• Biello, J., , and A. Majda, 2004a: The effect of meridional and vertical shear on the interaction of equatorial baroclinic and barotropic waves. Stud. Appl. Math., 112 , 341390.

    • Search Google Scholar
    • Export Citation
  • Biello, J., , and A. Majda, 2004b: Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic Rossby waves. Geophys. Astrophys. Fluid Dyn., 98 , 85127.

    • Search Google Scholar
    • Export Citation
  • Biello, J., , and A. Majda, 2005: A new multiscale model for the Madden–Julian oscillation. J. Atmos. Sci., 62 , 16941721.

  • Biello, J., , A. Majda, , and M. Moncrieff, 2007: Meridional momentum flux and superrotation in the multiscale IPESD MJO model. J. Atmos. Sci., 64 , 16361651.

    • Search Google Scholar
    • Export Citation
  • Boyd, J., 1980: Equatorial solitary waves. Part I: Rossby solitons. J. Phys. Oceanogr., 10 , 16991717.

  • Boyd, J., 2002: Equatorial solitary waves. Part V: Initial value experiments, coexisting branches, and tilted-pair instability. J. Phys. Oceanogr., 32 , 25892602.

    • Search Google Scholar
    • Export Citation
  • Boyd, J., , and G-Y. Chen, 2001: Weakly nonlinear wavepackets in the Korteweg–deVries equation: The KDV/NLS connection. Math. Comput. Simul., 55 , 317328.

    • Search Google Scholar
    • Export Citation
  • Charney, J., 1963: A note on large-scale motions in the tropics. J. Atmos. Sci., 20 , 607609.

  • Chen, T-C., , and J-M. Chen, 1997: On the relationship between the streamfunction and velocity potential of the Madden–Julian oscillation. J. Atmos. Sci., 54 , 679685.

    • Search Google Scholar
    • Export Citation
  • Delayen, K., , and J-I. Yano, 2009: Is asymptotic non-divergence of the large-scale tropical atmosphere consistent with equatorial wave theories? Tellus, 61A , 491497. doi:10.1111/j.1600-0870.2009.00404.x.

    • Search Google Scholar
    • Export Citation
  • Dodd, R., , J. Eilbeck, , J. Gibbon, , and H. Morris, 1982: Solitons and Nonlinear Wave Equations. Academic Press, 630 pp.

  • Domaradzki, J., , Z. Xiao, , and P. Smolarkiewicz, 2003: Effective eddy viscosities in implicit large eddy simulations of turbulent flows. Phys. Fluids, 15 , 38903893.

    • Search Google Scholar
    • Export Citation
  • ECMWF, 2003: Introduction. Proc. 2003 ECMWF/CLIVAR Workshop on Simulation and Prediction of Intra-Seasonal Variability with Emphasis on the MJO, Reading, United Kingdom, ECMWF, VII–XX.

    • Search Google Scholar
    • Export Citation
  • Flierl, G., 1987: Isolated eddy models in geophysics. Annu. Rev. Fluid Mech., 19 , 493530.

  • Fu, Z-T., , S-K. Liu, , and S-D. Liu, 2005: Equatorial Rossby solitary wave under the external forcing. Commun. Theor. Phys., 43 , 4548.

  • Gill, A., 1980: Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106 , 447462.

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

  • Hartmann, D. L., , and H. H. Hendon, 2007: Resolving an atmospheric enigma. Science, 318 , 17311732.

  • Held, I., , and M. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75 , 18251830.

    • Search Google Scholar
    • Export Citation
  • Hodyss, D., , and T. Nathan, 2002: Solitary Rossby waves in zonally varying jet flows. Geophys. Astrophys. Fluid Dyn., 96 , 239262.

  • Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3rd ed. International Geophysics Series, Vol. 23, Academic Press, 511 pp.

  • Hoskins, B. J., , and G-Y. Yang, 2000: The equatorial response to higher-latitude forcing. J. Atmos. Sci., 57 , 11971213.

  • Hsu, H-H., , B. J. Hoskins, , and F-F. Jin, 1990: The 1985/86 intraseasonal oscillation and the role of the extratropics. J. Atmos. Sci., 47 , 823839.

