Hostname: page-component-54dcc4c588-2bdfx Total loading time: 0 Render date: 2025-09-28T14:21:29.118Z Has data issue: false hasContentIssue false
  • English
  • Français

Propagation of weakly nonlinear waves in stratified media having mixed nonlinearity

Published online by Cambridge University Press:  26 April 2006

A. Kluwick  and
E. A. Cox
A. Kluwick
Affiliation:
Institute of Fluid Dynamics and Heat Transfer, Technical University, Vienna
E. A. Cox
Affiliation:
Department of Mathematical Physics, University College Dublin, Dublin 4, Ireland
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of small-amplitude finite-rate waves in fluids having high specific heats is studied adopting the assumption that the unperturbed state varies in the propagation direction. It is shown that this not only leads to quantitative changes of the results holding for homogeneous media but also gives rise to new phenomena. Most interesting, shocks are found to terminate at a finite distance from the origin if the fundamental derivative changes sign along the propagation path.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 171 - 185
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bethe H. A. 1942 The theory of shock waves for an arbitrary equation of state. Office Sci. Res. Dev. Rep. 545.Google Scholar
Borisov A. A., Borisov Al. A., Kutateladze, S. S. & Nakorykov V. E. 1983 Rarefraction shock wave near the critical liquid-vapour point. J. Fluid Mech. 126, 59–73.Google Scholar
Bremmer H. 1951 The WKB approximation as the first term of a geometrical-optical series. Commun. Pure Appl. Maths 4, 105–115.Google Scholar
Cates, A. T. & Crighton D. G. 1990 Nonlinear diffraction and caustic formation Proc. R. Soc. Lond. A 430, 69–88.Google Scholar
Cramer M. S. 1991 Nonclassical dynamics of classical gases. In Nonlinear Waves in Real Fluids, (ed. A. Kluwick), pp. 91–145. Springer.
Cramer, M. S. & Kluwick A 1984 On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142, 9–37.Google Scholar
Gubkin K. E. 1958 Propagation of discontinuities in sound wave. Prikl. Matem. Mekhan. 22, 561–564.Google Scholar
Hayes W. D. 1960 Gasdynamic Discontinuities. Princeton Series on High Speed Aerodynamics and Jet Propulsion. Princeton University Press.
Hayes W. D., Haefeli, R. C. & Kulsrud H. E. 1969 Sonic boom propagation in a stratified atmosphere, with computer program. NASA CR-1299.Google Scholar
Kluwick A. & Czemetschka, E. 1990 Kugel und Zylinderwellen in Medien mit positiver und negativer Nichtlinearitaet. Z. Angew. Math. Mech. 70 (4), T207–T208Google Scholar
Kluwick, A. & Koller F. 1988 Ausbreitung periodischer Wellen kleiner Amplitude in Gasen mit grossen spezifischen Waermen. Z. Angew. Math. Mech. 68 (4), T306–T307.Google Scholar
Mortell, M. P. & Seymour B. R. 1976 Wave propagation in a nonlinear laminated material: A derivation of geometric acoustics. Q. J. Mech. Appl. Maths 29, 457–466.Google Scholar
Sen, R. & Cramer M. S. 1987 A general Scheme for the derivation of evolution describing mixed nonlinearity. VPI-E-87–16 Rep.
Thompson, P. A. & Lambrakis K. C. 1973 Negative shock waves. J. Fluid Mech. 60, 187–208.Google Scholar
Zabolotskaya, E. A. & Khokhlov R. V. 1969 Quasi-plane waves in the nonlinear acoustics of confined rays. Sov. Phys.-Acoust. 15, 35–40.Google Scholar
Zabolotskaya, E. A. & Khokhlov R. V. 1970 Convergent and divergent sound beams in nonlinear media. Sov. Phys.-Acoust. 16, 39–42.Google Scholar
Zel'dovich Ya. B. 1946 On the possibility of rarefraction shock waves. Zh. Eksp. Teor. Fiz. 4, 363–364.Google Scholar