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Article
Article Type:
Research Article

The Latitudinal Dependence of Atmospheric Jet Scales and Macroturbulent Energy Cascades

Rei Chemke Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel

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Yohai Kaspi Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel

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Print Publication:
01 Oct 2015
DOI:
https://doi.org/10.1175/JAS-D-15-0007.1
Page(s):
3891–3907
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Abstract

The latitudinal width of atmospheric eddy-driven jets and scales of macroturbulence are examined latitude by latitude over a wide range of rotation rates using a high-resolution idealized GCM. It is found that for each latitude, through all rotation rates, the jet spacing scales with the Rhines scale. These simulations show the presence of a “supercriticality latitude” within the baroclinic zone, where poleward (equatorward) of this latitude, the Rhines scale is larger (smaller) than the Rossby deformation radius. Poleward of this latitude, a classic geostrophic turbulence picture appears with a − spectral slope of inverse cascade from the deformation radius up to the Rhines scale. A shallower slope than the −3 slope of enstrophy cascade is found from the deformation radius down to the viscosity scale as a result of the broad input of baroclinic eddy kinetic energy. At these latitudes, eddy–eddy interactions transfer barotropic eddy kinetic energy from the input scales of baroclinic eddy kinetic energy up to the jet scale and down to smaller scales. For the Earth case, this latitude is outside the baroclinic zone and therefore an inverse cascade does not appear. Equatorward of the supercriticality latitude, the − slope of inverse cascade vanishes, eddy–mean flow interactions play an important role in the balance, and the spectrum follows a −3 slope from the Rhines scale down to smaller scales, similar to what is observed on Earth. Moreover, the length scale of the energy-containing zonal wavenumber is equal to (larger than) the jet scale poleward (equatorward) of the supercriticality latitude.

Corresponding author address: Rei Chemke, Department of Earth and Planetary Sciences, Weizmann Institute of Science, 234 Herzl St., Rehovot 7610001, Israel. E-mail: rei.chemke@weizmann.ac.il

Abstract

The latitudinal width of atmospheric eddy-driven jets and scales of macroturbulence are examined latitude by latitude over a wide range of rotation rates using a high-resolution idealized GCM. It is found that for each latitude, through all rotation rates, the jet spacing scales with the Rhines scale. These simulations show the presence of a “supercriticality latitude” within the baroclinic zone, where poleward (equatorward) of this latitude, the Rhines scale is larger (smaller) than the Rossby deformation radius. Poleward of this latitude, a classic geostrophic turbulence picture appears with a − spectral slope of inverse cascade from the deformation radius up to the Rhines scale. A shallower slope than the −3 slope of enstrophy cascade is found from the deformation radius down to the viscosity scale as a result of the broad input of baroclinic eddy kinetic energy. At these latitudes, eddy–eddy interactions transfer barotropic eddy kinetic energy from the input scales of baroclinic eddy kinetic energy up to the jet scale and down to smaller scales. For the Earth case, this latitude is outside the baroclinic zone and therefore an inverse cascade does not appear. Equatorward of the supercriticality latitude, the − slope of inverse cascade vanishes, eddy–mean flow interactions play an important role in the balance, and the spectrum follows a −3 slope from the Rhines scale down to smaller scales, similar to what is observed on Earth. Moreover, the length scale of the energy-containing zonal wavenumber is equal to (larger than) the jet scale poleward (equatorward) of the supercriticality latitude.

Corresponding author address: Rei Chemke, Department of Earth and Planetary Sciences, Weizmann Institute of Science, 234 Herzl St., Rehovot 7610001, Israel. E-mail: rei.chemke@weizmann.ac.il
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  • Arbic, B. K., G. R. Flierl, and R. B. Scott, 2007: Cascade inequalities for forced–dissipated geostrophic turbulence. J. Phys. Oceanogr., 37, 1470–1487, doi:10.1175/JPO3067.1.

