Google Scholar
    • Export Citation
  • Haynes, P., , and E. Shuckburgh, 2000: Effective diffusivity as a diagnostic of atmospheric transport. 1. Stratosphere. J. Geophys. Res., 105 , 2277722794.

    • Search Google Scholar
    • Export Citation
  • Heimpel, M., , J. J. Aurnou, , and J. Wicht, 2005: Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model. Nature, 438 , 193196.

    • Search Google Scholar
    • Export Citation
  • Huang, H-P., , and W. A. Robinson, 1998: Two-dimensional turbulence and persistent zonal jets in a global barotropic model. J. Atmos. Sci., 55 , 611632.

    • Search Google Scholar
    • Export Citation
  • Ingersoll, A. P., , P. J. Gierasch, , D. Banfield, , and A. R. Vasavada, and the Galileo Imaging Team, 2000: Moist convection as an energy source for the large-scale motions in Jupiter’s atmosphere. Nature, 403 , 630632.

    • Search Google Scholar
    • Export Citation
  • Irwin, P. G. J., , A. L. Weir, , F. W. Taylor, , S. B. Calcutt, , and R. W. Carlson, 2001: The origin of belt/zone contrasts in the atmosphere of Jupiter and their correlation with 5-μm opacity. Icarus, 149 , 397415.

    • Search Google Scholar
    • Export Citation
  • Irwin, P. G. J., , K. Sihra, , N. Bowles, , F. W. Taylor, , and S. B. Calcutt, 2005: Methane absorption in the atmosphere of Jupiter from 1800 to 9500 cm−1 and implications for vertical cloud structure. Icarus, 176 , 255271.

    • Search Google Scholar
    • Export Citation
  • Jorba, Á, , and C. Simó, 1996: On quasi-periodic perturbations of elliptic equilibrium points. SIAM J. Math. Analy., 27 , 17041737.

  • Juckes, N. M., , and M. E. McIntyre, 1987: A high-resolution one-layer model of breaking planetary waves in the stratosphere. Nature, 328 , 590596.

    • Search Google Scholar
    • Export Citation
  • Manfroi, A. J., , and W. R. Young, 1999: Slow evolution of zonal jets on the beta plane. J. Atmos. Sci., 56 , 784800.

  • Marcus, P. S., , and C. Lee, 1998: A model for eastward and westward jets in laboratory experiments and planetary atmospheres. Phys. Fluids, 10 , 14741489.

    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., , B. Bang, , and H. Sasaki, 2005: Observational evidence of alternating zonal jets in the world ocean. Geophys. Res. Lett., 32 .L12607, doi:10.1029/2005GL022728.

    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., , O. V. Melnichenko, , P. P. Niiler, , and H. Sasaki, 2008: Stationary mesoscale jet-like features in the ocean. Geophys. Res. Lett, 35 .L08603, doi:10.1029/2008GL033267.

    • Search Google Scholar
    • Export Citation
  • Minschwaner, K., and Coauthors, 1996: Bulk properties of isentropic mixing into the tropics in the lower stratosphere. J. Geophys. Res., 101 , 94339440.

    • Search Google Scholar
    • Export Citation
  • Mote, P. W., , T. J. Dunkerton, , M. E. McIntyre, , E. A. Ray, , P. H. Haynes, , and J. M. Russell III, 1998: Vertical velocity, vertical diffusion, and dilution by midlatitude air in the tropical lower stratosphere. J. Geophys. Res., 103 , 86518666.

    • Search Google Scholar
    • Export Citation
  • Nozawa, T., , and S. Yoden, 1997: Formation of zonal bands structure in forced two-dimensional turbulence on a rotating sphere. Phys. Fluids, 9 , 20812093.

    • Search Google Scholar
    • Export Citation
  • Peltier, W. K., , and G. R. Stunhe, 2002: The upscale turbulent cascade: Shear layers, cyclones, and gas giant bands. Meteorology at the Millennium, R. P. Pierce, Ed., Academic Press, 43–61.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1996: A “tropical pipe” model of stratospheric transport. J. Geophys. Res., 101 , 39573972.

  • Porco, C. C., and Coauthors, 2003: Cassini imaging of Jupiter’s atmosphere, satellites, and rings. Science, 299 , 15411547.

  • Read, P. L., , P. J. Gierasch, , B. J. Conrath, , A. Simon-Miller, , T. Fouchet, , and Y. H. Yamazaki, 2006: Mapping potential-vorticity dynamics on Jupiter. I: Zonal-mean circulation from Cassini and Voyager 1 data. Quart. J. Roy. Meteor. Soc., 132 , 15771603.

    • Search Google Scholar
    • Export Citation
  • Read, P. L., , Y. H. Yamazaki, , S. R. Lewis, , P. D. Williams, , R. Wordsworth, , K. Miki-Yamazaki, , J. Sommeria, , and H. Didelle, 2007: Dynamics of convectively driven banded jets in the laboratory. J. Atmos. Sci., 64 , 40314052.

    • Search Google Scholar
    • Export Citation
  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69 , 417443.

  • Richards, K. J., , N. A. Maximenko, , F. O. Bryan, , and H. Sasaki, 2006: Zonal jets in the Pacific Ocean. Geophys. Res. Lett., 33 .L03605, doi:10.1029/2005GL024645.

    • Search Google Scholar
    • Export Citation
  • Rypina, I. I., , M. G. Brown, , F. J. Beron-Vera, , H. Koçak, , M. J. Olascoaga, , and I. A. Udovydchenkov, 2007a: On the Lagrangian dynamics of atmospheric zonal jets and the permeability of the stratospheric polar vortex. J. Atmos. Sci., 64 , 35953610.

