Adiabatic superbubble similarity solution
= Adiabatic superbubble similarity solution
{title2=$R=\alpha(\dot E/\rho_1)^{1/5}t^{3/5}$}
For constant injected power $\dot E$ and ambient <mass density> $\rho_1$, <dimensional analysis> gives $R=\alpha(\dot E/\rho_1)^{1/5}t^{3/5}$. In a <similarity solution>, set $\eta=r/R$, $\rho=\rho_1f(\eta)$, $p=\rho_1\dot R^2g(\eta)$ and $u=\dot Rh(\eta)$. The strong-shock values on the inner side of $\eta=1$ are $f=(\gamma+1)/(\gamma-1)$ and $g=h=2/(\gamma+1)$.