    • Search Google Scholar
    • Export Citation
  • Kartashova, E., , and V. S. L’vov, 2007: Model of intraseasonal oscillations in Earth’s atmosphere. Phys. Rev. Lett., 98 , 198501. doi:10.1103/PhysRevLett.98.198501.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., , and M. Wheeler, 1995: Horizontal and vertical structure of observed tropospheric equatorial Rossby waves. J. Geophys. Res., 100 , 2298122997.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., , K. Straub, , and P. Haertel, 2005: Zonal and vertical structure of the Madden–Julian oscillation. J. Atmos. Sci., 62 , 27902809.

    • Search Google Scholar
    • Export Citation
  • Kuo, H. L., 1972: On a generalized potential vorticity equation for quasi-geostrophic flow. Pure Appl. Geophys., 96 , 171175.

  • Lin, J-L., , M-I. Lee, , D. Kim, , I-S. Kang, , and D. M. Frierson, 2008: The impacts of convective parameterization and moisture triggering on AGCM-simulated convectively coupled equatorial waves. J. Climate, 21 , 883909.

    • 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 a 40–50-day period. J. Atmos. Sci., 29 , 11091123.

    • Search Google Scholar
    • Export Citation
  • Maicun, L., 1987a: Equatorial solitary waves of tropical atmospheric motion in shear flow. Adv. Atmos. Sci., 4 , 125136.

  • Maicun, L., 1987b: On the low-frequency, planetary-scale motion in the tropical atmosphere and oceans. Adv. Atmos. Sci., 4 , 249263.

  • Majda, A. J., , and J. Biello, 2003: The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves. J. Atmos. Sci., 60 , 18091821.

    • Search Google Scholar
    • Export Citation
  • Majda, A. J., , and J. Biello, 2004: A multiscale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. USA, 101 , 47364741.

    • Search Google Scholar
    • Export Citation
  • Mak, M-K., 1969: Laterally driven stochastic motions in the tropics. J. Atmos. Sci., 26 , 4164.

  • Malanotte-Rizzoli, P., 1980: Solitary Rossby waves over variable relief and their stability. Part II: Numerical experiments. Dyn. Atmos. Oceans, 4 , 261294.

    • Search Google Scholar
    • Export Citation
  • Malanotte-Rizzoli, P., , D. B. Haidvogel, , and R. E. Young, 1987: Numerical simulation of transient boundary-forced radiation. Part I: The linear regime. J. Phys. Oceanogr., 17 , 14391457.

    • Search Google Scholar
    • Export Citation
  • Malanotte-Rizzoli, P., , R. E. Young, , and D. B. Haidvogel, 1988: Numerical simulation of transient boundary-forced radiation. Part II: The modon regime. J. Phys. Oceanogr., 18 , 15461569.

    • Search Google Scholar
    • Export Citation
  • Margolin, L. G., , W. J. Rider, , and F. F. Grinstein, 2006: Modeling turbulent flow with implicit LES. J. Turbul., 7 , 127.

  • Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area. J. Meteor. Soc. Japan, 44 , 2543.

  • Matthews, A. J., 2008: Primary and successive events in the Madden–Julian oscillation. Quart. J. Roy. Meteor. Soc., 134 , 439453.

  • Miura, H., , M. Satoh, , T. Nasuno, , A. T. Noda, , and K. Oouchi, 2007: A Madden–Julian oscillation event realistically simulated by a global cloud-resolving model. Science, 318 , 17631765.

    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., 2004: Analytic representation of the large-scale organization of tropical convection. J. Atmos. Sci., 61 , 15211538.

    • Search Google Scholar
    • Export Citation
  • Neale, R. B., , and B. J. Hoskins, 2000: A standard test for AGCMs including their physical parameterizations. I: The proposal. Atmos. Sci. Lett., 1 , 101107.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2nd ed. Springer Verlag, 710 pp.

  • Phillips, O. M., 1981: Wave interactions—The evolution of an idea. J. Fluid Mech., 106 , 215227.

  • Piotrowski, Z. P., , P. K. Smolarkiewicz, , S. P. Malinowski, , and A. Wyszogrodzki, 2009: On numerical realizability of thermal convection. J. Comput. Phys., 228 , 62686290.

