• Alexander, M. J., , and J. R. Holton, 2004: On the spectrum of vertically propagating gravity waves generated by a transient heat source. Atmos. Chem. Phys., 4 , 923932.

    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., , J. R. Holton, , and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysics Series, Vol. 40, Academic Press, 489 pp.

    • Search Google Scholar
    • Export Citation
  • Baines, P. G., 1995: Topographic Effects in Stratified Flows. Cambridge University Press, 482 pp.

  • Baldwin, M. P., , and L. J. Gray, 2005: Tropical stratospheric zonal winds in ECMWF ERA-40 reanalysis, rocketsonde data, and rawinsonde data. Geophys. Res. Lett., 32 .L09806, doi:10.1029/2004GL022328.

    • Search Google Scholar
    • Export Citation
  • Baldwin, M. P., and Coauthors, 2001: The quasi-biennial oscillation. Rev. Geophys., 39 , 179229.

  • Booker, J. R., , and F. P. Bretherton, 1967: The critical layer for internal gravity waves in a shear flow. J. Fluid Mech., 27 , 513539.

    • Search Google Scholar
    • Export Citation
  • Bretherton, F. P., 1966: The propagation of groups of internal gravity waves in a shear flow. Quart. J. Roy. Meteor. Soc., 92 , 466480.

    • Search Google Scholar
    • Export Citation
  • Charbonnel, C., , and S. Talon, 2005: Influence of gravity waves on the internal rotation and Li abundance of solar-type stars. Science, 309 , 21892191.

    • Search Google Scholar
    • Export Citation
  • Dörnbrack, A., , J. D. Doyle, , T. P. Lane, , R. D. Sharman, , and P. K. Smolarkiewicz, 2005: On physical realizability and uncertainty of numerical solutions. Atmos. Sci. Lett., 6 , 118122.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., 1981a: Wave transience in a compressible atmosphere. Part I: Transient internal wave, mean-flow interaction. J. Atmos. Sci., 38 , 281297.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., 1981b: Wave transience in a compressible atmosphere. Part II: Transient equatorial waves in the quasi-biennial oscillation. J. Atmos. Sci., 38 , 298307.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., 1991: Nonlinear propagation of zonal winds in an atmosphere with Newtonian cooling and equatorial wave driving. J. Atmos. Sci., 48 , 236263.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., 1997a: The role of gravity waves in the quasi-biennial oscillation. J. Geophys. Res., 102 , 2605326076.

  • Dunkerton, T. J., 1997b: Shear instability of internal inertia-gravity waves. J. Atmos. Sci., 54 , 16281641.

  • Fels, S. B., 1982: A parameterization of scale-dependent radiative damping rates in the middle atmosphere. J. Atmos. Sci., 39 , 11411152.

    • Search Google Scholar
    • Export Citation
  • Fels, S. B., , and R. S. Lindzen, 1974: The interaction of thermally excited gravity waves with mean flows. Geophys. Fluid Dyn., 6 , 149191.

    • Search Google Scholar
    • Export Citation
  • Ford, R., , M. E. McIntyre, , and W. A. Norton, 2000: Balance and the slow quasimanifold: Some explicit results. J. Atmos. Sci., 57 , 12361254.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., , and M. J. Alexander, 2003: Gravity wave dynamics and effects in the middle atmosphere. Rev. Geophys., 41 , 168.

  • Gabis, I., , and O. A. Troshichev, 2005: QBO cycle identified by changes in height profile of the zonal winds: New regularities. J. Atmos. Sol. Terr. Phys., 67 , 3344.

    • Search Google Scholar
    • Export Citation
  • Galmiche, M., , O. Thual, , and P. Bonneton, 2000: Wave/wave interaction producing horizontal mean flows in stably stratified fluids. Dyn. Atmos. Oceans, 31 , 193207.

    • Search Google Scholar
    • Export Citation
  • GFD Dennou Club, cited. 2005: Atmosphere and ocean in a laboratory. [Available online at http://www.gfd-dennou.org/library/gfd_exp/exp_e/index.htm.].

