Why Eddy Momentum Fluxes are Concentrated in the Upper Troposphere

Farid Ait-Chaalal ETH Zürich, Zurich, Switzerland

Search for other papers by Farid Ait-Chaalal in
Current site
Google Scholar
PubMed
Close
and
Tapio Schneider ETH Zürich, Zurich, Switzerland, and California Institute of Technology, Pasadena, California

Search for other papers by Tapio Schneider in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The extratropical eddy momentum flux (EMF) is controlled by generation, propagation, and dissipation of large-scale eddies and is concentrated in Earth’s upper troposphere. An idealized GCM is used to investigate how this EMF structure arises. In simulations in which the poles are heated more strongly than the equator, EMF is concentrated near the surface, demonstrating that surface drag generally is not responsible for the upper-tropospheric EMF concentration. Although Earth’s upper troposphere favors linear wave propagation, quasi-linear simulations in which nonlinear eddy–eddy interactions are suppressed demonstrate that this is likewise not primarily responsible for the upper-tropospheric EMF concentration. The quasi-linear simulations reveal the essential role of nonlinear eddy–eddy interactions in the surf zone in the upper troposphere, where wave activity absorption away from the baroclinic generation regions occurs through the nonlinear generation of small scales. In Earth-like atmospheres, wave activity that is generated in the lower troposphere propagates upward and then turns meridionally, eventually being absorbed nonlinearly in the upper troposphere. The level at which the wave activity begins to propagate meridionally appears to be set by the typical height reached by baroclinic eddies. This can coincide with the tropopause height but also can lie below it if convection controls the tropopause height. In the latter case, EMF is maximal well below the tropopause. The simulations suggest that EMF is concentrated in Earth’s upper troposphere because typical baroclinic eddies reach the tropopause.

Corresponding author address: Farid Ait-Chaalal, Geological Institute, ETH, NOG 60, Sonnegstrasse 5, 8092 Zurich, Switzerland. E-mail: farid.chaalal@erdw.ethz.ch

Abstract

The extratropical eddy momentum flux (EMF) is controlled by generation, propagation, and dissipation of large-scale eddies and is concentrated in Earth’s upper troposphere. An idealized GCM is used to investigate how this EMF structure arises. In simulations in which the poles are heated more strongly than the equator, EMF is concentrated near the surface, demonstrating that surface drag generally is not responsible for the upper-tropospheric EMF concentration. Although Earth’s upper troposphere favors linear wave propagation, quasi-linear simulations in which nonlinear eddy–eddy interactions are suppressed demonstrate that this is likewise not primarily responsible for the upper-tropospheric EMF concentration. The quasi-linear simulations reveal the essential role of nonlinear eddy–eddy interactions in the surf zone in the upper troposphere, where wave activity absorption away from the baroclinic generation regions occurs through the nonlinear generation of small scales. In Earth-like atmospheres, wave activity that is generated in the lower troposphere propagates upward and then turns meridionally, eventually being absorbed nonlinearly in the upper troposphere. The level at which the wave activity begins to propagate meridionally appears to be set by the typical height reached by baroclinic eddies. This can coincide with the tropopause height but also can lie below it if convection controls the tropopause height. In the latter case, EMF is maximal well below the tropopause. The simulations suggest that EMF is concentrated in Earth’s upper troposphere because typical baroclinic eddies reach the tropopause.

Corresponding author address: Farid Ait-Chaalal, Geological Institute, ETH, NOG 60, Sonnegstrasse 5, 8092 Zurich, Switzerland. E-mail: farid.chaalal@erdw.ethz.ch
Save
  • Andrews, D., and M. E. McIntyre, 1976: Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci., 33, 20312048, doi:10.1175/1520-0469(1976)033<2031:PWIHAV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Andrews, D., and M. E. McIntyre, 1978: Generalized Eliassen-Palm and Charney-Drazin theorems for waves in axisymmetric mean flows in compressible atmospheres. J. Atmos. Sci., 35, 175185.

    • Search Google Scholar
    • Export Citation
  • Birner, T., D. J. Thompson, and T. Shepherd, 2013: Up-gradient eddy fluxes of potential vorticity near the subtropical jet. Geophys. Res. Lett., 40, 59885993, doi:10.1002/2013GL057728.

    • Search Google Scholar
    • Export Citation
  • Bouchet, F., C. Nardini, and T. Tangarife, 2013: Kinetic theory of jet dynamics in the stochastic barotropic and 2D Navier-Stokes equations. J. Stat. Phys., 153, 572625, doi:10.1007/s10955-013-0828-3.