    • 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
  • Prusa, J. M., , P. K. Smolarkiewicz, , and A. A. Wyszogrodzki, 2008: EULAG, a computational model for multiscale flows. Comput. Fluids, 37 , 11931207.

    • Search Google Scholar
    • Export Citation
  • Ray, P., , C. Zhang, , J. Dudhia, , and S. S. Chen, 2009: A numerical case study on the initiation of the Madden–Julian oscillation. J. Atmos. Sci., 66 , 310331.

    • Search Google Scholar
    • Export Citation
  • Redekopp, L., 1977: On the theory of solitary Rossby waves. J. Fluid Mech., 82 , 725745.

  • Rossby, C-G., 1940: Planetary flow patterns in the atmosphere. Quart. J. Roy. Meteor. Soc., 66 , 6887.

  • Saujani, S., , and T. G. Shepherd, 2006: A unified theory of balance in the extratropics. J. Fluid Mech., 569 , 447464.

  • 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., , and J. Szmelter, 2009: Iterated upwind schemes for gas dynamics. J. Comput. Phys., 228 , 3354.

  • Smolarkiewicz, P. K., , C. Temperton, , S. J. Thomas, , and A. A. Wyszogrodzki, 2004: Spectral preconditioners for nonhydrostatic atmospheric models: Extreme applications. Proc. Seminar on Recent Developments in Numerical Methods for Atmosphere and Ocean Modelling, Reading, United Kingdom, ECMWF, 203–220.

    • Search Google Scholar
    • Export Citation
  • Straub, K., , and G. N. Kiladis, 2003: Extratropical forcing of convectively coupled Kelvin waves during austral winter. J. Atmos. Sci., 60 , 526543.

    • Search Google Scholar
    • Export Citation
  • Strauss, D. M., , and R. Lindzen, 2000: Planetary-scale baroclinic instability and the MJO. J. Atmos. Sci., 57 , 36093626.

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

  • Van Tuyl, A. H., 1987: Nonlinearities in low-frequency equatorial waves. J. Atmos. Sci., 44 , 24782492.

  • Verkley, W., 2009: A balanced approximation of the one-layer shallow water equations on a sphere. J. Atmos. Sci., 66 , 17351748.

  • Wedi, N. P., 2004: Numerical simulation of internal gravity wave dynamics. Proc. ECMWF Workshop on Recent Developments in Numerical Methods for Atmosphere and Ocean Modelling, Reading, United Kingdom, ECMWF, 221–232.

    • Search Google Scholar
    • Export Citation
  • Wedi, N. P., , and P. K. Smolarkiewicz, 2004: Extending Gal-Chen & 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
  • Wedi, N. P., , and P. K. Smolarkiewicz, 2006: Direct numerical simulation of the Plumb–McEwan laboratory analog of the QBO. J. Atmos. Sci., 63 , 32263252.

    • Search Google Scholar
    • Export Citation
  • Wedi, N. P., , and P. K. Smolarkiewicz, 2008: A reduced model of the Madden–Julian oscillation. Int. J. Numer. Methods Fluids, 56 , 15831588.

    • Search Google Scholar
    • Export Citation
  • Wedi, N. P., , and P. K. Smolarkiewicz, 2009: A framework for testing global nonhydrostatic models. Quart. J. Roy. Meteor. Soc., 135 , 469484.

    • Search Google Scholar
    • Export Citation
  • Wheeler, M., , and G. N. Kiladis, 1999: Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber–frequency domain. J. Atmos. Sci., 56 , 374399.

    • Search Google Scholar
    • Export Citation
  • Yano, J-I., , and M. Bonazzola, 2009: Scale analysis for the large-scale tropical atmospheric dynamics. J. Atmos. Sci., 66 , 159172.

  • Yano, J-I., , S. Mulet, , and M. Bonazzola, 2009: Tropical large-scale circulations: asymptotically nondivergent? Tellus, 61 , 417427.

