Editorial Type:
Article
Article Type:
Research Article

The Effect of Eddy–Eddy Interactions on Jet Formation and Macroturbulent Scales

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

Search for other papers by Rei Chemke in
Current site
Google Scholar
PubMed Close
and
Yohai Kaspi Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel

Search for other papers by Yohai Kaspi in
Current site
Google Scholar
PubMed Close
Print Publication:
01 May 2016
DOI:
https://doi.org/10.1175/JAS-D-15-0375.1
Page(s):
2049–2059
Restricted access

Abstract

The effect of eddy–eddy interactions on zonal and meridional macroturbulent scales is investigated over a wide range of eddy scales, using high-resolution idealized GCM simulations with and without eddy–eddy interactions. The wide range of eddy scales is achieved through systematic variation of the planetary rotation rate and thus multiple-jet planets. It is found that not only are eddy–eddy interactions not essential for the formation of jets, but the existence of eddy–eddy interactions decreases the number of eddy-driven jets in the atmosphere. The eddy–eddy interactions have little effect on the jet scale, which in both types of simulations coincides with the Rhines scale through all latitudes. The decrease in the number of jets in the presence of eddy–eddy interactions occurs because of the narrowing of the latitudinal region where zonal jets appear. This narrowing occurs because eddy–eddy interactions are mostly important at latitudes poleward of where the Rhines scale is equal to the Rossby deformation radius. Thus, once eddy–eddy interactions are removed, the conversion from baroclinic to barotropic eddy kinetic energy increases, and eddy–mean flow interactions intrude into these latitudes and maintain additional jets there. The eddy–eddy interactions are found to increase the energy-containing zonal scale so it coincides with the jets’ scale and thus make the flow more isotropic. While the conversion scale coincides with the most unstable scale, the Rossby deformation radius does not provide a good indication to these scales in both types of simulations.

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

Abstract

The effect of eddy–eddy interactions on zonal and meridional macroturbulent scales is investigated over a wide range of eddy scales, using high-resolution idealized GCM simulations with and without eddy–eddy interactions. The wide range of eddy scales is achieved through systematic variation of the planetary rotation rate and thus multiple-jet planets. It is found that not only are eddy–eddy interactions not essential for the formation of jets, but the existence of eddy–eddy interactions decreases the number of eddy-driven jets in the atmosphere. The eddy–eddy interactions have little effect on the jet scale, which in both types of simulations coincides with the Rhines scale through all latitudes. The decrease in the number of jets in the presence of eddy–eddy interactions occurs because of the narrowing of the latitudinal region where zonal jets appear. This narrowing occurs because eddy–eddy interactions are mostly important at latitudes poleward of where the Rhines scale is equal to the Rossby deformation radius. Thus, once eddy–eddy interactions are removed, the conversion from baroclinic to barotropic eddy kinetic energy increases, and eddy–mean flow interactions intrude into these latitudes and maintain additional jets there. The eddy–eddy interactions are found to increase the energy-containing zonal scale so it coincides with the jets’ scale and thus make the flow more isotropic. While the conversion scale coincides with the most unstable scale, the Rossby deformation radius does not provide a good indication to these scales in both types of simulations.

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

  • Ait-Chaalal, F., and T. Schneider, 2015: Why eddy momentum fluxes are concentrated in the upper troposphere. J. Atmos. Sci., 72, 1585–1604, doi:10.1175/JAS-D-14-0243.1.

    • 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

  • Bakas, N. A., and P. J. Ioannou, 2014: A theory for the emergence of coherent structures in beta-plane turbulence. J. Fluid Mech., 740, 312–341, doi:10.1017/jfm.2013.663.

    • Search Google Scholar
    • Export Citation

  • Barry, L., G. C. Craig, and J. Thuburn, 2002: Poleward heat transport by the atmospheric heat engine. Nature, 415, 774–777, doi:10.1038/415774a.

    • 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

  • Boer, G. J., 1975: Zonal and eddy forms of the available potential energy equations in pressure coordinates. Tellus, 27A, 433–442, doi:10.1111/j.2153-3490.1975.tb01697.x.

    • 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

  • 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, 2015a: Poleward migration of eddy-driven jets. J. Adv. Model. Earth Syst., 7, 1457–1471, doi:10.1002/2015MS000481.

