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Internal gravity waves (GWs) in the atmosphere play a major role in the global circulation of the middle atmosphere (10-100 km height). The mean-flow effects of GWs consist of 1) the momentum deposition (corrected by the Stokes drift of the GWs), 2) the energy deposition (corresponding to the sum of mechanical and thermal dissipation), and 3) the convergence of the GW heat flux. This set of mean-flow effect is obtained from the anelastic equations with sensible heat as prognostic thermodynamc variable. Furthermore, we have to assume the Boussinesq limit for the waves, which means that the vertical wavelength, λz , is assumed to be small against 4π H, where H is the scale height. We show that these anelastic equations yield the usual dispersion and polarization relations for GWs. According to current wisdom, however, these solutions include the case λz ∼ 4π H. New linear theory for by Vadas (2013, J. Geophys. Res.) yields different polarization relations, but confirms the usual dispersion relation. The likely reason for different linear solutions in the case of λz ∼ 4π H is that usual linear theory starts out from the fully compressible equations, and the anelastic limit is calculated separately for the dispersion and polarization relations. In this contribution we present a set of anelastic equations where the Boussinesp limit for perturbations from the reference state is relaxed. We recover the more recent polarization relations for GWs, but obtain a different dispersion relation in the case of λz ∼ 4π H. The mean flow effects from GWs are consistently simulated in a high-resolution circulation model, provided the model is based on the compressible equations and includes a hydrodynamically diffusion schemes. However, a consistent theoretical approach for the mean-flow effects of GWs having large λz is not yet available. According to theory and high-resolution modeling, such GWs occur frequently in the thermosphere.