Inverse-radius viscous disk similarity
= Inverse-radius viscous disk similarity
{title2=$g=C e^{-1/(\tau\sqrt x)}$}
For a <Keplerian accretion disk> with $\bar\nu\propto r^{5/2}$, dimensionless $g=\bar\nu\Sigma/(\bar\nu_0\Sigma_0)$ satisfies $g_\tau=4x^{5/2}g_{xx}+6x^{3/2}g_x$. In $y=x^{-1/2}$ this is $g_\tau=y g_{yy}$. The ansatz $g=G(y/\tau)$ gives $G=A+B e^{-y/\tau}$; finite disk <mass> selects $A=0$. Its nonzero profile has logarithmically infinite disk <angular momentum> on an infinite radial domain.