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Resonant wave interactions in the equatorial waveguide


Reference:

Raupp, C. F. M., Silva Dias, P. L., Tabak, E. G. and Milewski, P. A., 2008. Resonant wave interactions in the equatorial waveguide. Journal of the Atmospheric Sciences, 65 (11), pp. 3398-3418.

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    Official URL:

    http://dx.doi.org/10.1175/2008JAS2387.1

    Abstract

    Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial β-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface–gravity waves in deep water and capillary–gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby–gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(ε) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

    Details

    Item Type Articles
    CreatorsRaupp, C. F. M., Silva Dias, P. L., Tabak, E. G. and Milewski, P. A.
    DOI10.1175/2008JAS2387.1
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher Statement2008jas2387%2E1.pdf: © Copyright 2008 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (http://www.ametsoc.org/) or from the AMS at 617-227-2425 or copyright@ametsoc.org.
    RefereedYes
    StatusPublished
    ID Code26364

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