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A transonic small-disturbance model for the propagation of weak shock waves in heterogeneous gases
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A transonic small-disturbance model for the propagation of weak shock waves in heterogeneous gases
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Journal Article
A transonic small-disturbance model for the propagation of weak shock waves in heterogeneous gases
2001
Overview
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).
Publisher
Cambridge University Press
