Editorial Type:
Article
Article Type:
Research Article

The Dynamics of Baroclinic Zonal Jets

Paul D. Williams Department of Meteorology, University of Reading, Reading, United Kingdom

Search for other papers by Paul D. Williams in
Current site
Google Scholar
PubMed Close
and
Christopher W. Kelsall Department of Meteorology, University of Reading, Reading, United Kingdom

Search for other papers by Christopher W. Kelsall in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Mar 2015
DOI:
https://doi.org/10.1175/JAS-D-14-0027.1
Page(s):
1137–1151
Restricted access

Abstract

Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-14-0027.s1.

Corresponding author address: Paul D. Williams, Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, United Kingdom. E-mail: p.d.williams@reading.ac.uk

Abstract

Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-14-0027.s1.

Corresponding author address: Paul D. Williams, Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, United Kingdom. E-mail: p.d.williams@reading.ac.uk

Supplementary Materials

    • Supplemental Materials (AVI 56.05 MB)
Save
Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Afanasyev, Y. D., S. O’Leary, P. B. Rhines, and E. Lindahl, 2012: On the origin of jets in the ocean. Geophys. Astrophys. Fluid Dyn., 106, 113–137, doi:10.1080/03091929.2011.562896.

    • Search Google Scholar
    • Export Citation

  • Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100, 487–490, doi:10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bakas, N. A., and P. I. Ioannou, 2013: On the mechanism underlying the spontaneous emergence of barotropic zonal jets. J. Atmos. Sci., 70, 2251–2271, doi:10.1175/JAS-D-12-0102.1.

    • Search Google Scholar
    • Export Citation

  • Bastin, M. E., and P. L. Read, 1997: A laboratory study of baroclinic waves and turbulence in an internally heated rotating fluid annulus with sloping endwalls. J. Fluid Mech., 339, 173–198, doi:10.1017/S0022112097005259.

    • Search Google Scholar
    • Export Citation

  • Bastin, M. E., and P. L. Read, 1998: Experiments on the structure of baroclinic waves and zonal jets in an internally heated, rotating, cylinder of fluid. Phys. Fluids, 10, 374–389, doi:10.1063/1.869530.

    • Search Google Scholar
    • Export Citation

  • Bouchet, F., and J. Sommeria, 2002: Emergence of intense jets and Jupiter’s Great Red Spot as maximum-entropy structures. J. Fluid Mech., 464, 165–207, doi:10.1017/S0022112002008789.

    • Search Google Scholar
    • Export Citation

  • Cattaneo, F., and J. E. Hart, 1990: Multiple states for quasi-geostrophic channel flows. Geophys. Astrophys. Fluid Dyn., 54, 1–33, doi:10.1080/03091929008208930.

    • Search Google Scholar
    • Export Citation

  • Cho, J. Y.-K., and L. M. Polvani, 1996a: The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluids, 8, 1531–1552, doi:10.1063/1.868929.

    • Search Google Scholar
    • Export Citation

  • Cho, J. Y.-K., and L. M. Polvani, 1996b: The morphogenesis of bands and zonal winds in the atmospheres on the giant outer planets. Science, 273, 335–337, doi:10.1126/science.273.5273.335.

    • Search Google Scholar
    • Export Citation

  • Di Nitto, G., S. Espa, and A. Cenedese, 2013: Simulating zonation in geophysical flows by laboratory experiments. Phys. Fluids, 25, 086602, doi:10.1063/1.4817540.

    • Search Google Scholar
    • Export Citation

  • Dritschel, D. G., and R. K. Scott, 2011: Jet sharpening by turbulent mixing. Philos. Trans. Roy. Soc. London, A369, 754–770, doi:10.1098/rsta.2010.0306.

    • 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, 1105–1136, doi:10.1175/2007JAS2223.1.

    • Search Google Scholar
    • Export Citation

  • Galperin, B., S. Sukoriansky, and H.-P. Huang, 2001: Universal n−5 spectrum of zonal flows on giant planets. Phys. Fluids, 13, 1545–1548, doi:10.1063/1.1373684.

