Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T03:40:24.824Z Has data issue: false hasContentIssue false
  • English
  • Français

On blast waves in exponential atmospheres

Published online by Cambridge University Press:  29 March 2006

G. G. Bach ,
A. L. Kuhl  and
A. K. Oppenheim
G. G. Bach
Affiliation:
University of California, Berkeley
A. L. Kuhl
Affiliation:
University of California, Berkeley
A. K. Oppenheim
Affiliation:
University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper presents a comprehensive analysis of gas motion created by a strong explosion in an atmosphere whose density is an exponential function of altitude. For the near field (i.e. short times after initiation), an exact analytical solution of the equations of motion is obtained by means of a perturbation technique. For the far field (i.e. long times after initiation), a similarity solution associated with a logarithmic front trajectory is derived. The two are shown to be well matched with each other. Finally, a fully-algebraic approximate solution is given that qualitatively reproduces all the salient features of the exact and asymptotic solutions, while quantitatively it is in fair agreement with their results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 1 , 9 September 1975 , pp. 105 - 122
Copyright
© 1975 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.)

References

Andriankin, E. I., Kogan, A. M., Kompaneets, A. S. & Krainov, V. P. 1962 The propagation of a strong explosion in a non-homogeneous atmosphere. Zh. Prikl. Mekl. Tekl. Fiz. 6, 3.Google Scholar
Bach, G. G. & Lee, J. H. 1969 Initial propagation of impulsively-generated converging cylindrical and spherical shock waves. J. Fluid Mech. 37, 513.Google Scholar
Brinkley, S. R. & Kirkwood, J. G. 1947 Theory of the propagation of shock waves. Phys. Rev. 71, 606.Google Scholar
Hayes, W. D. 1968a Self-similar strong shocks in an exponential medium. J. Fluid Mech. 32, 305.Google Scholar
Hayes, W. D. 1968b The propagation upwaid of a shock wave from a strong explosion in the atmosphere. J. Fluid Mech. 32, 317.Google Scholar
Kompaneets, A. S. 1960 A point explosion in an inhomogeneous atmosphere. Soviet Phys. Doklady, 5, 46.Google Scholar
Laumbach, D. D. & Probstein, R. F. 1969 A point explosion in a cold exponential atmosphere. J. Fluid Mech. 35, 53.Google Scholar
Lutzky, M. & Lehto, D. L. 1968 Shock propagation in spherically symmetric exponential atmospheres. Phys. Fluids, 11, 1466.Google Scholar
Oppenheim, A. K., Kuhl, A. L., Lundstrom, E. A. & Kamel, M. M. 1972 A parametric study of self-similar blast waves. J. Fluid Mech. 52, 657.Google Scholar
Oppenheim, A. K., Lundstrom, E. A., Kuhl, A. L. & Kamel, M. M. 1972 A systematic exposition of the conservation equations for blast waves. J. Appl. Mech. p. 783.Google Scholar
Raizer, Yu. P. 1964a Motion produced in an inhomogeneous atmosphere by a plane shock of short duration. Soviet Phys. Doklady, 8, 1056.Google Scholar
Raizer, Yu. P. 1964b The propagation of a shock wave in a non-homogeneous atmosphere in the direction of decreasing density. Zh. Prikl. Mekl. Tekl. Fiz. 4, 49.Google Scholar
Sachdev, P. L. 1972 Propagation of a blast wave in uniform or non-uniform media: a uniformly valid analytic solution. J. Fluid Mech. 52, 369.Google Scholar
Sakurai, A. 1953 On the propagation and structure of blast waves. J. Phys. Soc. Japan, 8, 662.Google Scholar
Sedov, L. 1957 Similarity and Dimensional Methods in Mechanics (4th edn). Academic.
Taylor, G. I. 1950 The formation of a blast wave by a very intense explosion. Proc. Roy. Soc. A 201, 159.Google Scholar
Zel'Dovich, Ya. B. & Raizer, Yu. P. 1967 Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, vol. 2. Academic.