    • Search Google Scholar
    • Export Citation

  • Baer, F., 1972: An alternate scale representation of atmospheric energy spectra. J. Atmos. Sci., 29, 649–664, doi:10.1175/1520-0469(1972)029<0649:AASROA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Berloff, P., and I. Kamenkovich, 2013a: On spectral analysis of mesoscale eddies. Part I: Linear analysis. J. Phys. Oceanogr., 43, 2505–2527, doi:10.1175/JPO-D-12-0232.1.

    • Search Google Scholar
    • Export Citation

  • Berloff, P., and I. Kamenkovich, 2013b: On spectral analysis of mesoscale eddies. Part II: Nonlinear analysis. J. Phys. Oceanogr., 43, 2528–2544, doi:10.1175/JPO-D-12-0233.1.

    • Search Google Scholar
    • Export Citation

  • Blackmon, M. L., 1976: A climatological spectral study of the 500 mb geopotential height of the Northern Hemisphere. J. Atmos. Sci., 33, 1607–1623, doi:10.1175/1520-0469(1976)033<1607:ACSSOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Blackmon, M. L., J. M. Wallace, N. Lau, and S. L. Mullen, 1977: An observational study of the Northern Hemisphere wintertime circulation. J. Atmos. Sci., 34, 1040–1053, doi:10.1175/1520-0469(1977)034<1040:AOSOTN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Boer, G. J., and T. G. Shepherd, 1983: Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci., 40, 164–184, doi:10.1175/1520-0469(1983)040<0164:LSTDTI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Cai, M., and M. Mak, 1990: Symbiotic relation between planetary and synoptic-scale waves. J. Atmos. Sci., 47, 2953–2968, doi:10.1175/1520-0469(1990)047<2953:SRBPAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Chai, J., and G. K. Vallis, 2014: The role of criticality on the horizontal and vertical scales of extratropical eddies in a dry GCM. J. Atmos. Sci., 71, 2300–2318, doi:10.1175/JAS-D-13-0351.1.

    • Search Google Scholar
    • Export Citation

  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28, 1087–1095, doi:10.1175/1520-0469(1971)028<1087:GT>2.0.CO;2.

  • Chelton, D. B., R. A. Deszoeke, M. G. Schlax, E. Naggar, and N. Siwertz, 1998: Geographical variability of the first baroclinic Rossby radius of deformation. J. Phys. Oceanogr., 28, 433–460, doi:10.1175/1520-0485(1998)028<0433:GVOTFB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Chemke, R., and Y. Kaspi, 2015: Poleward migration of eddy driven jets. J. Adv. Model. Earth Syst., doi:10.1002/2015MS000481, in press.

  • Choi, D. S., and A. P. Showman, 2011: Power spectral analysis of Jupiter’s clouds and kinetic energy from Cassini. Icarus, 216, 597–609, doi:10.1016/j.icarus.2011.10.001.

    • Search Google Scholar
    • Export Citation

  • Constantinou, N. C., B. F. Farrell, and P. J. Ioannou, 2014: Emergence and equilibration of jets in beta-plane turbulence: Applications of stochastic structural stability theory. J. Atmos. Sci., 71, 1818–1842, doi:10.1175/JAS-D-13-076.1.

    • Search Google Scholar
    • Export Citation

  • Danilov, S. D., and D. Gurarie, 2000: Quasi-two-dimensional turbulence. Usp. Fiz. Nauk, 170, 921–968, doi:10.3367/UFNr.0170.200009a.0921.

    • Search Google Scholar
    • Export Citation

  • Danilov, S. D., and D. Gurarie, 2002: Rhines scale and spectra of the beta plane turbulence with bottom drag. Phys. Rev., 65E, 067301, doi:10.1103/PhysRevE.65.067301.

  • Eady, E. T., 1949: Long waves and cyclonic waves. Tellus, 1, 33–52, doi:10.1111/j.2153-3490.1949.tb01265.x.

  • Eden, C., 2007: Eddy length scales in the North Atlantic Ocean. J. Geophys. Res., 112, C06004, doi:10.1029/2006JC003901.

