Viscous Internal Gravity Waves and Low–Frequency Oscillations in the Tropics

Abstract

In this paper we deal with the interpretation of observed oscillations in the tropical troposphere and stratosphere within the framework of the equatorial wave theory. A difficulty with this problem arises when one compares the short vertical wavelength (or equivalent depth) predicted by the classical theory and the observed large vertical scales associated with the low Doppler-shifted frequencies of the tropospheric oscillations. In this analysis it is shown that the inclusion of simple linear damping, justified by budget studies which revealed the important role of cumulus momentum transport, has a strong influence at low frequencies on the forced equatorial waves and results in two types of dispersive relationships. The first type is characteristic of the regular internal gravity waves which have fast phase speeds and weak vertical attenuation. The second type is dominated by the viscous damping time scale and has slow phase speeds and strong vertical trapping. The theory predicts that the stratosphere oscillations may be identified with the first type and the tropospheric oscillations with the second. In the case of Kelvin waves the results can be used to explain consistently both the observed stratospheric Kelvin waves and the planetary-scale Kelvin-like oscillations in the troposphere including the 40–50 day oscillation and the monsoon and Walker circulations. Possible implications with respect to other waves in the tropics are also discussed.