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A transonic small-disturbance model for the propagation of weak shock waves in heterogeneous gases

Published online by Cambridge University Press:  06 March 2001

THOMAS E. GIDDINGS ,
ZVI RUSAK  and
JACOB FISH
THOMAS E. GIDDINGS
Affiliation:
Metron Inc., 11911 Freedom Dr., Suite 800, Reston, VA 20190-5602, USA
ZVI RUSAK
Affiliation:
Department of Mechanical Engineering, Aeronautical Engineering, and Mechanics, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590, USA
JACOB FISH
Affiliation:
Department of Civil Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590, USA
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Abstract

The interaction of weak shock waves with small heterogeneities in gaseous media is studied. It is first shown that various linear theories proposed for this problem lead to pathological breakdowns or singularities in the solution near the wavefront and necessarily fail to describe this interaction. Then, a nonlinear small-disturbance model is developed. The nonlinear theory is uniformly valid and accounts for the competition between the near-sonic speed of the wavefront and the small variations of vorticity and sound speed in the heterogeneous media. This model is an extension of the transonic small-disturbance problem, with additional terms accounting for slight variations in the media. The model is used to analyse the propagation of the sonic-boom shock wave through the turbulent atmospheric boundary layer. It is found that, in this instance, the nonlinear model accounts for the observed behaviour. Various deterministic examples of interaction phenomena demonstrate good agreement with available experimental data and explain the main observed phenomena in Crow (1969).

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 429 , 25 February 2001 , pp. 255 - 280
Copyright
© 2001 Cambridge University Press

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