  • Farrell, B. F., and P. J. Ioannou, 2007: Structure and spacing of jets in barotropic turbulence. J. Atmos. Sci., 64, 3652–3665, doi:10.1175/JAS4016.1.

    • Search Google Scholar
    • Export Citation

  • Fjortoft, R., 1953: On the changes in the spectral distribution of kinetic energy for twodimensional, nondivergent flow. Tellus, 5, 225–230, doi:10.1111/j.2153-3490.1953.tb01051.x.

    • Search Google Scholar
    • Export Citation

  • Frierson, D. M. W., I. M. Held, and P. Zurita-Gotor, 2006: A gray-radiation aquaplanet moist GCM. Part I: Static stability and eddy scale. J. Atmos. Sci., 63, 2548–2566, doi:10.1175/JAS3753.1.

    • Search Google Scholar
    • Export Citation

  • Galperin, B., S. Sukoriansky, P. Read, Y. Yamazaki, and R. Wordsworth, 2006: Anisotropic turbulence and zonal jets in rotating flows with a beta effect. Nonlinear Processes Geophys., 13, 83–98, doi:10.5194/npg-13-83-2006.

    • Search Google Scholar
    • Export Citation

  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. International Geophysics Series, Vol. 30, Academic Press, 662 pp.

  • Goody, R. M., 1964: Atmospheric Radiation. Clarendon Press, 436 pp.

  • Grianik, N., I. M. Held, K. S. Smith, and G. K. Vallis, 2004: The effects of quadratic drag on the inverse cascade of two-dimensional turbulence. Phys. Fluids, 16, 73–78, doi:10.1063/1.1630054.

    • Search Google Scholar
    • Export Citation

  • Haidvogel, D. B., and I. M. Held, 1980: Homogeneous quasi-geostrophic turbulence driven by a uniform temperature gradient. J. Atmos. Sci., 37, 2644–1660, doi:10.1175/1520-0469(1980)037<2644:HQGTDB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Held, I. M., 1982: On the height of the tropopause and the static stability of the troposphere. J. Atmos. Sci., 39, 412–417, doi:10.1175/1520-0469(1982)039<0412:OTHOTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Held, I. M., and V. D. Larichev, 1996: A scaling theory for horizontally homogeneous, baroclinically unstable flow on a beta plane. J. Atmos. Sci., 53, 946–952, doi:10.1175/1520-0469(1996)053<0946:ASTFHH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Holloway, G., and M. C. Hendershott, 1977: Stochastic closure for nonlinear Rossby waves. J. Fluid Mech., 82, 747–765, doi:10.1017/S0022112077000962.

    • Search Google Scholar
    • Export Citation

  • Huang, H. P., and W. A. Robinson, 1998: Two-dimensional turbulence and persistent 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

  • Jansen, M., and R. Ferrari, 2012: Macroturbulent equilibration in a thermally forced primitive equation system. J. Atmos. Sci., 69, 695–713, doi:10.1175/JAS-D-11-041.1.

    • Search Google Scholar
    • Export Citation

  • Jansen, M., and R. Ferrari, 2013: Equilibration of an atmosphere by adiabatic eddy fluxes. J. Atmos. Sci., 70, 2948–2962, doi:10.1175/JAS-D-13-013.1.

    • Search Google Scholar
    • Export Citation

  • Jansen, M., and R. Ferrari, 2015: Diagnosing the vertical structure of the eddy diffusivity in real and idealized atmospheres. Quart. J. Roy. Meteor. Soc., 141, 631–641, doi:10.1002/qj.2387.

    • Search Google Scholar
    • Export Citation

  • Kaspi, Y., and G. R. Flierl, 2007: Formation of jets by baroclinic instability on gas planet atmospheres. J. Atmos. Sci., 64, 3177–3194, doi:10.1175/JAS4009.1.