  • Gibson, J. K., , P. Kallberg, , S. Uppala, , A. Hernandez, , A. Nomura, , and E. Serrano, 1999: ERA-15 description. ECMWF Re-analysis Project Report Series, Vol. 1, ECMWF, Reading, United Kingdom, 74 pp.

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

  • Giorgetta, M. A., , E. Manzini, , and E. Roeckner, 2002: Forcing of the quasi-biennial oscillation from a broad spectrum of atmospheric waves. Geophys. Res. Lett., 29 .1245, doi:10.1029/2002GL014756.

    • Search Google Scholar
    • Export Citation
  • Grimshaw, R., 1974: Internal gravity waves in a slowly varying dissipative medium. Geophys. Fluid Dyn., 6 , 131148.

  • Haynes, P. H., 2005: Stratospheric dynamics. Annu. Rev. Fluid Mech., 37 , 263293.

  • Held, I., 2005: The gap between simulation and understanding in climate modeling. Bull. Amer. Meteor. Soc., 86 , 16091614.

  • Holton, J. R., , and R. S. Lindzen, 1972: An updated theory for the quasi-biennial cycle of the tropical stratosphere. J. Atmos. Sci., 29 , 10761079.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R., , P. H. Haynes, , M. E. McIntyre, , A. R. Douglas, , R. B. Rood, , and L. Pfister, 1995: Stratosphere–troposphere exchange. Rev. Geophys., 33 , 403439.

    • Search Google Scholar
    • Export Citation
  • Horinouchi, T., , and S. Yoden, 1998: Wave–mean flow interaction associated with a QBO-like oscillation simulated in a simplified GCM. J. Atmos. Sci., 55 , 502525.

    • Search Google Scholar
    • Export Citation
  • Horinouchi, T., and Coauthors, 2003: Tropical cumulus convection and upward-propagating waves in middle-atmospheric GCMs. J. Atmos. Sci., 60 , 27652782.

    • Search Google Scholar
    • Export Citation
  • Hou, A. Y., , and B. F. Farrell, 1987: Superrotation induced by critical level absorption of gravity waves on Venus: An assessment. J. Atmos. Sci., 44 , 10491061.

    • Search Google Scholar
    • Export Citation
  • Hristov, T. S., , S. D. Miller, , and C. A. Friehe, 2003: Dynamical coupling of wind and ocean waves through wave-induced air flow. Nature, 422 , 5558.

    • Search Google Scholar
    • Export Citation
  • Kim, Y-J., , D. Eckermann, , and H-Y. Chun, 2003: An overview of the past, present and future of gravity-wave drag parameterization for numerical climate and weather prediction models. Dyn. Atmos. Oceans, 41 , 6598.

    • Search Google Scholar
    • Export Citation
  • Kondepudi, D., , and I. Prigogine, 1998: Modern Thermodynamics—From Heat Engines to Dissipative Structures. Wiley and Sons, 486 pp.

  • Koop, C. G., 1981: A preliminary investigation of the interaction of internal gravity waves with a steady shearing motion. J. Fluid Mech., 113 , 347386.

    • Search Google Scholar
    • Export Citation
  • Lane, T., , and J. C. Knievel, 2005: Some effects of model resolution on simulated gravity waves generated by deep, mesoscale convection. J. Atmos. Sci., 62 , 34083419.

    • Search Google Scholar
    • Export Citation
  • Laprise, R., , and W. R. Peltier, 1989a: The linear stability of nonlinear mountain waves: Implications for the understanding of severe downslope windstorms. J. Atmos. Sci., 46 , 545564.

    • Search Google Scholar
    • Export Citation
  • Laprise, R., , and W. R. Peltier, 1989b: The structure and energetics of transient eddies in a numerical simulation of breaking mountain waves. J. Atmos. Sci., 46 , 565585.

    • Search Google Scholar
    • Export Citation
  • Leovy, C. B., 1973: Rotation of the upper atmosphere of Venus. J. Atmos. Sci., 30 , 12181220.

  • Lie, X., , and P. L. Read, 2000: A mechanistic model of the quasi-quadrennial oscillation in Jupiter’s stratosphere. Planet. Space Sci., 48 , 637669.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., 1987: On the development of the theory of the QBO. Bull. Amer. Meteor. Soc., 68 , 329337.

