A Dynamical mechanism for Selective Excitation of the Kelvin Mode at Timescale of 30–50 Days

P. Goswami CSIR Centre for Mathematical Modelling and Computer Simulation, NAL Belur Campus, Bangalore, India

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R. Koteswar Rao CSIR Centre for Mathematical Modelling and Computer Simulation, NAL Belur Campus, Bangalore, India

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Abstract

This work presents a dynamical mechanism for selective excitation of the equatorial Kelvin wave at timescale of 30–50 days. The setting is analytical: the basic idea involves modeling of an implicit scale interaction in the moist tropical atmosphere between large-scale flow and convection. The moist tropical atmosphere is modeled by shallow-water equations along with a time-dependent moisture equation. The internal heating is provided by precipitation, which is modeled as a relaxation process for the moisture variable with an appropriate timescale. This is unlike the usual approach adopted in earlier studies in which precipitation is parameterized through wave-CISK. Several new features emerge from the new formalism. In particular, the moist processes drive the Kelvin mode unstable. However, in sharp contrast to earlier results with similar linear models, the Kelvin mode in the present model has a maximally growing wave with period about 30–50 days. On the other hand, the high-frequency waves are damped. The associated wavelength for the maximally growing wave lies close to the planetary scale, as observed. The sensitivity of the results to various physical parameters is discussed to demonstrate that the appearance of a maximally growing Kelvin wave with a period in the range of 30–50 days is persistent over a wide range of parameters. The model also predicts a northward propagation of the maximally growing wave, with phase speed very close to the observed value. Finally, a simple dynamical picture is presented to account for the source of scale selection in the model.

Abstract

This work presents a dynamical mechanism for selective excitation of the equatorial Kelvin wave at timescale of 30–50 days. The setting is analytical: the basic idea involves modeling of an implicit scale interaction in the moist tropical atmosphere between large-scale flow and convection. The moist tropical atmosphere is modeled by shallow-water equations along with a time-dependent moisture equation. The internal heating is provided by precipitation, which is modeled as a relaxation process for the moisture variable with an appropriate timescale. This is unlike the usual approach adopted in earlier studies in which precipitation is parameterized through wave-CISK. Several new features emerge from the new formalism. In particular, the moist processes drive the Kelvin mode unstable. However, in sharp contrast to earlier results with similar linear models, the Kelvin mode in the present model has a maximally growing wave with period about 30–50 days. On the other hand, the high-frequency waves are damped. The associated wavelength for the maximally growing wave lies close to the planetary scale, as observed. The sensitivity of the results to various physical parameters is discussed to demonstrate that the appearance of a maximally growing Kelvin wave with a period in the range of 30–50 days is persistent over a wide range of parameters. The model also predicts a northward propagation of the maximally growing wave, with phase speed very close to the observed value. Finally, a simple dynamical picture is presented to account for the source of scale selection in the model.

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