    • Search Google Scholar
    • Export Citation
  • Rypina, I. I., , M. G. Brown, , F. J. Beron-Vera, , H. Koçak, , M. J. Olascoaga, , and I. A. Udovydchenkov, 2007b: Robust transport barriers resulting from strong Kolmogorov–Arnold–Moser stability. Phys. Rev. Lett., 98 .104102, doi:10.1103/PhysRevLett.98.104102.

    • Search Google Scholar
    • Export Citation
  • Scott, R. K., , and L. M. Polvani, 2007: Forced–dissipative shallow-water turbulence on the sphere and the atmospheric circulation of the giant planets. J. Atmos. Sci., 64 , 31583176.

    • Search Google Scholar
    • Export Citation
  • Sevryuk, M. B., 2007: Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman’s method. Discrete Contin. Dyn. Syst., 18 , 569595.

    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 2007: Transport in the middle atmosphere. J. Meteor. Soc. Japan, 85B , 165191.

  • Showman, A. P., , and I. de Pater, 2005: Dynamical implications of Jupiter’s tropospheric ammonia abundance. Icarus, 174 , 192204.

  • Simon-Miller, A. A., , D. Banfield, , and P. J. Gierasch, 2001: Color and the vertical structure in Jupiter’s belts, zones, and weather systems. Icarus, 154 , 459474.

    • Search Google Scholar
    • Export Citation
  • Trepte, C. R., , and M. H. Hitchman, 1992: Tropical stratospheric circulation deduced from satellite aerosol data. Nature, 355 , 626628.

    • Search Google Scholar
    • Export Citation
  • Trepte, C. R., , R. E. Veiga, , and M. P. McCormick, 1993: The poleward dispersal of Mount Pinatubo volcanic aerosol. J. Geophys. Res., 98 , 1856318574.

    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., , and M. E. Maltrud, 1993: Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr., 23 , 13461362.

    • Search Google Scholar
    • Export Citation
  • Vasavada, A. R., , and A. P. Showman, 2005: Jovian atmospheric dynamics: An update after Galileo and Cassini. Rep. Prog. Phys., 68 , 19351996.

    • Search Google Scholar
    • Export Citation
  • Waugh, D. W., 1996: Seasonal variation of isentropic transport out of the tropical stratosphere. J. Geophys. Res., 101 , 40074023.

  • Williams, G. P., 1978: Planetary circulations. I. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci., 35 , 13991426.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

(left) Zonal velocity and (right) potential vorticity in a PV staircase zonal flow. The zonal velocity structure shown corresponds to the finite LD case, Eq. (4), with LD = b/2 = 2000 km, roughly approximating midlatitude conditions on Jupiter. In this figure the ideal PV jumps have smooth transition regions with tanh dependence on y locally.

Citation: Journal of the Atmospheric Sciences 65, 10; 10.1175/2008JAS2579.1

Fig. 2.
Fig. 2.

Instantaneous zonally averaged (left) zonal velocity and (middle) potential vorticity, and (right) the potential vorticity after a 1-yr simulation of the quasigeostrophic equations (1)(2) using as the initial state a perturbation to the PV staircase flow of Fig. 1.

Citation: Journal of the Atmospheric Sciences 65, 10; 10.1175/2008JAS2579.1

Fig. 3.
Fig. 3.

(a) Zonally averaged zonal velocity u(y) at t = 1 yr. (b) Initial positions [x(0), y(0)] of color-coded passive tracers. (c) Positions [x(τ), y(τ)] of color-coded passive tracers at t = τ = 1 yr. (d) Finite-time Lyapunov exponent (FTLE) field as a function of initial position computed using a 1-yr integration time interval. The time-dependent velocity field whose final state is shown in Fig. 2 was used to construct (a), (c), and (d).

Citation: Journal of the Atmospheric Sciences 65, 10; 10.1175/2008JAS2579.1

Fig. 4.
Fig. 4.

(left) Zonally averaged zonal wind speed as a function of latitude on Jupiter at the cloud top level as inferred from images taken in December 2000 by the Cassini spacecraft (Porco et al. 2003). Gray and white zonal bands indicate belts and zones, respectively. (right) Near-instantaneous visible band image of Jupiter constructed from images taken by Cassini in December 2000. Note that many features of Jupiter’s weather layer that are not seen in this image may be revealed by radiative transfer analyses outside of the visible band of the electromagnetic spectrum. NASA image PIA07782 (PIA images are available at NASA’s planetary photojournal Web site, http://photojournal.jpl.nasa.gov).

Citation: Journal of the Atmospheric Sciences 65, 10; 10.1175/2008JAS2579.1

Fig. 5.
Fig. 5.

Meridional distribution of zonally averaged (left) zonal wind u0(y), (center) potential vorticity q0(y), and (right) potential vorticity gradient q0(y) in Jupiter’s weather layer based on Cassini data. Both unsmoothed and smoothed wind profiles are plotted; the smoothed wind profile was used to compute q0(y) and q0(y). Solid and dashed horizontal lines are drawn at the latitudes of the cores of westward and eastward jets, respectively. Note that large positive values of q0(y) coincide with the cores of eastward jets. A spherical planet (rather than a β-plane, which is used elsewhere in this paper) was assumed to compute the q0(y) and q0(y) structures shown.

Citation: Journal of the Atmospheric Sciences 65, 10; 10.1175/2008JAS2579.1

Fig. 6.
Fig. 6.

Seven-year (1992–98) monthly average of zonally averaged zonal wind and potential vorticity on the 460 K isentropic surface based on the ERA-40 reanalysis product. Contours show zonal winds (m s−1). Solid and dashed contours represent eastward and westward flow, respectively. Colors indicate Ertel’s potential vorticity.

Citation: Journal of the Atmospheric Sciences 65, 10; 10.1175/2008JAS2579.1

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