Shock Formation in Acoustic Gravity Waves
Published Online: 17 MAR 2013
Copyright © 1974 by the American Geophysical Union.
The Upper Atmosphere in Motion
How to Cite
Hines, C. O. (1974) Shock Formation in Acoustic Gravity Waves, in The Upper Atmosphere in Motion, American Geophysical Union, Washington, D. C.. doi: 10.1029/GM018p0347
- Published Online: 17 MAR 2013
- Published Print: 1 JAN 1974
Print ISBN: 9780875900186
Online ISBN: 9781118663578
- Atmosphere, Upper—Addresses, essays, lectures;
- Dynamic meteorology—Addresses, essays, lectures
A new approximate solution for the propagation of acoustic gravity waves is presented. Not only the dependent variables, but also the independent ones are expanded in the form of asymptotic series, the terms of which can be found by an iterative procedure. An ordinary parameter ∊ is introduced, which is proportional to, say, the initial amplitude of the velocity perturbation. The expansion of the independent variables enables us to correct, at each stage of the expansion, the forward characteristic surfaces of the governing equations and in turn to determine the crossing of adjacent characteristics. The formation of shocks is discussed, and a comparison with the usual linear theory is given for certain values of ω and k.