    • Search Google Scholar
    • Export Citation

  • Chemke, R., and Y. Kaspi, 2015b: The latitudinal dependence of atmospheric jet scales and macroturbulent energy cascades. J. Atmos. Sci., 72, 3891–3907, doi:10.1175/JAS-D-15-0007.1.

    • Search Google Scholar
    • Export Citation

  • Chemke, R., and Y. Kaspi, 2016: The latitudinal dependence of the oceanic barotropic eddy kinetic energy and macroturbulence energy transport. Geophys. Res. Lett., doi:10.1002/2016GL067847, in press.

    • 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

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

  • 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

  • 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

  • Fu, L.-L., and G. R. Flierl, 1980: Nonlinear energy and enstrophy transfers in a realistically stratified ocean. Dyn. Atmos. Oceans, 4, 219–246, doi:10.1016/0377-0265(80)90029-9.

    • 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, 426 pp.

  • 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 A. Y. Hou, 1980: Nonlinear axially symmetric circulations in a nearly inviscid atmosphere. J. Atmos. Sci., 37, 515–533, doi:10.1175/1520-0469(1980)037<0515:NASCIA>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

  • 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

  • Hunt, B. G., 1979: The influence of the earth’s rotation rate on the general circulation of the atmosphere. J. Atmos. Sci., 36, 1392–1408, doi:10.1175/1520-0469(1979)036<1392:TIOTER>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

  • 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 T. Schneider, 2011: Downstream self-destruction of storm tracks. J. Atmos. Sci., 68, 2459–2464, doi:10.1175/JAS-D-10-05002.1.

    • Search Google Scholar
    • Export Citation

  • Kaspi, Y., and A. P. Showman, 2015: Atmospheric dynamics of terrestrial 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, L21809, doi:10.1029/2010GL044849.

    • 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

  • 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.

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

    • Search Google Scholar
    • Export Citation

  • Marston, J. B., 2012: Planetary atmospheres as nonequilibrium condensed matter. Annu. Rev. Condens. Matter Phys., 3, 285–310, doi:10.1146/annurev-conmatphys-020911-125114.

    • 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

  • Navarra, A., and G. Boccaletti, 2002: Numerical general circulation experiments of sensitivity to Earth rotation rate. Climate Dyn., 19, 467–483, doi:10.1007/s00382-002-0238-8.

    • 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.

    • Search Google Scholar
    • Export Citation

  • 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

  • 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

  • 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, Ed., The Sea—Ideas and Observations on Progress in the Study of the Seas, Vol. 6, Harvard University Press, 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.

  • 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

  • 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

  • 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

  • Simmons, A. J., 1974: The meridional scale of baroclinic waves. J. Atmos. Sci., 31, 1515–1525, doi:10.1175/1520-0469(1974)031<1515:TMSOBW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smith, K. S., 2007: The geography of linear baroclinic instability in Earth’s oceans. J. Mar. Res., 65, 655–683, doi:10.1357/002224007783649484.

    • Search Google Scholar
    • Export Citation

  • Smith, K. S., and G. K. Vallis, 2001: The scales and equilibration of midocean eddies: Freely evolving flow. J. Phys. Oceanogr., 31, 554–571, doi:10.1175/1520-0485(2001)031<0554:TSAEOM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smith, K. S., and G. K. Vallis, 2002: The scales and equilibration of midocean eddies: Forced–dissipative flow. J. Phys. Oceanogr., 32, 1699–1720, doi:10.1175/1520-0485(2002)032<1699:TSAEOM>2.0.CO;2.

    • 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.

  • 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.

    • Search Google Scholar
    • Export Citation

  • Tobias, S. M., K. Dagon, and J. B. Marston, 2011: Astrophysical fluid dynamics via direct statistical simulation. Astrophys. J., 727, 127, doi:10.1088/0004-637X/727/2/127.

    • 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

  • Walker, C. C., and T. Schneider, 2006: Eddy influences on Hadley circulations: Simulations with an idealized GCM. J. Atmos. Sci., 63, 3333–3350, doi:10.1175/JAS3821.1.

    • 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

  • Williams, G. P., and J. L. Holloway, 1982: The range and unity of planetary circulations. Nature, 297, 295–299, doi:10.1038/297295a0.

  • 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
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 581 154 9
PDF Downloads 458 95 2