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The Taylor internal structure of weak shock waves

Published online by Cambridge University Press:  21 April 2006

D. G. Crighton
D. G. Crighton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

G. I. Taylor's solution in 1910 for the interior structure of a weak shock wave is, with appropriate generalization, an essential component of weak-shock theory. The Taylor balance between nonlinear convection and thermoviscous diffusion is, however, endangered when other linear mechanisms - such as density stratification, geometrical spreading effects, tube wall attenuation and dispersion, etc. - are included. The ways in which some of these linear mechanisms cause the Taylor shock structure to break down when a weak shock has propagated over a large (and in some cases quite moderate) distance will be studied. Different forms of breakdown of the Taylor shock structure will be identified, both for quadratic (gasdynamic) nonlinearity and also for cubic nonlinearity appropriate to transverse waves in solid media or electromagnetic waves in nonlinear dielectrics. From this a description will be given of the fate of a nonlinear wave containing a pattern of weak shock waves, as it propagates over large ranges under the influence of linear and nonlinear mechanisms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 173 , December 1986 , pp. 625 - 642
Copyright
© 1986 Cambridge University Press

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