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Abstract A 2D nonlinear, compressible model is used to simulate the acoustic‐gravity wave (AGW, i.e., encompassing the spectrum of acoustic and gravity waves) response to a thunderstorm squall‐line type source. We investigate the primary and secondary neutral AGW response in the thermosphere, consistent with waves that can couple to the F‐region ionospheric plasma, and manifest as Traveling Ionospheric Disturbances (TIDs). We find that primary waves atz = 240 km altitude have wavelengths and phase speeds in the range 170–270 km, and 180–320 m/s, respectively. The secondary waves generated have wavelengths ranging from ∼100 to 600 km, and phase speeds from 300 to 630 m/s. While there is overlap in the wave spectra, we find that the secondary waves (i.e., those that have been nonlinearly transformed or generated secondarily/subsequently from the primary wave) generally have faster phases than the primary waves. We also assess the notion that waves with fast phase speeds (that exceed proposed theoretical upper limits on passing from the mesosphere to thermosphere) observed at F‐region heights must be secondary waves, for example, those generated in situ by wave breaking in the lower thermosphere, rather than directly propagating primary waves from their sources. We find that primary waves with phase speeds greater than this proposed upper limit can tunnel through a deep portion of the lower/middle atmosphere and emerge as propagating waves in the thermosphere. Therefore, comparing a TID's/GWs phase speed with this upper limit is not a robust method of identifying whether an observed TID originates from a primary versus secondary AGW.