Compatibility Conditions, Complex Frequency, and Complex Vertical Wave Number for Models of Gravity Waves in the Thermosphere

TL;DR: In this paper , a general method for computing solutions of systems of linear gravity-wave governing equations, allowing for vertically varying background parameters, is introduced and applied to two sets of governing equations for gravity waves in the thermosphere, both of which include molecular viscosity and thermal diffusion.

TL;DR: A numerical approach is developed to solve thermospheric gravity wave governing equations with realistic background parameters, enabling efficient computation of wave behavior with molecular viscosity and thermal diffusion, and providing a framework for studying viscous/diffusive gravity waves.

TL;DR: The new numerical-multilayer modeling approach removes unwanted terms from the dispersion-relation polynomial associated with the system of governing equations for thermospheric gravity waves, enabling the use of realistic background parameters with strong vertical gradients.

TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.

TL;DR: NRLMSISE‐00 empirical model of the atmosphere extends from the ground to the exobase and includes new data sets on total mass density, temperature, and molecular oxygen number density. The model includes a new component for anomalous oxygen and extensive comparisons with other models and data sets are provided.

Abstract: This book gives a self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations. Parts and chapter titles are as follows: fundamentals - ordinary differential equations, difference equations; local analysis - approximate solution of linear differential equations, approximate solution of nonlinear differential equations, approximate solution of difference equations, asymptotic expansion of integrals; perturbation methods - perturbation series, summation series; and global analysis - boundary layer theory, WKB theory, multiple-scale analysis. An appendix of useful formulas is included. 147 figures, 43 tables. (RWR)

TL;DR: In this article, a review of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape are discussed.