Weakly nonlinear dynamics of short acoustic waves in exponentially stratified gas

The types of linear motion over an ideal gas affected by
gravity are specified approximately in the case of large characteristic wave
number of perturbation k: k[ampersand]gt;[ampersand]gt; 1/H, where H is the scale of density and
pressure decrease of the background gas, the so-called height of the uniform
gas. The corresponding approximate operators projecting the overall vector of
perturbations into specific types are derived, along with equations governing
sound in a weakly nonlinear flow. The validity of approximate formulae are
verified for the concrete examples of initial waveforms. The numerical analysis
reveals a good agreement of these approximate expressions with the exact ones
obtained previously by the author. The analysis applies to the weakly nonlinear
flow as well, with the small Mach numbers (M[ampersand]lt;[ampersand]lt;1). The links inside modes
are redetermined by including terms of order M2 and M2/kH.