  • Lindzen, R. S., , and J. R. Holton, 1968: A theory of the quasi-biennial oscillation. J. Atmos. Sci., 25 , 10951107.

  • Lindzen, R. S., , and C-Y. Tsay, 1975: Wave structure of the tropical stratosphere over the Marshall Islands area during 1 April–1 July 1958. J. Atmos. Sci., 32 , 20082021.

    • Search Google Scholar
    • Export Citation
  • Madden, R. A., , and P. R. Julian, 1971: Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28 , 702708.

    • Search Google Scholar
    • Export Citation
  • Madden, R. A., , and P. R. Julian, 1972: Description of global scale circulation cells in the tropics with 40–50 day period. J. Atmos. Sci., 29 , 11091123.

    • Search Google Scholar
    • Export Citation
  • McIntyre, M. E., 1994: The quasi-biennial oscillation (QBO): Some points about the terrestrial QBO and the possibility of related phenomena in the solar interior. The Solar Engine and Its Influence on the Terrestrial Atmosphere and Climate, E. Nesme-Ribes, Ed., NATO ASI Subseries I, Vol. 25, Springer-Verlag, 293–320.

    • Search Google Scholar
    • Export Citation
  • McIntyre, M. E., 2003: On global-scale atmospheric circulations. Perspectives in Fluid Dynamics: A Collective Introduction to Current Research, G. Batchelor, H. Moffatt, and M. Worster, Eds., Cambridge University Press, 557–624.

    • Search Google Scholar
    • Export Citation
  • McIntyre, M. E., , and T. N. Palmer, 1984: The “surf zone” in the stratosphere. J. Atmos. Terr. Phys., 46 , 825849.

  • McLandress, C., , and J. F. Scinocca, 2005: The GCM response to current parameterizations of nonorographic gravity wave drag. J. Atmos. Sci., 62 , 23942413.

    • Search Google Scholar
    • Export Citation
  • Moin, P., , and K. Mahesh, 1998: Direct numerical simulation: A tool in turbulence research. Annu. Rev. Fluid Mech., 30 , 539578.

  • Otobe, N., , S. Sakai, , S. Yoden, , and M. Shiotani, 1998: Visualization and WKB analysis of the internal gravity wave in the QBO experiment. Nagare: Japan Soc. Fluid Mech., 17 .(3). [Available online at http://www.nagare.or.jp/mm/98/otobe/index.htm.].

    • Search Google Scholar
    • Export Citation
  • Pascoe, C. L., , L. J. Gray, , S. A. Crooks, , M. N. Juckes, , and M. P. Baldwin, 2005: The quasi-biennial oscillation: Analysis using ERA-40 data. J. Geophys. Res., 110 .D08105, doi:10.1029/2004JD004941.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1977: The interaction of two internal waves with the mean flow: Implications for the theory of the quasi-biennial oscillation. J. Atmos. Sci., 34 , 18471858.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., , and D. McEwan, 1978: The instability of a forced standing wave in a viscous stratified fluid: A laboratory analogue of the quasi-biennial oscillation. J. Atmos. Sci., 35 , 18271839.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., , and R. C. Bell, 1982: A model of the quasi-biennial oscillation on an equatorial beta plane. Quart. J. Roy. Meteor. Soc., 108 , 335352.

    • Search Google Scholar
    • Export Citation
  • Prusa, J. M., , and P. K. Smolarkiewicz, 2003: An all-scale anelastic model for geophysical flows: Dynamic grid deformation. J. Comput. Phys., 190 , 601622.

    • Search Google Scholar
    • Export Citation
  • Read, P. L., , S. R. Lewis, , and R. Hide, 1997: Laboratory and numerical studies of baroclinic waves in an internally heated rotating fluid annulus: A case of wave/vortex duality? J. Fluid Mech., 337 , 155191.

    • Search Google Scholar
    • Export Citation
  • Saravanan, R., 1990: A multiwave model of the quasi-biennial oscillation. J. Atmos. Sci., 47 , 24652474.

