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Shock formation in the presence of entropy gradients

Published online by Cambridge University Press:  22 June 2001

HAO LIN  and
ANDREW J. SZERI
HAO LIN
Affiliation:
Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1740, USA
ANDREW J. SZERI
Affiliation:
Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1740, USA
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Abstract

The steepening of a normal compression wave into a shock in a homentropic flow field is understood well through the method of characteristics. In a non-homentropic flow field, however, shock formation from a compression wave is more complex. The effects of entropy (or sound speed) gradients on shock formation from a compression wave are determined using a wave front expansion in Cartesian and in spherical polar coordinates. The latter problem has application to the intense energy focusing of sonoluminescence, particularly when applied to a spherically collapsing gas. The principal result is an analytical criterion for the time and place of shock formation, for a wave propagating into a field of smoothly varying entropy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 431 , 25 March 2001 , pp. 161 - 188
Copyright
© 2001 Cambridge University Press

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