On the propagation of atmospheric gravity waves in a non-uniform wind field: Introducing a modified acoustic-gravity wave equation

Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth’s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without the use of the well-known Boussinesq approximation which have been used extensively in previous studies. We utilize the complete set of governing equations for a compressible atmosphere with nonuniform airflows to determine an equation for vertical velocity of possible atmospheric waves. This intricate wave equation is simplified by a proper substitution producing a useful new wavelike equation for acoustic-gravity waves. The substitution introduces a term Ω (intrinsic frequency) in the amplitude of the wave solution for the vertical velocity of acoustic-gravity waves. This term may play a significant role in directional filtering of atmospheric waves in realistic atmospheres exhibiting strong and highly variable winds. It is also proven that the only difference in the wave equation of compressible fluid when non-uniform wind is added to the equations of motion is the term with second derivative of lnΩ with respect to height. These new solutions may be particularly important for improved gravity wave propagation studies in the upper mesosphere and thermosphere/ionosphere regions.