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On the possibility of turbulent thickening of weak shock waves

Published online by Cambridge University Press:  29 March 2006

J. E. Ffowcs Williams  and
M. S. Howe
J. E. Ffowcs Williams
Affiliation:
Engineering Department, University of Cambridge
M. S. Howe
Affiliation:
Engineering Department, University of Cambridge
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Abstract

This paper examines the possible thickening of an initially sharp sonic boom by the turbulence it encounters in passing to the ground. Three apparently different viewpoints, all indicating substantial thickening, are shown to be actually identical and to give an irrelevant upper bound on wave thickness. All three approaches describe only the apparent mean diffusion induced by random convection of a sharp wave about its nominal position. Although a wave-front folding mechanism ultimately accounts for an apparent thickening as individual rays are weakened and tangled by turbulence, this process is too slow to be effective in the practical boom situation. The paper then considers what linear thickening of a wave packet results from propagation trough atmospheric turbulence and concludes that, in the relevant limit, a wave may be thickened by a factor of about 2 at the most. The conclusion is therefore reached that atmospheric turbulence cannot be the cause of the thousandfold discrepancy between the measured wave fronts and their Taylor thickness.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 3 , 8 May 1973 , pp. 461 - 480
Copyright
© 1973 Cambridge University Press

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bradshaw, P., Ferris, D. H. & Atwell, N. P. 1967 J. Fluid Mech. 28, 593–616.
Corrsin, S. & Karweit, M. J. 1972 J. Fluid Mech. 55, 289–300.
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics. Interscience.
Crow, S. C. 1969 J. Fluid Mech. 37, 529–563.
Hodgson, J. P. 1972 Vibrational relaxa.tion effects in weak shock waves in air and the structure of sonic bangs. Aero. Res. Coulzc. Rep. no. 34, p. 120.
Hodgson, J. P. & Johannegen, N. H. 1971 J. Fluid Mech. 50, 17–20.
Howe, M. S. 1971a J. Fluid Mech. 45, 769–783.
Howe, M. S. 1971b J. Fluid Mech. 45, 785–804.
Howe, M. S. 1973 Multiple scattering of sound by turbulence and other inhomogeneities. J. Sound & Vibratwn, 27 (in press).Google Scholar
Lighthill, M. J. 1952 Proc. Roy. Soc. A 211, 564–587.
Lighthill, M. J. 1953 Proc. Camb. Phil. Soc. 49, 531–551.
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. In Surveys in Mechanics (ed. Batchelor & Davies), p. 250. Cambridge University Press.
Lumley, J. L. & Panofsky, H. A. 1964 The Structure of Atmospheric Turbulence. Interscience.
Pierce, A. D. 1971 J. Acoust. Soc. Am. 49, 906–924.
Plotkin, J. & George, A. R. 1972 J. Fluid Mech. 54, 449–467.
Rice, C. G. 1972 Startle due to sonic boom. I.S.V.R. Southampton Rep. (March 1972).
Rice, C. G. & Lilley, G. M. 1969 Rep. on the Sonic Boom Preparedfor the O.E.C.D. Conf, on Sonic Boom Res. 20-2-1 October, 1969, part 4.
Sheih, C. M., Tennekes, H. & Lumley, J. L. 1971 Phys. Pluids, 14, 201–216.
Tatarski, V. I. 1961 Wave Propugatwn in a Turbulent Medium. McGraw-Hill.
Whitfiam, G. B. 1956 J. Fluid Mech. 1, 290–318.