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Bifurcation of Nonlinear Kelvin Wave-CISK with Conditional Heating in a Truncated Spectral Model: A Possible Mechanism of 30-60-Day Osculation at the Equator


doi: 10.1007/BF02973088

  • In this paper, the nonlinear Kelvin wave equations with “positive-only” nonlinear (conditional) heating at the equator are reduced to a sixth-order nonlinear ordinary differential equation by using the Galerkin spectral truncated method. The stability analysis indicates that when the heating parameter increases, the supercritical pitchfork and Hopf bifurcations can occur for the prescribed three heating profiles. Numerical calculations are made with the help of the fourth-order Rung-Kutta method. It is found that the convec-tion heating-related Hopf bifurcation can lead to limit cycle and chaotic solutions. In a wide range of heat-ing parameter, the solutions possess 30-60-day periods, and are dominated by wavenumbers one and two, especially by wavenurnber-one. In addition, the zonal winds of the low-frequency solutions have a phase reversal between the upper and lower tropospheres. Thus, it appears that the convection heating-related Hopf bifurcation might be a possible mechanism of 30-60-day oscillation in the tropical atmosphere.
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Manuscript History

Manuscript received: 10 April 1999
Manuscript revised: 10 April 1999
通讯作者: 陈斌, bchen63@163.com
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Bifurcation of Nonlinear Kelvin Wave-CISK with Conditional Heating in a Truncated Spectral Model: A Possible Mechanism of 30-60-Day Osculation at the Equator

  • 1. Department of Atmospheric and Oceanic Sciences, Ocean University of Qingdao, Qingdao 266003

Abstract: In this paper, the nonlinear Kelvin wave equations with “positive-only” nonlinear (conditional) heating at the equator are reduced to a sixth-order nonlinear ordinary differential equation by using the Galerkin spectral truncated method. The stability analysis indicates that when the heating parameter increases, the supercritical pitchfork and Hopf bifurcations can occur for the prescribed three heating profiles. Numerical calculations are made with the help of the fourth-order Rung-Kutta method. It is found that the convec-tion heating-related Hopf bifurcation can lead to limit cycle and chaotic solutions. In a wide range of heat-ing parameter, the solutions possess 30-60-day periods, and are dominated by wavenumbers one and two, especially by wavenurnber-one. In addition, the zonal winds of the low-frequency solutions have a phase reversal between the upper and lower tropospheres. Thus, it appears that the convection heating-related Hopf bifurcation might be a possible mechanism of 30-60-day oscillation in the tropical atmosphere.

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