    • Search Google Scholar
    • Export Citation

  • Galperin, B., H. Nakano, H.-P. Huang, and S. Sukoriansky, 2004: The ubiquitous zonal jets in the atmospheres of giant planets and Earth’s oceans. Geophys. Res. Lett., 31, L13303, doi:10.1029/2004GL019691.

    • Search Google Scholar
    • Export Citation

  • Galperin, B., S. Sukoriansky, and N. Dikovskaya, 2010: Geophysical flows with anisotropic turbulence and dispersive waves: Flows with a β-effect. Ocean Dyn., 60, 427–441, doi:10.1007/s10236-010-0278-2.

    • Search Google Scholar
    • Export Citation

  • Hovmöller, E., 1949: The trough-and-ridge diagram. Tellus, 1A, 62–66, doi:10.1111/j.2153-3490.1949.tb01260.x.

  • Huang, H.-P., and W. A. Robinson, 1998: Two-dimensional turbulence and persistent zonal jets in a global barotropic model. J. Atmos. Sci., 55, 611–632, doi:10.1175/1520-0469(1998)055<0611:TDTAPZ>2.0.CO;2.

    • 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, 225–240, doi:10.1063/1.1327594.

    • Search Google Scholar
    • Export Citation

  • Kwon, H. J., and M. Mak, 1988: On the equilibration in nonlinear barotropic instability. J. Atmos. Sci., 45, 294–308, doi:10.1175/1520-0469(1988)045<0294:OTEINB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lee, S., 2005: Baroclinic multiple zonal jets on the sphere. J. Atmos. Sci., 62, 2484–2498, doi:10.1175/JAS3481.1.

  • Limaye, S. S., 1986: Jupiter: New estimates of the mean zonal flow at the cloud level. Icarus, 65, 335–352, doi:10.1016/0019-1035(86)90142-9.

    • 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, 321–342, doi:10.1017/S0022112091002720.

    • 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, 784–800, doi:10.1175/1520-0469(1999)056<0784:SEOZJO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Marcus, P. S., and C. Lee, 1998: A model for eastward and westward jets in laboratory experiments and planetary atmospheres. Phys. Fluids, 10, 1474–1489, doi:10.1063/1.869668.

    • 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

  • Panetta, R. L., 1993: Zonal jets in wide baroclinically unstable regions: Persistence and scale selection. J. Atmos. Sci., 50, 2073–2106, doi:10.1175/1520-0469(1993)050<2073:ZJIWBU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Read, P. L., Y. H. Yamazaki, S. R. Lewis, P. D. Williams, K. Miki-Yamazaki, J. Sommeria, H. Didelle, and A. Fincham, 2004: Jupiter’s and Saturn’s convectively driven banded jets in the laboratory. Geophys. Res. Lett., 31, doi:10.1029/2004GL020106.

    • 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, 4031–4052, doi:10.1175/2007JAS2219.1.

    • Search Google Scholar
    • Export Citation

  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69, 417–443, doi:10.1017/S0022112075001504.

  • Saito, I., and K. Ishioka, 2013: Angular distribution of energy spectrum in two-dimensional β-plane turbulence in the long-wave limit. Phys. Fluids, 25, 076602, doi:10.1063/1.4813808.

    • Search Google Scholar
    • Export Citation

  • Sanchez-Lavega, A., J. F. Rojas, and P. V. Sada, 2000: Saturn’s zonal winds at cloud level. Icarus, 147, 405–420, doi:10.1006/icar.2000.6449.

    • Search Google Scholar
    • Export Citation

  • Scott, R. K., 2010: The structure of zonal jets in shallow water turbulence on the sphere. IUTAM Symposium on Turbulence in the Atmosphere and Oceans, D. Dritschel, Ed., IUTAM Bookseries, Vol. 28, Springer Netherlands, 243–252.

