Barotropic Beta-Plane Turbulence in a Regime with Strong Zonal Jets Revisited

S. Danilov Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany, and A. M. Obukhov Institute of Atmospheric Physics, Moscow, Russia

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V. M. Gryanik Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany, and A. M. Obukhov Institute of Atmospheric Physics, Moscow, Russia

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Abstract

The problem of quantification of barotropic beta-plane turbulence driven by small-scale stochastic forcing into regimes dominated by quasi-periodic zonal jets is revisited. It is shown that the large-scale relative vorticity in such regimes is organized into a sequence of zonal bands. Its zonal mean profile varies approximately linearly within the bands. Its mean negative slope β∗ is less than the meridional gradient of the Coriolis parameter β, and depends on the external parameters (friction, forcing, and β). The neighboring bands are connected through the vorticity fronts where the zonal mean meridional gradient is large and positive.

The frontal-band vorticity structure defines piecewise parabolic profiles of asymmetric eastward and westward jets, and strong peaks in the low-k interval of turbulent zonal energy spectra, which store most of the zonal energy. The slope of their envelope depends on the structure of the frontal zones and is always steeper than −4. The presence of peaks invalidates the recent hypothesis on the universal power-law scaling Ez(k) = Czβ2k−5, Cz = O(1), for the zonal energy spectra of beta-plane turbulence in strongly anisotropic regimes.

The power-law intervals could appear at large k and are linked to uncorrelated fluctuations of band profiles. It is shown that they could contain a part that slopes close to −5. However, its Cz is not universal and depends on the external parameters.

A simple kinematic model of multijet beta-plane flows is proposed that explains the shape of the coherent part of zonal energy spectra and asymmetry between westward and eastward jets generated by vorticity bands, and quantifies the zonal wavenumber of jets kj in terms of the ratio of zonal enstrophy to zonal energy.

Corresponding author address: Dr. V. M. Gryanik, Climate System Department, Busse str. 24, 27570 Bremerhaven, Germany. Email: vgryanik@awi-bremerhaven.de

Abstract

The problem of quantification of barotropic beta-plane turbulence driven by small-scale stochastic forcing into regimes dominated by quasi-periodic zonal jets is revisited. It is shown that the large-scale relative vorticity in such regimes is organized into a sequence of zonal bands. Its zonal mean profile varies approximately linearly within the bands. Its mean negative slope β∗ is less than the meridional gradient of the Coriolis parameter β, and depends on the external parameters (friction, forcing, and β). The neighboring bands are connected through the vorticity fronts where the zonal mean meridional gradient is large and positive.

The frontal-band vorticity structure defines piecewise parabolic profiles of asymmetric eastward and westward jets, and strong peaks in the low-k interval of turbulent zonal energy spectra, which store most of the zonal energy. The slope of their envelope depends on the structure of the frontal zones and is always steeper than −4. The presence of peaks invalidates the recent hypothesis on the universal power-law scaling Ez(k) = Czβ2k−5, Cz = O(1), for the zonal energy spectra of beta-plane turbulence in strongly anisotropic regimes.

The power-law intervals could appear at large k and are linked to uncorrelated fluctuations of band profiles. It is shown that they could contain a part that slopes close to −5. However, its Cz is not universal and depends on the external parameters.

A simple kinematic model of multijet beta-plane flows is proposed that explains the shape of the coherent part of zonal energy spectra and asymmetry between westward and eastward jets generated by vorticity bands, and quantifies the zonal wavenumber of jets kj in terms of the ratio of zonal enstrophy to zonal energy.

Corresponding author address: Dr. V. M. Gryanik, Climate System Department, Busse str. 24, 27570 Bremerhaven, Germany. Email: vgryanik@awi-bremerhaven.de

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  • Borue, V., 1994: Inverse energy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett, 72 , 14751478.

  • Chekhlov, A., S. A. Orszag, S. Sukoriansky, B. Galperin, and I. Staroselsky, 1996: The effect of small-scale forcing on large-scale structures in two-dimensional flows. Physica D, 98 , 321334.

