Middle atmosphere dynamics with gravity wave interactions in the numerical spectral model: Tides and planetary waves

► Theoretical model simulates middle atmosphere tides, planetary waves (PW), 10-h oscillations. ► Model studies with parameterized gravity waves (GW) provide understanding of observed phenomena. ► GW interactions producing stratospheric QBO amplify mesospheric tides, PW, 10-h oscillations. ► GW filtering with amplification of tides and PW generate seasonal and inter-annual variations. ► GW generate non-migrating tides through nonlinear interaction between migrating tides and PW.