The Longitudinal Variation of Equatorial Waves due to Propagation on a Varying Zonal Flow

Brian J. Hoskins University of Reading, Reading, and Grantham Institute for Climate Change, Imperial College London, London, United Kingdom

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Gui-Ying Yang National Centre for Atmospheric Science, and University of Reading, Reading, United Kingdom

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Abstract

The general 1D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behavior are found, depending on the sign of the group velocity cg and a wave property B. For B positive, the wave energy and the wavenumber vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang occurs where cg goes to zero. However, for B negative, they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analyzed in detail using the theory. For nondispersive Kelvin waves, B reduces to 2, and an analytic solution is possible. For all the waves considered, B is positive, except for the westward-moving mixed Rossby–gravity (WMRG) wave, which can have negative B as well as positive B.

Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper-tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However, the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic Oceans are generally not in accord with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher-latitude wave activity.

Denotes Open Access content.

Corresponding author address: Gui-Ying Yang, Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, United Kingdom. E-mail: g.y.yang@reading.ac.uk

Abstract

The general 1D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behavior are found, depending on the sign of the group velocity cg and a wave property B. For B positive, the wave energy and the wavenumber vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang occurs where cg goes to zero. However, for B negative, they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analyzed in detail using the theory. For nondispersive Kelvin waves, B reduces to 2, and an analytic solution is possible. For all the waves considered, B is positive, except for the westward-moving mixed Rossby–gravity (WMRG) wave, which can have negative B as well as positive B.

Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper-tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However, the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic Oceans are generally not in accord with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher-latitude wave activity.

Denotes Open Access content.

Corresponding author address: Gui-Ying Yang, Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, United Kingdom. E-mail: g.y.yang@reading.ac.uk
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  • Bretherton, F. P, and C. J. R. Garrett, 1968: Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. London, 302A, 529554, doi:10.1098/rspa.1968.0034.

    • Search Google Scholar
    • Export Citation
  • Chang, H.-R., and P. J. Webster, 1995: Energy accumulation and emanation at low latitudes. Part III: Forward and backward accumulation. J. Atmos. Sci., 52, 23842403, doi:10.1175/1520-0469(1995)052<2384:EAAEAL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dias, J., and G. N. Kiladis, 2014: Influence of the basic state zonal flow on convectively coupled equatorial waves. Geophys. Res. Lett., 41, 69046913, doi:10.1002/2014GL061476.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Hoskins, B. J., and G.-Y. Yang, 2000: The equatorial response to higher-latitude forcing. J. Atmos. Sci., 57, 11971213, doi:10.1175/1520-0469(2000)057<1197:TERTHL>2.0.CO;2.

    • 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, 22 98122 997, doi:10.1029/95JD02415.

    • Search Google Scholar
    • Export Citation
  • Lighthill, J., 1978: Waves in Fluid. Cambridge University Press, 504 pp.

  • Tomas, R. A., and P. J. Webster, 1994: Horizontal and vertical structure of cross-equatorial wave propagation. J. Atmos. Sci., 51, 14171430, doi:10.1175/1520-0469(1994)051<1417:HAVSOC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Webster, P. J., and J. R. Holton, 1982: Cross-equatorial response to midlatitude forcing in a zonally varying basic state. J. Atmos. Sci., 39, 722733, doi:10.1175/1520-0469(1982)039<0722:CERTML>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Webster, P. J., and H.-R. Chang, 1988: Equatorial energy accumulation and emanation regions: Impacts of a zonally varying basic state. J. Atmos. Sci., 45, 803829, doi:10.1175/1520-0469(1988)045<0803:EEAAER>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., and B. J. Hoskins, 2013: ENSO impact on Kelvin waves and associated tropical convection. J. Atmos. Sci., 70, 35133532, doi:10.1175/JAS-D-13-081.1.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., B. J. Hoskins, and J. M. Slingo, 2003: Convectively coupled equatorial waves: A new methodology for identifying wave structures in observational data. J. Atmos. Sci., 60, 16371654, doi:10.1175/1520-0469(2003)060<1637:CCEWAN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., B. J. Hoskins, and J. M. Slingo, 2007a: Convectively coupled equatorial waves. Part I: Horizontal structure. J. Atmos. Sci., 64, 34063423, doi:10.1175/JAS4017.1.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., B. J. Hoskins, and J. M. Slingo, 2007b: Convectively coupled equatorial waves. Part II: Zonal propagation. J. Atmos. Sci., 64, 34243437, doi:10.1175/JAS4018.1.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., B. J. Hoskins, and J. M. Slingo, 2007c: Convectively coupled equatorial waves. Part III: Synthesis structures and extratropical forcing. J. Atmos. Sci., 64, 34383451, doi:10.1175/JAS4019.1.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., B. J. Hoskins, and J. M. Slingo, 2011: Equatorial waves in opposite QBO phases. J. Atmos. Sci., 68, 839862, doi:10.1175/2010JAS3514.1.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., B. Hoskins, and L. Gray, 2012: The influence of the QBO on the propagation of equatorial waves into the stratosphere. J. Atmos. Sci., 69, 29592982, doi:10.1175/JAS-D-11-0342.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, C., 1993: Laterally forced equatorial perturbations in a linear model. Part II: Mobile forcing. J. Atmos. Sci., 50, 807821, doi:10.1175/1520-0469(1993)050<0807:LFEPIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
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