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

    • Search Google Scholar
    • Export Citation
  • Danilov, S., and D. Gurarie, 2001: Forced two-dimensional turbulence in spectral and physical space. Phys. Rev, E63 , 061208-1061208-12.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., and D. Gurarie, 2002: Rhines scale and spectra of the β-plane turbulence with bottom drag. Phys. Rev, E65 , 067301-1067301-3.

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

  • Galperin, B., S. Sukoriansky, and H-P. Huang, 2001: Universal n−5 spectrum of zonal flows on giant planets. Phys. Fluids, 13 , 15451548.

    • Search Google Scholar
    • Export Citation
  • Gierash, P. J., and Coauthors, 2000: Observation of moist convection in Jupiter's atmosphere. Nature, 403 , 628629.

  • Gryanik, V. M., 2004: Vortex dynamics and β-plane turbulence. Marine Turbulence: Theories, Observations and Models, H. Baumert, J. Simpson, and J. Sündermann, Ed., Cambridge University Press, 767–790.

    • Search Google Scholar
    • Export Citation
  • Holloway, G., and M. Hendershott, 1977: Stochastic closure for nonlinear Rossby waves. J. Fluid Mech, 82 , 747765.

  • 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
  • Huang, H-P., B. Galperin, and S. Sukoriansky, 2001: Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere. Phys. Fluids, 13 , 225240.

    • Search Google Scholar
    • Export Citation
  • Hunt, J. C. R., 2000: Dynamics and statistics of vortical eddies in turbulence. Turbulence Structure and Vortex Dynamics, J. C. R. Hunt and J. C. Vassilicos, Eds., Cambridge University Press, 183–210.

    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1967: Inertial ranges in two-dimensional turbulence. Phys. Fluids, 10 , 14171423.

  • Kukharkin, N., S. A. Orszag, and V. Yakhot, 1995: Quasicrystallization of vortices in drift-wave turbulence. Phys. Rev. Lett, 75 , 24862489.

    • Search Google Scholar
    • Export Citation
  • 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 , 321342.

    • Search Google Scholar
    • Export Citation
  • Marcus, P. S., 1993: Jupiter's Great Red Spot and other vortices. Annu. Rev. Astron. Astrophys, 31 , 523573.

  • 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
  • Marcus, P. S., T. Kundu, and C. Lee, 2000: Vortex dynamics and zonal flows. Phys. Plasmas, 7 , 16301640.

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

    • Search Google Scholar
    • Export Citation
  • Nozawa, T., and S. Yoden, 1997b: Spectral anisotropy in forced two-dimensional turbulence on a rotating sphere. Phys. Fluids, 9 , 38343842.

    • Search Google Scholar
    • Export Citation
  • Panetta, R. L., 1993: Zonal jets in wide baroclinically unstable regions: Persistence and scale selection. J. Atmos. Sci, 50 , 20732106.

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

  • Rhines, P. B., 1994: Jets. Chaos, 4 , 313339.

  • Rhines, P. B., and W. R. Young, 1982: Homogenization of potential vorticity in planetary gyres. J. Fluid. Mech, 122 , 347367.

  • Saffman, P. G., 1971: On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number. Stud. Appl. Math, 50 , 377383.

    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 1987: Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere. J. Fluid Mech, 184 , 289302.

    • Search Google Scholar
    • Export Citation
  • Smith, K. S., G. Boccaletti, C. C. Henning, I. Marinov, C. Y. Tam, I. M. Held, and G. K. Vallis, 2002: Turbulent diffusion in the geostrophic inverse cascade. J. Fluid Mech, 469 , 1348.

    • Search Google Scholar
    • Export Citation
  • Smith, L. M., and V. Yakhot, 1994: Finite-size effect in forced two-dimensional turbulence. J. Fluid Mech, 274 , 115138.

  • Smith, L. M., and F. Waleffe, 1999: Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids, 11 , 16081622.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., B. Galperin, and N. Dikovskaya, 2002: Universal spectrum of two-dimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets. Phys. Rev. Lett, 89 , 124501-1124501-4.

    • 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
  • Williams, G. P., 1978: Planetary circulations. 1. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci, 35 , 13991426.

    • Search Google Scholar
    • Export Citation
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