On the gas dynamics of an intense explosion with an expanding contact surface

The structure of a strong blast wave under the influence of an expanding inner contact surface is studied asymptotically in the Newtonian limit: $\epsilon \equiv (\gamma - 1)/2\gamma \ll 1, \epsilon \dot{y}^2_s \gg a^2_{\infty}$. The theory treats the interaction of a shock layer and an inner flow region (the entropy wake) and reduces the problem to an ordinary differential equation for the shock radius. The pressure–volume relation of Cheng et al. (1961) is recovered and extended to a higher order of ε.It is shown that, depending on the rate of growth of the contact surface, the shock layer may ‘reattach’ to the surface at large time. In a number of cases, the reattachment is approached in an oscillatory manner which leads to a period of non-uniformity. The associated problem of multiple time scales (treated in sequels to this paper) is identified.