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.
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