In a paper published in Atmos. Chem. Phy. Andreas Dörnbrack and collaborators presented a case study of stratosphere-generated gravity waves during a minor sudden stratospheric warming (SSW) on on 30 January 2016.  They present a rich evidence for a stratospheric source of inertio-gravity waves. The MODES decomposition of the flow into a balanced component and inertia-gravity waves showed that coherent wave packets preferentially occurred at the inner edge of the Arctic polar vortex where a sub-vortex formed during the minor SSW. 

The full article: Atmos. Chem. Phys., 18, 12915-12931, 2018,  https://doi.org/10.5194/acp-18-12915-2018

Figure: Left panel shows a composite of the magnitude of inertio-gravity wind speed (colours, in m/s) obtained using MODES and the geopotential height (gpm, black contour lines) from the ECMWF operational analyses. Right panel shows a composite of the magnitude of the balanced wind (colours, in m/s) from MODES and horizontal wind divergence from ECMWF analyses (values larger or smaller than +/- 2e-4 s^-1 are filled with red and blue, respectively). The plots are at 1 hPa (~48 km) and they are valid at 06:00 UTC on 30 January 2016. This is Figure 4a,b from the paper.