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Abstract We analyze the gravity waves (GWs) from the ground to the thermosphere during 11–14 January 2016 using the nudged HI Altitude Mechanistic general Circulation Model. We find that the entrance, core and exit regions of the polar vortex jet are important for generating primary GWs and amplifying GWs from below. These primary GWs dissipate in the upper stratosphere/lower mesosphere and deposit momentum there; the atmosphere responds by generating secondary GWs. This process is repeated, resulting in medium to large‐scale higher‐order, thermospheric GWs. We find that the amplitudes of the secondary/higher‐order GWs from sources below the polar vortex jet are exponentially magnified. The higher‐order, thermospheric GWs have concentric ring, arc‐like and planar structures, and spread out latitudinally to 10 − 90°N. Those GWs with the largest amplitudes propagate against the background wind. Some of the higher‐order GWs generated over Europe propagate over the Arctic region then southward over the US to ∼15–20°N daily at ∼14 − 24 UT (∼9 − 16 LT) due to the favorable background wind. These GWs have horizontal wavelengthsλ_H ∼ 200 − 2,200 km, horizontal phase speedsc_H ∼ 165 − 260 m/s, and periodsτ_r ∼ 0.3 − 2.4 hr. Such GWs could be misidentified as being generated by auroral activity. The large‐scale, higher‐order GWs are generated in the lower thermosphere and propagate southwestward daily across the northern mid‐thermosphere at ∼8–16 LT withλ_H ∼ 3,000 km andc_H ∼ 650 m/s. We compare the simulated GWs with those observed by AIRS, VIIRS/DNB, lidar and meteor radars and find reasonable to good agreement. Thus the polar vortex jet is important for facilitating the global generation of medium to large‐scale, higher‐order thermospheric GWs via multi‐step vertical coupling.