Nonlinear progressive wave equation for stratified atmospheres

• Published in: The Journal of the Acoustical Society of America Vol. 130; no. 5; p. 2648
• Main Authors: Edward McDonald, B, Piacsek, Andrew A
• Format: Journal Article
• Language: English
• Published: United States 01.11.2011
• Subjects: Acoustics; Atmosphere; Atmospheric Pressure; Computer Simulation; Mathematical Computing; Nonlinear Dynamics; Sound; Temperature; Time Factors
• DOI: 10.1121/1.3641403

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.