Blast wave

A blast wave is the expanding disturbance produced by localized rapid release of energy, initially led by a strong shock wave. An energy-conserving self-similar blast wave ties front speed to the mass swept up. Once the front is only weakly supersonic, a strong-shock approximation ceases to apply; a subsequent acoustic wave is not excluded by that transition.

For an explosion confined approximately to a thin atmospheric layer with column mass density $\Sigma =\int \rho dz$, an optimistic conserved-energy scaling is $E\sim \pi D^2\Sigma U^2$. The strong blast wave approximation becomes invalid near front speed $U\sim c_a$, where $c_a$ is the ambient speed of sound, giving the displayed distance scale. Its numerical coefficient depends on the flow profiles, geometry and heat capacity ratio. Vertical energy escape makes full confinement an optimistic approximation. The criterion estimates survival of a strong shock wave, rather than whether any later acoustic wave is detectable.