A model study is presented to clarify the relationship between gravity-wave properties observed in the stratosphere and the sources for the waves, presumed to be in the troposphere. The observations are balloon-borne radiosondes launched from Cocos Island in the tropical Indian Ocean (12 ¿S, 97 ¿E), and the analysis of these data is described in a companion paper <Vincent and Alexander, this issue>. The dominant time variations in the observed gravity wave activity are annual and quasi-biennial patterns in the zonal momentum flux and kinetic energy density. The background zonal winds at this site vary with the same periods, and these are known to be capable of causing dramatic variations in the observable properties of the waves even if the sources for the waves are constant in time. The results presented here clarify (1) the nature of the sources for the gravity waves observed in the stratosphere, (2) the limitations of the observations for observing the full range of gravity wave perturbations potentially present in the atmosphere, and (3) the role the observed waves can play in forcing the quasibiennial oscillation (QBO) in the zonal winds at this latitude. The stratospheric waves appear to originate near the height of the tropopause, so the source is apparently related to deep convection. No seasonal or interannual variations in the convection need be assumed to understand the observations. The waves at the tropopause appear to have a phase speed distribution that is narrowly confined near zero phase speed relative to the ground. The source is likely related to slowly propagating tropospheric convection and the wind near the tropopause. Variations observed in the stratospheric data are caused by both the wind shear in the stratosphere and the ability of waves with these characteristics to propagate vertically without severe dissipation. Higher phase speed waves may be present and could carry significant momentum flux vertically into the stratosphere and mesosphere but would be extremely difficult to see in these radiosonde data. The observed waves can contribute substantially to the descent of the eastward shear zones characteristic of the westerly phase of the QBO in the lower stratosphere zonal winds.