  • Scott, R. K., and D. G. Dritschel, 2012: The structure of zonal jets in geostrophic turbulence. J. Fluid Mech., 711, 576–598, doi:10.1017/jfm.2012.410.

    • Search Google Scholar
    • Export Citation

  • Slavin, A. G., and Y. D. Afanasyev, 2012: Multiple zonal jets on the polar beta plane. Phys. Fluids, 24, 016603, doi:10.1063/1.3678017.

  • Smith, C. A., K. G. Speer, and R. W. Griffiths, 2014: Multiple zonal jets in a differentially heated rotating annulus. J. Phys. Oceanogr., 44, 2273–2291, doi:10.1175/JPO-D-13-0255.1.

    • Search Google Scholar
    • Export Citation

  • Sommeria, J., S. D. Meyers, and H. L. Swinney, 1989: Laboratory model of a planetary eastward jet. Nature, 337, 58–61, doi:10.1038/337058a0.

    • 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, doi:10.1103/PhysRevLett.89.124501.

    • Search Google Scholar
    • Export Citation

  • Sukoriansky, S., N. Dikovskaya, and B. Galperin, 2007: On the arrest of inverse energy cascade and the Rhines scale. J. Atmos. Sci., 64, 3312–3327, doi:10.1175/JAS4013.1.

    • Search Google Scholar
    • Export Citation

  • Thompson, A. F., and W. R. Young, 2007: Two-layer baroclinic eddy heat fluxes: Zonal flows and energy balance. J. Atmos. Sci., 64, 3214–3231, doi:10.1175/JAS4000.1.

    • 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, 1346–1362, doi:10.1175/1520-0485(1993)023<1346:GOMFAJ>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., 2009: A proposed modification to the Robert–Asselin time filter. Mon. Wea. Rev., 137, 2538–2546, doi:10.1175/2009MWR2724.1.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., 2011: The RAW filter: An improvement to the Robert–Asselin filter in semi-implicit integrations. Mon. Wea. Rev., 139, 1996–2007, doi:10.1175/2010MWR3601.1.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., 2013: Achieving seventh-order amplitude accuracy in leapfrog integrations. Mon. Wea. Rev., 141, 3037–3051, doi:10.1175/MWR-D-12-00303.1.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., P. L. Read, and T. W. N. Haine, 2003: Spontaneous generation and impact of inertia–gravity waves in a stratified, two-layer shear flow. Geophys. Res. Lett., 30, 2255, doi:10.1029/2003GL018498.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., T. W. N. Haine, and P. L. Read, 2004: Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia–gravity wave parameterization. Nonlinear Processes Geophys., 11, 127–135, doi:10.5194/npg-11-127-2004.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., T. W. N. Haine, and P. L. Read, 2005: On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear. J. Fluid Mech., 528, 1–22, doi:10.1017/S0022112004002873.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., T. W. N. Haine, P. L. Read, S. R. Lewis, and Y. H. Yamazaki, 2009: QUAGMIRE v1.3: A quasi-geostrophic model for investigating rotating fluids experiments. Geosci. Model Dev., 2, 13–32, doi:10.5194/gmd-2-13-2009.

    • Search Google Scholar
    • Export Citation

  • Williams, P. D., P. L. Read, and T. W. N. Haine, 2010: Testing the limits of quasi-geostrophic theory: Application to observed laboratory flows outside the quasi-geostrophic regime. J. Fluid Mech., 649, 187–203, doi:10.1017/S0022112009993405.

    • Search Google Scholar
    • Export Citation

  • Wordsworth, R. D., P. L. Read, and Y. H. Yamazaki, 2008: Turbulence, waves, and jets in a differentially heated rotating annulus experiment. Phys. Fluids, 20, 126602, doi:10.1063/1.2990042.

    • Search Google Scholar
    • Export Citation

  • Yoden, S., and M. Yamada, 1993: A numerical experiment on two-dimensional decaying turbulence on a rotating sphere. J. Atmos. Sci., 50, 631–644, doi:10.1017/S0022112091002720.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1123 798 147
PDF Downloads 266 50 3