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The nonlinear progressive wave equation (NPE) [McDonald and Kuperman, J. Acoust. Soc. Am. 81, 1406–1417 (1987)] is expressed in a form to accommodate changes in the ambient atmospheric density, pressure, and sound speed as the time-stepping computational window moves along a path possibly traversing significant altitude differences (in pressure scale heights). The modification is accomplished by the addition of a stratification term related to that derived in the 1970s for linear range-stepping calculations and later adopted into Khokhlov-Zabolotskaya-Kuznetsov-type nonlinear models. The modified NPE is shown to preserve acoustic energy in a ray tube and yields analytic similarity solutions for vertically propagating N waves in isothermal and thermally stratified atmospheres.


Copyright 2011 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in The Journal of the Acoustical Society of America 130, 2648 (2011), and may be found here.


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© 2011 Acoustical Society of America