= Linear-profile spherical blast wave
{title2=$\beta=(7-\gamma)/(\gamma+1)$}
The <similarity profiles> $U=2\xi/(\gamma+1)$, $D=(\gamma+1)\xi/(\gamma-1)$ and $P=2\xi^3/(\gamma+1)$ solve the spherical blast equations at the displayed ambient exponent. For $\gamma=5/3$, $\beta=2$ and $R^3=3Et^2/(2\pi C)$. The dimensional fields are $u=r/(2t)$, $\rho=8\pi C^2r/(3Et^2)$ and $p=2\pi C^2r^3/(9Et^4)$ for $0<r<R$. Their kinetic and internal <energies> are equal. Substituting these profiles into all three equations and the shock conditions verifies the solution.
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