    • Search Google Scholar
    • Export Citation

  • Kaspi, Y., and A. P. Showman, 2015: Three dimensional atmospheric dynamics of terrestial exoplanets over a wide range of orbital and atmospheric parameters. Astrophys. J., 804, 60, doi:10.1088/0004-637X/804/1/60.

    • Search Google Scholar
    • Export Citation

  • Kidston, J., and G. K. Vallis, 2010: Relationship between eddy-driven jet latitude and width. Geophys. Res. Lett., 37, doi:10.1029/2010GL044849.

    • Search Google Scholar
    • Export Citation

  • Kobashi, F., and H. Kawamura, 2002: Seasonal variation and instability nature of the North Pacific Subtropical Countercurrent and the Hawaiian Lee Countercurrent. J. Geophys. Res., 107, 3185, doi:10.1029/2001JC001225.

    • Search Google Scholar
    • Export Citation

  • Koshyk, J. N., and K. Hamilton, 2001: The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere–stratosphere–mesosphere GCM. J. Atmos. Sci., 58, 329–348, doi:10.1175/1520-0469(2001)058<0329:THKESA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kraichnan, R. H., 1967: Inertial ranges in two-dimensional turbulence. Phys. Fluids, 10, 1417–1423, doi:10.1063/1.1762301.

  • Kuo, H. L., 1949: Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere. J. Meteor., 6, 105–122, doi:10.1175/1520-0469(1949)006<0105:DIOTDN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lambert, S. J., 1984: A global available potential energy-kinetic energy budget in terms of the two-dimensional wavenumber for the FGGE year. Atmos.–Ocean, 22, 265–282, doi:10.1080/07055900.1984.9649199.

    • Search Google Scholar
    • Export Citation

  • Larichev, V. D., and I. M. Held, 1995: Eddy amplitudes and fluxes in a homogeneous model of fully developed baroclinic instability. J. Phys. Oceanogr., 25, 2285–2297, doi:10.1175/1520-0485(1995)025<2285:EAAFIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lee, S., 2005: Baroclinic multiple zonal jets on the sphere. J. Atmos. Sci., 62, 2482–2498, doi:10.1175/JAS3481.1.

  • Lilly, D. K., 1969: Numerical simulation of two-dimensional turbulence. Phys. Fluids, 12, 240–249, doi:10.1063/1.1692444.

  • Lindborg, E., 1999: Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech., 388, 259–288, doi:10.1017/S0022112099004851.

    • Search Google Scholar
    • Export Citation

  • Liu, J., and T. Schneider, 2015: Scaling of off-equatorial jets in giant planet atmospheres. J. Atmos. Sci., 72, 389–408, doi:10.1175/JAS-D-13-0391.1.

    • Search Google Scholar
    • Export Citation

  • Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7, 157–167, doi:10.1111/j.2153-3490.1955.tb01148.x.

    • Search Google Scholar
    • Export Citation

  • Merlis, T. M., and T. Schneider, 2009: Scales of linear baroclinic instability and macroturbulence in dry atmospheres. J. Atmos. Sci., 66, 1821–1833, doi:10.1175/2008JAS2884.1.

    • Search Google Scholar
    • Export Citation

  • Nastrom, G. D., and K. A. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42, 950–960, doi:10.1175/1520-0469(1985)042<0950:ACOAWS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • O’Gorman, P. A., and T. Schneider, 2007: Recovery of atmospheric flow statistics in a general circulation model without nonlinear eddy-eddy interactions. Geophys. Res. Lett., 34, L22801, doi:10.1029/2007GL031779.

  • O’Gorman, P. A., and T. Schneider, 2008a: The hydrological cycle over a wide range of climates simulated with an idealized GCM. J. Climate, 21, 3815–3832, doi:10.1175/2007JCLI2065.1.

    • Search Google Scholar
    • Export Citation

  • O’Gorman, P. A., and T. Schneider, 2008b: Weather-layer dynamics of baroclinic eddies and multiple jets in an idealized general circulation model. J. Atmos. Sci., 65, 524–535, doi:10.1175/2007JAS2280.1.

