Compressible and anelastic governing-equation solution methods for thermospheric gravity waveswith realistic background parameters

Abstract A previously developed numerical-multilayer modeling approach for systems of governing equationsis extended so that unwanted terms can be removed from the dispersion-relation polynomialassociated with the system. The new approach is applied to linearized anelastic and compressiblesystems of governing equations for gravity waves including molecular viscosity and thermaldiffusion. The ability to remove unwanted terms from the dispersion-relation polynomialis crucial for solving the governing equations when realistic background parameters, such as horizontal velocity and temperature, with strong vertical gradients, are included. With the unwanted terms removed, previously studied dispersion-relation polynomials, for which methods for defining upgoing and downgoing vertical wavenumber rootsalready exist, are obtained. The new methods are applied to a comprehensive set of medium-scale time-wavepacketexamples, with realistic background parameters, lower boundary conditions at 30 km altitude, and modeled wavefields extending up to 500 km altitude. Result from the compressibleand anelastic model versions are compared, with compressible governing-equation solutionsunderstood as the more physically accurate of the two. The new methods provide significantlyless computationally expensive alternatives to nonlinear time-step methods, which makesthem useful for comprehensive studies of the behavior of viscous/diffusive gravity wavesand also for large studies of cases based on observational data.Additionally, they generalize previously existing Fourier methods that have been applied to inviscidproblems while providing a theoretical framework for the study of viscous/diffusive gravity waves.