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Abstract Gravity waves dispersing upward through the tropical stratosphere during opposing phases of the QBO are investigated using ERA5 data for 1979–2019. Log–log plots of two-sided zonal wavenumber–frequency spectra of vertical velocity, and cospectra representing the vertical flux of zonal momentum in the tropical lower stratosphere, exhibit distinctive gravity wave signatures across space and time scales ranging over two orders of magnitude. Spectra of the vertical flux of momentum are indicative of a strong dissipation of westward-propagating gravity waves during the easterly phase and vice versa. This selective “wind filtering” of the waves as they disperse upward imprints the vertical structure of the zonal flow on the resolved wave spectra, characteristic of (re)analysis and/or free-running models. The three-dimensional structures of the gravity waves are documented in composites of the vertical velocity field relative to grid-resolved tropospheric downwelling events at individual reference grid points along the equator. In the absence of a background zonal flow, the waves radiate outward and upward from their respective reference grid points in concentric rings. When a zonal flow is present, the rings are displaced downstream relative to the source and they are amplified upstream of the source and attenuated downstream of it, such that instead of rings, they assume the form of arcs. The log–log spectral representation of wind filtering of equatorial waves by the zonal flow in this paper can be used to diagnose the performance of high-resolution models designed to simulate the circulation of the tropical stratosphere.