  • Scaife, A., , N. Butchart, , C. D. Warner, , D. Stainforth, , and W. Norton, 2000: Realistic quasi-biennial oscillations in a simulation of the global climate. Geophys. Res. Lett., 27 , 34813484.

    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., , and N. A. McFarlane, 2004: The variability of modeled tropical precipitation. J. Atmos. Sci., 61 , 19932015.

  • Smith, L. M., , and S. L. Woodruff, 1998: Renormalization-group analysis of turbulence. Annu. Rev. Fluid Mech., 30 , 275310.

  • Smith, R. B., 1980: Linear theory of stratified hydrostatic flow past an isolated mountain. Tellus, 32 , 348364.

  • Smith, R. B., 1985: On severe downslope winds. J. Atmos. Sci., 42 , 25972603.

  • Smolarkiewicz, P. K., 2006: Multidimensional positive definite advection transport algorithm: An overview. Int. J. Numer. Methods Fluids, 50 , 11231144.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., , and J. A. Pudykiewicz, 1992: A class of semi-Lagrangian approximations for fluids. J. Atmos. Sci., 49 , 20822096.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., , and L. G. Margolin, 1993: On forward-in-time differencing for fluids: Extension to a curvilinear framework. Mon. Wea. Rev., 121 , 18471859.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., , and L. G. Margolin, 1998: MPDATA: A finite difference solver for geophysical flows. J. Comput. Phys., 140 , 459480.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., , and L. G. Margolin, 2000: Variational methods for elliptic problems in fluid models. Proc. ECMWF Workshop on Developments in Numerical Methods for Very High Resolution Global Models, Reading, United Kingdom, ECMWF, 137–159.

  • Smolarkiewicz, P. K., , and J. M. Prusa, 2002: Forward-in-time differencing for fluids: Simulation of geophysical turbulence. Turbulent Flow Computation, D. Drikakis and B. Guertz, Eds., Kluwer Academic, 279–312.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., , and J. M. Prusa, 2005: Towards mesh adaptivity for geophysical turbulence: Continuous mapping approach. Int. J. Numer. Methods Fluids, 47 , 789801.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., , V. Grubišić, , and L. G. Margolin, 1997: On forward-in-time differencing for fluids: Stopping criteria for iterative solutions of anelastic pressure equations. Mon. Wea. Rev., 125 , 647654.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., , L. G. Margolin, , and A. A. Wyszogrodzki, 2001: A class of nonhydrostatic global models. J. Atmos. Sci., 58 , 349364.

    • Search Google Scholar
    • Export Citation
  • Staquet, C., , and J. Sommeria, 2002: Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Mech., 34 , 559593.

  • Takahashi, M., , and B. A. Boville, 1992: A three-dimensional simulation of the equatorial quasi-biennial oscillation. J. Atmos. Sci., 49 , 10201035.

    • Search Google Scholar
    • Export Citation
  • Tindall, J. C., 2003: Dynamics of the tropical tropopause and lower stratosphere. Ph.D. thesis, University of Reading, Reading, United Kingdom, 210 pp.

  • Tompkins, A., and Coauthors, 2004: Moist physical processes in the IFS: Progress and plans. ECMWF Tech. Memo. 452, Reading, United Kingdom, 91 pp. [Available online at http://www.ecmwf.int/publications/library/do/references/show?id=86472.].

  • Uppala, S. M., and Coauthors, 2005: The ERA-40 re-analysis. Quart. J. Roy. Meteor. Soc., 131 , 29613012.

  • Wedi, N. P., 2004: Time-dependent boundaries in numerical models. Ph.D. thesis, Ludwig-Maximilians-Universität München, Munich, Germany, 118 pp. [Available online at http://edoc.ub.unimuenchen.de/archive/00003142.].

  • Wedi, N. P., 2006: The energetics of wave-driven mean flow oscillations. Int. J. Numer. Methods Fluids, 50 , 11751191.

  • Wedi, N. P., , and P. K. Smolarkiewicz, 2004: Extending Gal-Chen and Somerville terrain-following coordinate transformation on time-dependent curvilinear boundaries. J. Comput. Phys., 193 , 120.

