NONLINEAR RESONANCE INTERACTIONS AND INDEX CYCLES IN THE ATMOSPHERE

Li Xianlang

doi:10.1007/BF02656750

Impact Factor: 5.8

Volume 5 Issue 3

Jul. 1988

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 1988 > 5(3): 253-264

NONLINEAR RESONANCE INTERACTIONS AND INDEX CYCLES IN THE ATMOSPHERE

Li Xianlang

1.
Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, U.S.A.

Li Xianlang

doi: 10.1007/BF02656750

Abstract
References
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Abstract:
A barotropic spectral model is used to study the planetary-scale motions of an atmosphere whose wave ensemble modes are externally driven. Pertubations are induced by a barotropic analogue of thermal driving and by Ekman friction, bottom topography, and the vanished internal dissipation. The use of complete spectral expansions without truncation leads to that the nonlinear coupling equations between the low-index mode and the high-index mode are obtained by means of the random phase approximation and the projec-tion operator techniques. The nonlinear coupling equations are entirely equivalent to the Volterra systems in ecology.In the phase-plane, the orbits of the nonlinear coupling equations are the family of closed curves, indicat-ing a bound, and periodic motion. The qualitative behaviors of low-index and high-index modes as functions of time picture the motion of atmospheric flows, with exchanges of energy between the low-index mode and the high-index mode by nonlinear resonance interaction. It is suggested that the phenomenon of blocking be exponentially grown of the low-index mode, the atmospheric motion then evolved to the high-index mode due to relaxation process. The results therefore lead to a plausible hypothesis concerning index cycles in the atmosphere discussed by Lorenz’s early works.
References

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Manuscript History

Manuscript received: 10 July 1988

Manuscript revised: 10 July 1988

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

NONLINEAR RESONANCE INTERACTIONS AND INDEX CYCLES IN THE ATMOSPHERE

Li Xianlang

1. Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, U.S.A.

Manuscript received: 1988-07-10
Manuscript revised: 1988-07-10

Abstract: A barotropic spectral model is used to study the planetary-scale motions of an atmosphere whose wave ensemble modes are externally driven. Pertubations are induced by a barotropic analogue of thermal driving and by Ekman friction, bottom topography, and the vanished internal dissipation. The use of complete spectral expansions without truncation leads to that the nonlinear coupling equations between the low-index mode and the high-index mode are obtained by means of the random phase approximation and the projec-tion operator techniques. The nonlinear coupling equations are entirely equivalent to the Volterra systems in ecology.In the phase-plane, the orbits of the nonlinear coupling equations are the family of closed curves, indicat-ing a bound, and periodic motion. The qualitative behaviors of low-index and high-index modes as functions of time picture the motion of atmospheric flows, with exchanges of energy between the low-index mode and the high-index mode by nonlinear resonance interaction. It is suggested that the phenomenon of blocking be exponentially grown of the low-index mode, the atmospheric motion then evolved to the high-index mode due to relaxation process. The results therefore lead to a plausible hypothesis concerning index cycles in the atmosphere discussed by Lorenz’s early works.