    • Search Google Scholar
    • Export Citation

  • Okuno, A., and A. Masuda, 2003: Effect of horizontal divergence on the geostrophic turbulence on a beta-plane: Suppression of the Rhines effect. Phys. Fluids, 15, 56–65, doi:10.1063/1.1524188.

    • 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

  • Phillips, N. A., 1954: Energy transformations and meridional circulations associated with simple baroclinic waves in a two level quasi-geostrophic model. Tellus, 6, 273–286, doi:10.1111/j.2153-3490.1954.tb01123.x.

    • 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.

  • Rhines, P. B., 1977: The dynamics of unsteady currents. Marine Modeling, E. D. Goldberg et al., Eds., The Sea: Ideas and Observations on Progress in the Study of the Seas, Vol. 6, Wiley, 189–318.

  • Rhines, P. B., 1979: Geostrophic turbulence. Annu. Rev. Fluid Mech., 11, 401–441, doi:10.1146/annurev.fl.11.010179.002153.

  • Rhines, P. B., 1994: Jets. Chaos, 4, 313–339, doi:10.1063/1.166011.

  • Rivera, M., and X. L. Wu, 2000: External dissipation in driven two-dimensional turbulence. Phys. Rev. Lett., 85, 976, doi:10.1103/PhysRevLett.85.976.

    • Search Google Scholar
    • Export Citation

  • Robinson, W. A., 2006: On the self-maintenance of midlatitude jets. J. Atmos. Sci., 63, 2109–2122, doi:10.1175/JAS3732.1.

  • Salmon, R., 1978: Two-layer quasi-geostrophic turbulence in a simple special case. Geophys. Astrophys. Fluid Dyn., 10, 25–52, doi:10.1080/03091927808242628.

    • Search Google Scholar
    • Export Citation

  • Saltsman, B., 1957: Equations governing the energetics of the larger scales of atmospheric turbulence in the domain of wave number. J. Meteor., 14, 513–523, doi:10.1175/1520-0469(1957)014<0513:EGTEOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Sayanagi, K. M., A. P. Showman, and T. E. Dowling, 2008: The emergence of multiple robust zonal jets from freely evolving, three-dimensional stratified geostrophic turbulence with applications to Jupiter. J. Atmos. Sci., 65, 3947–3962, doi:10.1175/2008JAS2558.1.

    • Search Google Scholar
    • Export Citation

  • Schneider, T., 2004: The tropopause and the thermal stratification in the extratropics of a dry atmosphere. J. Atmos. Sci., 61, 1317–1340, doi:10.1175/1520-0469(2004)061<1317:TTATTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Schneider, T., 2006: The general circulation of the atmosphere. Annu. Rev. Earth Planet. Sci., 34, 655–688, doi:10.1146/annurev.earth.34.031405.125144.

    • Search Google Scholar
    • Export Citation

  • Schneider, T., and C. C. Walker, 2006: Self-organization of atmospheric macroturbulence into critical states of weak nonlinear eddy–eddy interactions. J. Atmos. Sci., 63, 1569–1586, doi:10.1175/JAS3699.1.

    • Search Google Scholar
    • Export Citation

  • Schneider, T., and J. Liu, 2009: Formation of jets and equatorial superrotation on Jupiter. J. Atmos. Sci., 66, 579–601, doi:10.1175/2008JAS2798.1.

    • Search Google Scholar
    • Export Citation

  • Scott, R. B., 2001: Evolution of energy and enstrophy containing scales in decaying, two-dimensional turbulence with friction. Phys. Fluids, 13, 2739–2742, doi:10.1063/1.1388181.

    • Search Google Scholar
    • Export Citation

  • Scott, R. B., and F. Wang, 2005: Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J. Phys. Oceanogr., 35, 1650–1666, doi:10.1175/JPO2771.1.

    • Search Google Scholar
    • Export Citation

  • Scott, R. B., 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, 3158–3176, doi:10.1175/JAS4003.1.