    • Search Google Scholar
    • Export Citation
  • Wedi, N. P., , and P. K. Smolarkiewicz, 2005: Laboratory for internal gravity-wave dynamics: The numerical equivalent to the quasi-biennial oscillation (QBO) analogue. Int. J. Numer. Methods Fluids, 47 , 13691374.

    • Search Google Scholar
    • Export Citation
  • Yamamoto, M., , and M. Takahashi, 2003: The fully developed superrotation simulated by a general circulation model of a Venus-like atmosphere. J. Atmos. Sci., 60 , 561574.

    • Search Google Scholar
    • Export Citation
  • Yoden, S., , and J. R. Holton, 1988: A new look at equatorial quasi-biennial oscillation models. J. Atmos. Sci., 45 , 27032717.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 38 38 3
PDF Downloads 25 25 3

Direct Numerical Simulation of the Plumb–McEwan Laboratory Analog of the QBO

View More View Less
  • 1 European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom
  • 2 National Center for Atmospheric Research, Boulder, Colorado
© Get Permissions
Restricted access

Abstract

The laboratory experiment of Plumb and McEwan demonstrates the principal mechanism of periodically reversing winds observed in the stratosphere—the quasi-biennial oscillation (QBO). However, despite numerous studies, some aspects of the QBO and the connection to its laboratory analog remain unclear. Incorporating the rapidly undulating boundaries of the laboratory experiment into the numerical algorithm—via time-dependent curvilinear coordinates—allows for the reproduction of the experimental setup, while minimizing numerical uncertainties. Results are presented of the first direct numerical simulation of the phenomena that lead to the zonal-mean flow reversal in the laboratory analog The aim of this research is to narrow the widening gap between the theoretical understanding of laboratory-scale, internal-gravity wave processes and the complexity of global-scale circulations. A detailed study is presented on the parametric and numerical sensitivities of the oscillation. The results confirm a number of sensitivities, addressed in earlier studies. The analogy of radiative damping in the atmosphere and the role of molecular viscosity in the zonally varying laboratory flow are discussed, emphasizing the dominant role of wave–wave and wave–mean flow interactions in the latter, and in particular the retroaction of the induced mean flow on the waves. The findings elevate the importance of the laboratory setup for its fundamental similarity to the atmosphere. Implications are discussed for the theory and numerical realizability of equatorial zonal-mean zonal flow oscillations. The study corroborates the dependence of global-scale motions on small-scale wave-driven fluctuations, while being independent of parameterized or approximated means of forcing and wave dissipation.

Corresponding author address: Nils Wedi, ECMWF, Reading RG2 9AX, United Kingdom. Email: wedi@ecmwf.int

Abstract

The laboratory experiment of Plumb and McEwan demonstrates the principal mechanism of periodically reversing winds observed in the stratosphere—the quasi-biennial oscillation (QBO). However, despite numerous studies, some aspects of the QBO and the connection to its laboratory analog remain unclear. Incorporating the rapidly undulating boundaries of the laboratory experiment into the numerical algorithm—via time-dependent curvilinear coordinates—allows for the reproduction of the experimental setup, while minimizing numerical uncertainties. Results are presented of the first direct numerical simulation of the phenomena that lead to the zonal-mean flow reversal in the laboratory analog The aim of this research is to narrow the widening gap between the theoretical understanding of laboratory-scale, internal-gravity wave processes and the complexity of global-scale circulations. A detailed study is presented on the parametric and numerical sensitivities of the oscillation. The results confirm a number of sensitivities, addressed in earlier studies. The analogy of radiative damping in the atmosphere and the role of molecular viscosity in the zonally varying laboratory flow are discussed, emphasizing the dominant role of wave–wave and wave–mean flow interactions in the latter, and in particular the retroaction of the induced mean flow on the waves. The findings elevate the importance of the laboratory setup for its fundamental similarity to the atmosphere. Implications are discussed for the theory and numerical realizability of equatorial zonal-mean zonal flow oscillations. The study corroborates the dependence of global-scale motions on small-scale wave-driven fluctuations, while being independent of parameterized or approximated means of forcing and wave dissipation.

Corresponding author address: Nils Wedi, ECMWF, Reading RG2 9AX, United Kingdom. Email: wedi@ecmwf.int

Save