A numerical model characterizing internal gravity wave propagation into the upper atmosphere

A new two-dimensional, time-dependent and fully nonlinear model is developed to numerically simulate plane wave motions for internal gravity waves in a non-isothermal and windy atmosphere that accounts for the dissipation due to eddy and molecular processes. The atmosphere has been treated as a well mixed total gas with a constant mean molecular weight. The effects of Rayleigh friction and Newtonian cooling are applied near the upper boundary of the model to simulate the radiation conditions as well as to act as a sponge layer; lateral boundaries are periodic over a horizontal wavelength to simulate a horizontally infinite domain. The thermal excitation to initiate upward propagating waves is spatially localized in the troposphere and is a Gaussian function of time. A time-splitting technique is applied to the finite difference equations that are derived from the Navier–Stokes equations. The time integration for these highly coupled equations is performed using an explicit second order Lax–Wendroff scheme and an implicit Newton–Raphson scheme. The wave solutions derived from the model are found to be broadly agreeable with those derived from a Wentzel–Kramers–Brillouin theory.