    • Search Google Scholar
    • Export Citation

  • Shepherd, T. G., 1987a: Rossby waves and two-dimensional turbulence in a large-scale zonal jet. J. Fluid Mech., 183, 467–509, doi:10.1017/S0022112087002738.

    • Search Google Scholar
    • Export Citation

  • Shepherd, T. G., 1987b: A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere. J. Atmos. Sci., 44, 1166–1147, doi:10.1175/1520-0469(1987)044<1166:ASVONF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smith, K. S., 2004: A local model for planetary atmospheres forced by small-scale convection. J. Atmos. Sci., 61, 1420–1433, doi:10.1175/1520-0469(2004)061<1420:ALMFPA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smith, K. S., G. Boccaletti, C. C. Henning, I. Marinov, C. Y. Tam, and I. M. Held, 2002: Turbulent diffusion in the geostrophic inverse cascade. J. Fluid Mech., 469, 13–48, doi:10.1017/S0022112002001763.

    • Search Google Scholar
    • Export Citation

  • Srinivasan, K., and W. R. Young, 2012: Zonostrophic instability. J. Atmos. Sci., 69, 1633–1656, doi:10.1175/JAS-D-11-0200.1.

  • Stone, P. H., 1978: Baroclinic adjustment. J. Atmos. Sci., 35, 561–571, doi:10.1175/1520-0469(1978)035<0561:BA>2.0.CO;2.

  • 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

  • Theiss, J., 2004: Equatorward energy cascade, critical latitude, and the predominance of cyclonic vortices in geostrophic turbulence. J. Phys. Oceanogr., 34, 1663–1678, doi:10.1175/1520-0485(2004)034<1663:EECCLA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Theiss, J., 2006: A generalized Rhines effect and storms on Jupiter. Geophys. Res. Lett., 33, L08809, doi:10.1029/2005GL025379.

  • Thompson, A. F., 2010: Jet formation and evolution in baroclinic turbulence with simple topography. J. Phys. Oceanogr., 40, 257–278, doi:10.1175/2009JPO4218.1.

    • Search Google Scholar
    • Export Citation

  • Tobias, S. M., and J. B. Marston, 2013: Direct statistical simulation of out-of-equilibrium jets. Phys. Rev. Lett., 110, 104502, doi:10.1103/PhysRevLett.110.104502.

  • Tsang, Y.-K., and W. R. Young, 2009: Forced-dissipative two-dimensional turbulence: A scaling regime controlled by drag. Phys. Rev., 79, 045308, doi:10.1103/PhysRevE.79.045308.

  • Tung, K. K., and W. W. Oralndo, 2003: The k−3 and k−5/3 energy spectrum of atmospheric turbulence: Quasigeostrophic two-level model simulation. J. Atmos. Sci., 60, 824–835, doi:10.1175/1520-0469(2003)060<0824:TKAKES>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 770 pp.

  • 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

  • Vasavada, A. R., and A. P. Showman, 2005: Jovian atmospheric dynamics: An update after Galileo and Cassini. Rep. Prog. Phys., 68, 1935–1996, doi:10.1088/0034-4885/68/8/R06.

    • Search Google Scholar
    • Export Citation

  • Williams, G. P., 1978: Planetary circulations: 1. Barotropic representation of the Jovian and terrestrial turbulence. J. Atmos. Sci., 35, 1399–1426, doi:10.1175/1520-0469(1978)035<1399:PCBROJ>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Zurita-Gotor, P., 2008: The sensitivity of the isentropic slope in a primitive equation dry model. J. Atmos. Sci., 65, 43–65, doi:10.1175/2007JAS2284.1.

    • Search Google Scholar
    • Export Citation

  • Zurita-Gotor, P., and G. K. Vallis, 2009: Equilibration of baroclinic turbulence in primitive equations and quasigeostrophic models. J. Atmos. Sci., 66, 837–863, doi:10.1175/2008JAS2848.1.

    • Search Google Scholar
    • Export Citation
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