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On the development of Mach waves radiated by small disturbances

Published online by Cambridge University Press:  28 March 2006

J. E. Ffowcs Williams
J. E. Ffowcs Williams
Affiliation:
Bolt Beranek and Newman Inc., 50 Moulton Street, Cambridge, Massachusetts Now at Imperial College, University of London.
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Abstract

Mach wave radiation studies have, so far, been concentrated on the sound radiated to large distances from the flow. Then, both a turbulent eddy and the distance it may travel during its coherent life, appear small to the distant observer, so that the sound arrives from one direction. When that direction is the Mach angle, a Mach wave is heard. This paper deals with a different situation, where, although a turbulent eddy appears small, the distance it travels does not. Sound arriving at the observer then comes from different directions at different times in the eddy's life, so that Mach waves can only be radiated over a relatively small range, where the radiation angle corresponds to the Mach angle. In that range the far field equations no longer apply. It is shown that, whereas the distant field increases with the cube of convection Mach number, M, and inversely with the square of distance travelled, 1/r2, this particular near field is of a type where the mean square density, $\overline {\rho^2}$, has the proportionality $\overline {\rho^2} \sim \rho^{-2} {\frac {l^{3/2}}{r^{3/2}}}{\frac {M^{7/3}}{(M-1)^{1/2}}}$

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 22 , Issue 1 , May 1965 , pp. 49 - 55
Copyright
© 1965 Cambridge University Press

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References

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