A Model for the Interaction between 2-Day Waves and Moist Kelvin Waves*

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Abstract The eastward-propagating tropical low-frequency disturbances, such as the moist Kelvin waves or the Madden–Julian oscillation (MJO), are often observed to experience convective enhancement when meeting with the westward-propagating 2-day waves. A scale interaction (SI) model is built to understand the nature of the interaction between the 2-day waves and moist Kelvin waves or MJO. In this model, the convective complex of moist Kelvin waves modulates the strength and location of the 2-day waves, which feed back through the upscale eddy transfer. An ageostrophic model describing the 2-day waves is first solved, and the resultant westward-propagating, backward-tilted disturbances are consistent with the observed 2-day waves. An explicit representation of eddy momentum transfer (EMT), eddy heating transfer (EHT), and eddy moisture transfer (EQT) arising from the 2-day waves is then formulated. The SI model shows that the 2-day waves in front of moist Kelvin waves produce an EMT accelerating the low-frequency easterly in the lower troposphere, an EHT cooling down the middle troposphere, and an EQT moistening the middle troposphere. These three transfer terms have comparable magnitude. Although the negative EHT tends to damp the moist Kelvin waves, both the EMT and EQT provide instability sources for the moist Kelvin waves. The 2-day waves also slow down the moist Kelvin waves, mainly through the advective effects of the EMT. So the unstable moist Kelvin waves may exhibit convective enhancement when meeting with the 2-day waves. The theoretical results presented here point to the need to further observe the multiscale structures within the moist Kelvin waves and the MJO.