Conditional stability of shock waves—a criterion for detonation

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Abstract
The stability of plane shock waves is treated by examining the amplitudes of acoustic waves reflected from shock fronts, and by methods of irreversible thermodynamics. Both approaches yield the same conditions for stability, −1⩽j 2(d V/d P) H ⩽1, where j 2 is the negative slope of the Rayleigh line, and the derivative is taken along the Hugoniot P‐V curve. The thermodynamic method indicates that instabilities are associated either with local maxima in the entropy, or shock velocity; or with local minima in the reduced internal energy, or particle velocity, along the Hugoniot curve. It is proposed that the latter case corresponds to detonation with the detonation state given by the particle velocity minimum.

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