Shock Formation in Acoustic Gravity Waves

  1. C. O. Hines
  1. F. Einaudi

Published Online: 17 MAR 2013

DOI: 10.1029/GM018p0347

The Upper Atmosphere in Motion

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

Author Information

  1. Physics Department, University of Toronto, Toronto, Ontario, Canada

Publication History

  1. Published Online: 17 MAR 2013
  2. Published Print: 1 JAN 1974

ISBN Information

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.