• Arnol’d, V. I., 1965: Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Dokl. Akad. Nauk SSSR,162, 975–978; Sov. Math. (English translation), 6, 331–334.

  • Basdevant, C., B. Legras, R. Sadourny, and M. Béland, 1981: A study of barotropic model flows: Intermittency, waves, and predictability. J. Atmos. Sci.,38, 2305–2326.

  • Boer, G. J., 1983: Homogeneous and isotropic turbulence on the sphere. J. Atmos. Sci.,40, 154–163.

  • Branstator, G., and I. Held, 1995: Westward propagating normal modes in the presence of stationary background waves. J. Atmos. Sci.,52, 247–262.

  • Cho, J. Y.-K., and L. M. Polvani, 1996: The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluid,8, 1531–1552.

  • Dikiy, L. A., 1965: On the nonlinear theory of the stability of zonal flows. Izv. Atmos. Oceanic Phys.,1, 1117–1122.

  • ——, and V. V. Katayev, 1971: Calculation of the planetary wave spectrum by the Galerkin method. Izv. Atmos. Oceanic Phys.,7, 1031–1038.

  • Fjørtoft, R., 1953: On the changes in the spectral distribution of kinetic energy for two-dimensional, nondivergent flow. Tellus,5, 225–230.

  • Frederiksen, J. S., M. R. Dix, and S. M. Kepert, 1996: Systematic energy errors and the tendency toward canonical equilibrium in atmospheric circulation models. J. Atmos. Sci.,53, 887–904.

  • Held, I. M., 1985: Pseudomomentum and the orthogonality of modes in shear flows. J. Atmos. Sci.,42, 2280–2288.

  • Kraichnan, R. H., 1967: Inertial ranges in two-dimensional turbulence. Phys. Fluid,10, 1417–1423.

  • Legras, B., 1980: Turbulent phase shift of Rossby waves. Geophys. Astrophys. Fluid Dyn.,15, 253–281.

  • Leith, C. E., 1971: Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci.,28, 145–161.

  • ——, and R. H. Kraichnan, 1972: Predictability of turbulent flows. J. Atmos. Sci.,29, 1041–1058.

  • Lilly, D. K., 1969: Numerical simulation of two-dimensional turbulence. Phys. Fluid (Suppl. II), 240–249.

  • ——, 1989: Two-dimensional turbulence generated by energy sources at two scales. J. Atmos. Sci.,46, 2026–2030.

  • Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus,21, 289–307.

  • Maltrud, M. E., and G. K. Vallis, 1991: Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence. J. Fluid Mech.,228, 321–342.

  • McWilliams, J. C., 1984: The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech.,146, 21–43.

  • Nozawa, T., and S. Yoden, 1995: Coherent structures in forced two-dimensional turbulence on a rotating sphere. Preprints, 10th Conf. on Atmospheric and Oceanic Waves and Stability, Big Sky, MT, Amer. Meteor. Soc., 70–71.

  • Orszag, S. A., 1970: Transform method for the calculation of vector-coupled sum: Application to the spectral form of the vorticity equation. J. Atmos. Sci.,27, 890–895.

  • Panetta, R. L., 1993: Zonal jets in wide baroclinically unstableregions: Persistence and scale selection. J. Atmos. Sci.,50, 2073–2106.

  • Platzman, G. W., 1960: The spectral form of the vorticity equation. J. Meteor.,17, 635–644.

  • ——, 1962: The analytical dynamics of the spectral vorticity equation. J. Atmos. Sci.,19, 313–328.

  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech.,69, 417–443.

  • ——, 1994: Jets. Chaos,4, 313–339.

  • ——, and W. R. Young, 1982: Homogenization of potential vorticity in planetary gyres. J. Fluid Mech.,122, 347–367.

  • Sadourny, R., and C. Basdevant, 1985: Parameterization of subgrid scale barotropic and baroclinic eddies in quasi-geostrophic models: Anticipated potential vorticity method. J. Atmos. Sci.,42, 1353–1368.

  • Shepherd, T. G., 1987a: Rossby waves and two-dimensional turbulence in a large-scale zonal jet. J. Fluid Mech.,183, 467–509.

  • ——, 1987b: A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere. J. Atmos. Sci.,44, 1166–1178.

  • ——, 1987c: Non-ergodicity of inviscid two-dimensional flow on abeta-plane and on the surface of a rotating sphere. J. Fluid Mech.,184, 289–302.

  • Silberman, I., 1954: Planetary waves in the atmosphere. J. Meteor.,11, 27–34.

  • Srinivasa Rao, K., and V. Rajeswari, 1993: Quantum Theory of Angular Momentum. Springer-Verlag, 315 pp.

  • Tang, C. M., and S. A. Orszag, 1978: Two-dimensional turbulence on the surface of a sphere. J. Fluid Mech.,87, 305–319.

