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We analyzed the characteristics of small-scale wave disturbances emerging during the evolution and transformation of the jet stream (JS) in the winter stratosphere and the lower mesosphere of the northern hemisphere, including the periods of sudden stratospheric warming (SSW) events. Continuous generation of small-scale wave disturbances is shown to occur over quiet geomagnetic winter periods in the region of a steady jet stream in the strato–mesosphere. We studied spatial spectra for the vertical velocity variations, determined by the parameters of emerging wave disturbances. The greatest intensities of disturbances are recorded in the regions corresponding to the high velocities of the JS (from 100 m/s and higher). In the northern hemisphere, those latitudes encompass ~40–60° N. When a steady jet stream forms, the horizontal length and periods of the most intensive wavelike disturbances are shown to vary within 300–1000 km and 50–150 min correspondingly (which match the characteristic scales of internal gravity waves, or IGWs). During the SSW prewarming stage, the JS transforms substantially. Over the same periods, a disturbance intensification is recorded, as well as the emergence of larger-scale disturbances with 3000–5000-km horizontal wavelengths, and even higher. After the SSW peak and during the stratosphere circulation recovery, the velocity in the JS substantially decreases and an essential reduction in wave-disturbance generation occurs. There are decreases in the average amplitude values (by factors of 1.8–6.7). The strongest amplitude drop was observed for short waves (zonal wavelength λU = 300 km). The maximum attenuation for all wavelengths was observed for the strongest 2008/2009 winter SSW. For the analyzed events, such attenuation was observed for up to about a month after the SSW peak. Thus, JS disruption during major SSWs leads to deactivating the source for generating small-scale wave disturbances in the stratosphere. This may affect disturbances in higher atmospheric layers. The results obtained are the experimental evidence that JS itself is the primary source for the generation of IGWs in the stratosphere–lower mesosphere.