Gravity wave propagation in a nonisothermal atmosphere with height varying background wind

Abstract

We derive a gravity wave propagation equation for a compressible and non-isothermal atmosphere with a variable background wind profile. Impact of all the gradient terms on the vertical wavenumber depends only on the intrinsic horizontal phase velocity and the background atmosphere. For the background wind variation, any one of the linear first order derivative, second order derivative and the square of the first order derivative terms can be the dominant term under different conditions. For temperature variation, only the linear first order derivative is important for waves having a slow intrinsic horizontal phase velocity. Our equation indicates that the effect of wind shear on the vertical wavenumber is opposite to that predicted by the Taylor-Goldstein equation, which assumes an incompressible fluid. We also derive an expression for the amplitude of the vertical wind perturbation. Copyright 2007 by the American Geophysical Union.