Kelvin Wave-CISK: A Possible Mechanism for the 30–50 Day Oscillations

C-P. Chang Department of Meteorology, Naval Postgraduate School, Monterey, California

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H. Lim Department of Physics, National University of Singapore, Singapore

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Abstract

Two categories of theories have been proposed to explain the observed tropical intraseasonal oscillations whose main periodicity is between 30–50 days: (i) those based on eastward propagating Kelvin waves maintained by cumulus heating; and (ii) those based on interactions with stationary oscillations of the basic state. Recent numerical modeling studies have simulated certain important aspects of the oscillation particularly the slower propagation speed as compared with the normal Kelvin waves. Motivated by these results which lend support to the first category, a linear theoretical analysis of the equatorial β-plane wave-CISK was carried out with a focus on the Kelvin modes.

Our results show that two types of CISK modes may arise from an interaction of vertical modes. For heating with a maximum in the lower troposphere, the instability is due to the lowest internal mode which gives a stationary, east-west symmetrical structure. When heating is maximum in the midtroposphere, eastward propagating CISK modes resembling the observed and numerically-simulated oscillations occur. These modes result from the interaction between two internal modes which are locked in-phase vertically. A time-lagged CISK analysis suggests that the shallower mode, with its stronger influence on the low-level moisture convergence, slows down the deeper mode resulting in a combined mode which has a deep vertical structure with a relatively slow propagating speed. This slower phase speed may also be understood from the consideration of two effects: a CISK growth effect which is analogous to a viscous effect, and the reduction in effective static stability. A single mode analysis also suggests that the Rossby modes are less likely to become unstable. The results further imply that, in the absence of wave-CISK, the observed oscillation cannot be excited by stationary oscillations.

Abstract

Two categories of theories have been proposed to explain the observed tropical intraseasonal oscillations whose main periodicity is between 30–50 days: (i) those based on eastward propagating Kelvin waves maintained by cumulus heating; and (ii) those based on interactions with stationary oscillations of the basic state. Recent numerical modeling studies have simulated certain important aspects of the oscillation particularly the slower propagation speed as compared with the normal Kelvin waves. Motivated by these results which lend support to the first category, a linear theoretical analysis of the equatorial β-plane wave-CISK was carried out with a focus on the Kelvin modes.

Our results show that two types of CISK modes may arise from an interaction of vertical modes. For heating with a maximum in the lower troposphere, the instability is due to the lowest internal mode which gives a stationary, east-west symmetrical structure. When heating is maximum in the midtroposphere, eastward propagating CISK modes resembling the observed and numerically-simulated oscillations occur. These modes result from the interaction between two internal modes which are locked in-phase vertically. A time-lagged CISK analysis suggests that the shallower mode, with its stronger influence on the low-level moisture convergence, slows down the deeper mode resulting in a combined mode which has a deep vertical structure with a relatively slow propagating speed. This slower phase speed may also be understood from the consideration of two effects: a CISK growth effect which is analogous to a viscous effect, and the reduction in effective static stability. A single mode analysis also suggests that the Rossby modes are less likely to become unstable. The results further imply that, in the absence of wave-CISK, the observed oscillation cannot be excited by stationary oscillations.

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