    • Search Google Scholar
    • Export Citation
  • Bourke, W., 1974: A multi-level spectral model. I. Formulation and hemispheric integrations. Mon. Wea. Rev., 102, 687701, doi:10.1175/1520-0493(1974)102<0687:AMLSMI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Boyd, J. P., 1976: The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships on eddy fluxes of energy, heat and momentum. J. Atmos. Sci., 33, 22852291, doi:10.1175/1520-0469(1976)033<2285:TNOWWT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., and P. Drazin, 1961: Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83109, doi:10.1029/JZ066i001p00083.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., and M. E. Stern, 1962: On the stability of internal baroclinic jets in a rotating atmosphere. J. Atmos. Sci., 19, 159172, doi:10.1175/1520-0469(1962)019<0159:OTSOIB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, G., I. M. Held, and W. A. Robinson, 2007: Sensitivity of the latitude of the surface westerlies to surface friction. J. Atmos. Sci., 64, 28992915, doi:10.1175/JAS3995.1.

    • Search Google Scholar
    • Export Citation
  • Del Genio, A. D., J. M. Barbara, J. Ferrier, A. P. Ingersoll, R. A. West, A. R. Vasavada, J. Spitale, and C. C. Porco, 2007: Saturn eddy momentum fluxes and convection: First estimates from Cassini images. Icarus, 189, 479492, doi:10.1016/j.icarus.2007.02.013.

    • Search Google Scholar
    • Export Citation
  • DelSole, T., 2001: A simple model for transient eddy momentum fluxes in the upper troposphere. J. Atmos. Sci., 58, 30193035, doi:10.1175/1520-0469(2001)058<3019:ASMFTE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • DelSole, T., 2004: Stochastic models of quasigeostrophic turbulence. Surv. Geophys., 25, 107149, doi:10.1023/B:GEOP.0000028164.58516.b2.

    • Search Google Scholar
    • Export Citation
  • Dickinson, R. E., 1969: Theory of planetary wave-zonal flow interaction. J. Atmos. Sci., 26, 7381, doi:10.1175/1520-0469(1969)026<0073:TOPWZF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dickinson, R. E., 1970: Development of a Rossby wave critical level. J. Atmos. Sci., 27, 627633, doi:10.1175/1520-0469(1970)027<0627:DOARWC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dritschel, D., and M. McIntyre, 2008: Multiple jets as PV staircases: The Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65, 855874, doi:10.1175/2007JAS2227.1.

    • Search Google Scholar
    • Export Citation
  • Edmon, H. J., Jr., B. J. Hoskins, and M. E. McIntyre, 1980: Eliassen-Palm cross sections for the troposphere. J. Atmos. Sci., 37, 26002616, doi:10.1175/1520-0469(1980)037<2600:EPCSFT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., and E. Palm, 1961: On the transfer of energy in stationary mountain waves. Geofys. Publ., 22, 123.

  • Farrell, B., 1987: Developing disturbances in shear. J. Atmos. Sci., 44, 21912199, doi:10.1175/1520-0469(1987)044<2191:DDIS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Farrell, B., and P. J. Ioannou, 1996a: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci., 53, 20252040, doi:10.1175/1520-0469(1996)053<2025:GSTPIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Farrell, B., and P. J. Ioannou, 1996b: Generalized stability theory. Part II: Nonautonomous operators. J. Atmos. Sci., 53, 20412053, doi:10.1175/1520-0469(1996)053<2041:GSTPIN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ferreira, D., J. Marshall, P. A. O. Gorman, and S. Seager, 2014: Climate at high-obliquity. Icarus, 243, 236–248, doi:10.1016/j.icarus.2014.09.015.

    • Search Google Scholar
    • Export Citation
  • Harnik, N., and R. S. Lindzen, 2001: The effect of reflecting surfaces on the vertical structure and variability of stratospheric planetary waves. J. Atmos. Sci., 58, 28722894, doi:10.1175/1520-0469(2001)058<2872:TEORSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hayes, M., 1977: A note on group velocity. Proc. Roy. Soc. London,354A, 533–535.