  • Vallis, G. K., 1992: Problems and phenomenology in two-dimensional turbulence. Nonlinear Phenomena in Atmospheric and Oceanic sciences, G. F. Carnevale and R. T. Pierrehumbert, Eds., Springer-Verlag, 1–25.

  • ——, and M. E. Maltrud, 1993: Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr.,23, 1346–1362.

  • Wigner, E. P., 1959: Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Academic Press, 372 pp.

  • Williams, G. P., 1978: Planetary circulations: 1. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci.,35, 1399–1426.

  • Yoden, S., and M. Yamada, 1993: A numerical experiment on two-dimensional decaying turbulence on a rotating sphere. J. Atmos. Sci.,50, 631–643.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 206 206 9
PDF Downloads 61 61 8

Two-Dimensional Turbulence and Persistent Zonal Jets in a Global Barotropic Model

View More View Less
  • 1 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
© Get Permissions
Restricted access

Abstract

The dynamics of two-dimensional turbulence on a rotating sphere are examined. The anisotropic Rhines scale is derived and verified in decaying turbulence simulations. Due to the anisotropic nature of the Rossby waves, the Rhines barrier is displaced toward small total wavenumber n with decreasing zonal wavenumber m. Up-scale energy transfer along the zonal axis (m = 0) is not directly arrested by beta. A forced dissipative model with high-wavenumber forcing is used to investigate the dynamics of persistent zonal jets. Persistent jets form in the low energy (strong rotation) cases with the root-mean-square velocity V*rmsaΩ. Under a fixed rotation rate, the jet scale decreases with the energy. The equilibrated jets generally stay at fixed latitudes. The zonal bands are nearly uniformly distributed in latitude, except that bands in the high latitudes tend to be wider and weaker, as clearly affected by a decreasing beta with latitude. The time-mean zonal winds in the forced simulations appear to be stable, with their absolute vorticity gradient dominated by beta. The increase of the jet scale with energy as required by stability is consistent with the simulated results.

Diagnostic analysis shows that the persistent jets are primarily maintained by the shear-straining mechanism involving small-scale eddies and large-scale zonal jets, with a clear scale separation between them. Although large-scale eddies, those at scales near the Rhines scale, possess most of the eddy energy, in the time mean they contribute little to the maintenance of the zonal jets. Thus, despite the similarity between the Rhines scale and the jet scale, their dynamical link is not obvious in the time-mean statistics. The presence of persistent zonal jets modifies the normal modes of the system. Pure Rossby–Haurwitz modes at small and medium scales are severely modified and fall into the continuum. Large-scale modes, however, may remain discrete. The discreteness of the large-scale modes limits their ability to exchange energy with the zonal jets in the time mean.

* Current affiliation: Cooperative Institute for Research in the Environmental Sciences, University of Colorado, Boulder, Colorado.

Corresponding author address: Dr. Huei-Ping Huang, University of Colorado, CIRES, Campus Box 449, Boulder, CO 80309.

Email: hp@cdc.noaa.gov

Abstract

The dynamics of two-dimensional turbulence on a rotating sphere are examined. The anisotropic Rhines scale is derived and verified in decaying turbulence simulations. Due to the anisotropic nature of the Rossby waves, the Rhines barrier is displaced toward small total wavenumber n with decreasing zonal wavenumber m. Up-scale energy transfer along the zonal axis (m = 0) is not directly arrested by beta. A forced dissipative model with high-wavenumber forcing is used to investigate the dynamics of persistent zonal jets. Persistent jets form in the low energy (strong rotation) cases with the root-mean-square velocity V*rmsaΩ. Under a fixed rotation rate, the jet scale decreases with the energy. The equilibrated jets generally stay at fixed latitudes. The zonal bands are nearly uniformly distributed in latitude, except that bands in the high latitudes tend to be wider and weaker, as clearly affected by a decreasing beta with latitude. The time-mean zonal winds in the forced simulations appear to be stable, with their absolute vorticity gradient dominated by beta. The increase of the jet scale with energy as required by stability is consistent with the simulated results.

Diagnostic analysis shows that the persistent jets are primarily maintained by the shear-straining mechanism involving small-scale eddies and large-scale zonal jets, with a clear scale separation between them. Although large-scale eddies, those at scales near the Rhines scale, possess most of the eddy energy, in the time mean they contribute little to the maintenance of the zonal jets. Thus, despite the similarity between the Rhines scale and the jet scale, their dynamical link is not obvious in the time-mean statistics. The presence of persistent zonal jets modifies the normal modes of the system. Pure Rossby–Haurwitz modes at small and medium scales are severely modified and fall into the continuum. Large-scale modes, however, may remain discrete. The discreteness of the large-scale modes limits their ability to exchange energy with the zonal jets in the time mean.

* Current affiliation: Cooperative Institute for Research in the Environmental Sciences, University of Colorado, Boulder, Colorado.

Corresponding author address: Dr. Huei-Ping Huang, University of Colorado, CIRES, Campus Box 449, Boulder, CO 80309.

Email: hp@cdc.noaa.gov

Save