Weakly nonlinear dynamics of short acoustic waves in exponentially stratified gas

Abstract

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.