  • Haynes, P. H., and M. E. McIntyre, 1987: On the representation of Rossby wave critical layers and wave breaking in zonally truncated models. J. Atmos. Sci., 44, 23592382, doi:10.1175/1520-0469(1987)044<2359:OTRORW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., 1975: Momentum transport by quasi-geostrophic eddies. J. Atmos. Sci., 32, 14941497, doi:10.1175/1520-0469(1975)032<1494:MTBQGE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., 1978: The vertical scale of an unstable baroclinic wave and its importance for eddy heat flux parameterizations. J. Atmos. Sci., 35, 572576, doi:10.1175/1520-0469(1978)035<0572:TVSOAU>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, 412417, doi:10.1175/1520-0469(1982)039<0412:OTHOTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., 1999: The macroturbulence of the troposphere. Tellus, 51B, 5970, doi:10.1034/j.1600-0889.1999.00006.x.

  • Held, I. M., 2000: The general circulation of the atmosphere. Woods Hole Lecture Notes, 70 pp. [Available online at http://www.gfdl.noaa.gov/cms-filesystem-action/user_files/ih/lectures/woods_hole.pdf.]

  • Held, I. M., 2007: Progress and problems in large-scale atmospheric dynamics. The Global Circulation of the Atmosphere, T. Schneider and A. Sobel, Eds., Princeton University Press, 1–21.

  • Held, I. M., and B. J. Hoskins, 1985: Large-scale eddies and the general circulation of the troposphere. Advances in Geophysics, Vol. 28, Academic Press, 331, doi:10.1016/S0065-2687(08)60218-6.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., and P. J. Phillips, 1987: Linear and nonlinear barotropic decay on the sphere. J. Atmos. Sci., 44, 200207, doi:10.1175/1520-0469(1987)044<0200:LANBDO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75, 18251830, doi:10.1175/1520-0477(1994)075<1825:APFTIO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877946, doi:10.1002/qj.49711147002.

    • Search Google Scholar
    • Export Citation
  • James, I., and L. Gray, 1986: Concerning the effect of surface drag on the circulation of a baroclinic planetary atmosphere. Quart. J. Roy. Meteor. Soc., 112, 12311250, doi:10.1002/qj.49711247417.

    • Search Google Scholar
    • Export Citation
  • Killworth, P. R. D., and M. E. McIntyre, 1985: Do Rossby-wave critical layers absorb, reflect, or over-reflect? J. Fluid Mech., 161, 449492, doi:10.1017/S0022112085003019.

    • Search Google Scholar
    • Export Citation
  • Kushner, P. J., and I. M. Held, 1998: A test, using atmospheric data, of a method for estimating oceanic eddy diffusivity. Geophys. Res. Lett., 25, 42134216, doi:10.1029/1998GL900142.

    • Search Google Scholar
    • Export Citation
  • Lighthill, M. J., and M. Lighthill, 1960: Studies on magneto-hydrodynamic waves and other anisotropic wave motions. Philos. Trans. Roy. Soc. London, A252, 397430, doi:10.1098/rsta.1960.0010.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., 1988: Instability of plane parallel shear flow (toward a mechanistic picture of how it works). Pure Appl. Geophys., 126, 103121, doi:10.1007/BF00876917.

    • Search Google Scholar
    • Export Citation
  • Liu, J., and T. Schneider, 2010: Mechanisms of jet formation on the giant planets. J. Atmos. Sci., 67, 36523672, doi:10.1175/2010JAS3492.1.

    • 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, 157167, doi:10.1111/j.2153-3490.1955.tb01148.x.

    • Search Google Scholar
    • Export Citation
  • Marston, J. B., E. Conover, and T. Schneider, 2008: Statistics of an unstable barotropic jet from a cumulant expansion. J. Atmos. Sci., 65, 19551966, doi:10.1175/2007JAS2510.1.

    • Search Google Scholar
    • Export Citation
  • Marston, J. B., W. Qi, and S. M. Tobias, 2015: Direct statistical simulation of a jet. Big Book of Jets, B. Galperin and P. Read, Eds., Cambridge University Press, in press.

  • Merlis, T. M., and T. Schneider, 2009: Scales of linear baroclinic instability and macroturbulence in dry atmospheres. J. Atmos. Sci., 66, 18211833, doi:10.1175/2008JAS2884.1.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., and D. Zhu, 2010: Finite-amplitude wave activity and diffusive flux of potential vorticity in eddy–mean flow interaction. J. Atmos. Sci., 67, 27012716, doi:10.1175/2010JAS3432.1.

    • Search Google Scholar
    • Export Citation
  • O’Gorman, P. A., 2011: The effective static stability experienced by eddies in a moist atmosphere. J. Atmos. Sci., 68, 7590, doi:10.1175/2010JAS3537.1.

    • 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.