  • Yano, J-I., , J. J. Tribbia, , and F. Reichmann, 1997: Jovian vortex dynamics from a historical perspective. Proceedings of the CP414 Research Workshop: Two-Dimensional Turbulence in Plasmas and Fluids, R. L. Dewar and R. W. Griffiths, Eds., AIP, 155–172.

    • Search Google Scholar
    • Export Citation
  • Zagar, N., , E. Andersson, , and M. Fisher, 2005: Balanced tropical data assimilation based on a study of equatorial waves in ECMWF short-range forecast errors. Quart. J. Roy. Meteor. Soc., 131 , 9871011.

    • Search Google Scholar
    • Export Citation
  • Zhang, C., 2005: Madden–Julian oscillation. Rev. Geophys., 43 , RG2003. doi:10.1029/2004RG000158.

  • Zou, J., , and H-R. Cho, 2000: A nonlinear Schrödinger equation model of the intraseasonal oscillation. J. Atmos. Sci., 57 , 24352444.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 23 23 7
PDF Downloads 20 20 7

A Nonlinear Perspective on the Dynamics of the MJO: Idealized Large-Eddy Simulations

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 30–60-day intraseasonal atmospheric oscillation in the equatorial atmosphere, the Madden–Julian oscillation (MJO), is most visible in its signature of outgoing longwave radiation and associated convective centers. Diabatic processes related to tropical convection and two-way atmosphere–ocean interaction are hence generally believed to be crucial in explaining the origin of the MJO phenomenon. However, reliable deterministic forecasting of the MJO in global circulation models and understanding its mechanism remains unsatisfactory. Here a different approach is taken, where the hypothesis is tested that eastward-propagating MJO-like structures originate fundamentally as a result of nonlinear (dry) Rossby wave dynamics. A laboratory-scale numerical model is constructed, where the generation of solitary structures is excited and maintained via zonally propagating meanders of the meridional boundaries of a zonally periodic β plane. The large-eddy simulations capture details of the formation of solitary structures and of their impact on the convective organization. The horizontal structure and the propagation of anomalous streamfunction patterns, a diagnostic typically used in tracing the equatorial MJO, are similar to archetype solutions of the Korteweg–deVries equation, which extends the linear shallow water theory—commonly used to explain equatorial wave motions—to a weakly nonlinear regime for small Rossby numbers. Furthermore, the characteristics of the three-dimensional laboratory-scale numerical results compare well with observed features of the equatorial MJO and thus the study provides indirect evidence of the basic principles underlying the wave-driven eastward propagation of the MJO.

Corresponding author address: N. P. Wedi, ECMWF, Shinfield Park, Reading, RG2 9AX, United Kingdom. Email: wedi@ecmwf.int

Abstract

The 30–60-day intraseasonal atmospheric oscillation in the equatorial atmosphere, the Madden–Julian oscillation (MJO), is most visible in its signature of outgoing longwave radiation and associated convective centers. Diabatic processes related to tropical convection and two-way atmosphere–ocean interaction are hence generally believed to be crucial in explaining the origin of the MJO phenomenon. However, reliable deterministic forecasting of the MJO in global circulation models and understanding its mechanism remains unsatisfactory. Here a different approach is taken, where the hypothesis is tested that eastward-propagating MJO-like structures originate fundamentally as a result of nonlinear (dry) Rossby wave dynamics. A laboratory-scale numerical model is constructed, where the generation of solitary structures is excited and maintained via zonally propagating meanders of the meridional boundaries of a zonally periodic β plane. The large-eddy simulations capture details of the formation of solitary structures and of their impact on the convective organization. The horizontal structure and the propagation of anomalous streamfunction patterns, a diagnostic typically used in tracing the equatorial MJO, are similar to archetype solutions of the Korteweg–deVries equation, which extends the linear shallow water theory—commonly used to explain equatorial wave motions—to a weakly nonlinear regime for small Rossby numbers. Furthermore, the characteristics of the three-dimensional laboratory-scale numerical results compare well with observed features of the equatorial MJO and thus the study provides indirect evidence of the basic principles underlying the wave-driven eastward propagation of the MJO.

Corresponding author address: N. P. Wedi, ECMWF, Shinfield Park, Reading, RG2 9AX, United Kingdom. Email: wedi@ecmwf.int

Save