  Nonlinear distortion of infrasonic waves through atmospheres up to
thermospheric altitudes govern large-range ground-level observations of
explosive noise sources, causing large differences between the near and far
field. Propagation modelling in this scenario to include realistic nonlinear
effects has thus far been limited to high-fidelity, numerically intensive
Direct Numerical Simulations of the Navier-Stokes equations, or nonlinear
parabolic equations with restrictions on the mean flow Mach number. For the
accurate modelling of nonlinear waveform synthesis through realistic
atmospheric winds up to thermospheric altitudes, this work presents nonlinear
wave equation analysis which results in in a Westervelt equation for weakly
stratified, arbitrary Mach number atmospheres. This is intended to be used as a
benchmark for model development and numerical analyses such that alternative
low-fidelity numerical calculations to Direct Numerical Simulations can be
sought.
