Acoustic-gravity waves detected by the Jicamarca VHF radar at tropospheric and stratospheric heights have properties that cannot be explained by simple theoretical models. The sign of the vertical wavenumber, in particular, reverses in a region with considerable background wind shear indicating wave-wind interaction in a critical layer. A model is analyzed in which a gravity wave propagates into a critical layer with small Richardson number so that near total reflection and strong transmission take place due to the extraction of momentum and energy from the mean flow. Solutions of the linearized hydrodynamic equations describing gravity wave propagation in a viscid compressible atmosphere with shear flow show that this model is consistent with the observed data.