  • Potter, S. F., T. Spengler, and I. M. Held, 2013: Reflection of barotropic Rossby waves in sheared flow and validity of the WKB approximation. J. Atmos. Sci., 70, 21702178, doi:10.1175/JAS-D-12-0315.1.

    • Search Google Scholar
    • Export Citation
  • Randel, W., and I. Held, 1991: Phase speed spectra of transient eddy fluxes and critical layer absorption. J. Atmos. Sci., 48, 688697, doi:10.1175/1520-0469(1991)048<0688:PSSOTE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Robinson, W. A., 1997: Dissipation dependence of the jet latitude. J. Climate, 10, 176182, doi:10.1175/1520-0442(1997)010<0176:DDOTJL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Salyk, C., A. P. Ingersoll, J. Lorre, A. Vasavada, and A. D. Del Genio, 2006: Interaction between eddies and mean flow in Jupiter’s atmosphere: Analysis of Cassini imaging data. Icarus, 185, 430442, doi:10.1016/j.icarus.2006.08.007.

    • 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, 13171340, 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, 655688, 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, 15691586, doi:10.1175/JAS3699.1.

    • Search Google Scholar
    • Export Citation
  • Schneider, T., and P. A. O’Gorman, 2008: Moist convection and the thermal stratification of the extratropical troposphere. J. Atmos. Sci., 65, 35713583, doi:10.1175/2008JAS2652.1.

    • Search Google Scholar
    • Export Citation
  • Schneider, T., and C. C. Walker, 2008: Scaling laws and regime transitions of macroturbulence in dry atmospheres. J. Atmos. Sci., 65, 21532173, doi:10.1175/2007JAS2616.1.

    • 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
  • Seager, R., N. Harnik, Y. Kushnir, W. Robinson, and J. Miller, 2003: Mechanisms of hemispherically symmetric climate variability. J. Climate, 16, 29602978, doi:10.1175/1520-0442(2003)016<2960:MOHSCV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 1987: A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere. J. Atmos. Sci., 44, 11661179, doi:10.1175/1520-0469(1987)044<1166:ASVONF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., and B. J. Hoskins, 1978: The life cycles of some nonlinear baroclinic waves. J. Atmos. Sci., 35, 414432, doi:10.1175/1520-0469(1978)035<0414:TLCOSN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., and B. J. Hoskins, 1980: Barotropic influences on the growth and decay of nonlinear baroclinic waves. J. Atmos. Sci., 37, 16791684, doi:10.1175/1520-0469(1980)037<1679:BIOTGA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., and D. M. Burridge, 1981: An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109, 758766, doi:10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., S. Manabe, and J. L. Holloway Jr., 1965: Numerical results from a nine-level general circulation model of the atmosphere. Mon. Wea. Rev., 93, 727768, doi:10.1175/1520-0493(1965)093<0727:NRFANL>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Srinivasan, K., and W. R. Young, 2012: Zonostrophic instability. J. Atmos. Sci., 69, 16331656, doi:10.1175/JAS-D-11-0200.1.

  • Stewartson, K., 1977: The evolution of the critical layer of a Rossby wave. Geophys. Astrophys. Fluid Dyn., 9, 185200, doi:10.1080/03091927708242326.

    • Search Google Scholar
    • Export Citation
  • Stone, P. H., 1972: A simplified radiative-dynamical model for the static stability of rotating atmospheres. J. Atmos. Sci., 29, 405418, doi:10.1175/1520-0469(1972)029<0405:ASRDMF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorncroft, C., B. J. Hoskins, and M. E. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behaviour. Quart. J. Roy. Meteor. Soc., 119, 1755, doi:10.1002/qj.49711950903.

    • 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
  • Uppala, S. M., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, 29613012, doi:10.1256/qj.04.176.

  • Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press, 745 pp.

  • Warn, T., and H. Warn, 1978: The evolution of a nonlinear critical level. Stud. Appl. Math., 59, 3771.

  • Whitaker, J. S., and P. D. Sardeshmukh, 1998: A linear theory of extratropical synoptic eddy statistics. J. Atmos. Sci., 55, 237258, doi:10.1175/1520-0469(1998)055<0237:ALTOES>2.0.CO;2.

    • 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, 19962007, doi:10.1175/2010MWR3601.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, Y., and I. M. Held, 1999: A linear stochastic model of a GCM’s midlatitude storm tracks. J. Atmos. Sci., 56, 34163435, doi:10.1175/1520-0469(1999)056<3416:ALSMOA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 865 257 20
PDF Downloads 750 214 28