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Interaction of Large-Scale Equatorial Waves and Dispersion of Kelvin Waves through Topographic Resonances

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  • 1 Courant Institute of Mathematical Sciences, New York University, New York, New York
  • | 2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts
  • | 3 Courant Institute of Mathematical Sciences, New York University, New York, New York
  • | 4 F.A.M.A.F., University of Cordoba, Cordoba, Argentina
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Abstract

A new theoretical mechanism is developed in which large-scale equatorial Kelvin waves can modify their speed through dispersion and interaction with other large-scale equatorial waves, such as Yanai or Rossby modes, through topographic resonance. This resonance mechanism can prevent the breaking of a propagating nonlinear Kelvin wave, slow down its speed, and concentrate most of its energy in large-scale zonal wavenumbers while simultaneously generating large-scale Yanai or Rossby modes with specific zonal wavelengths. Simplified reduced dynamic equations for this resonant interaction are developed here via suitable asymptotic expansions of the equatorial shallow water equations with topography. Explicit exact solutions for the reduced equations and numerical experiments are utilized to display explicitly the features of large-scale dispersion and topographic resonance for equatorial Kelvin waves mentioned earlier. Two examples of this theory, corresponding to the barotropic and first baroclinic modes of the equatorial troposphere, are emphasized.

Corresponding author address: Prof. Andrew J. Majda, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012.

Email: krouhaus@cims.nyu.edu

Abstract

A new theoretical mechanism is developed in which large-scale equatorial Kelvin waves can modify their speed through dispersion and interaction with other large-scale equatorial waves, such as Yanai or Rossby modes, through topographic resonance. This resonance mechanism can prevent the breaking of a propagating nonlinear Kelvin wave, slow down its speed, and concentrate most of its energy in large-scale zonal wavenumbers while simultaneously generating large-scale Yanai or Rossby modes with specific zonal wavelengths. Simplified reduced dynamic equations for this resonant interaction are developed here via suitable asymptotic expansions of the equatorial shallow water equations with topography. Explicit exact solutions for the reduced equations and numerical experiments are utilized to display explicitly the features of large-scale dispersion and topographic resonance for equatorial Kelvin waves mentioned earlier. Two examples of this theory, corresponding to the barotropic and first baroclinic modes of the equatorial troposphere, are emphasized.

Corresponding author address: Prof. Andrew J. Majda, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012.

Email: krouhaus@cims.nyu.edu

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