  Supernova (SN) explosions can potentially affect the structure and evolution
of circumnuclear disks in active galactic nuclei (AGN). Some previous studies
have suggested that a relatively low rate of SN explosions can provide an
effective value of alpha viscosity between 0.1 and 1 in AGN accretion disks
within 1 pc scale. In order to test this possibility, we provide some analytic
scalings of the evolution of a SN remnant embedded in a differentially rotating
smooth disk. We calibrate our estimates using three-dimensional hydrodynamical
simulations where the gas is modeled as adiabatic with index $\gamma$. Our
simulations are suited to include the fact that a fraction of the momentum
injected by the SN escapes from the disk into the corona. Based on these
results, we calculate the contribution of SN explosions to the effective alpha
viscosity, denoted by $\alpha_{SNe}$, in a model AGN accretion disk, where
accretion is driven by the local viscosity $\alpha$. We find that for AGN
galaxies with a central black hole of $~ 10^8M_{\cdot}$ and a disk with
viscosity $\alpha=0.1$, the contribution of SN explosions may be as large as
$\alpha_{SNe} \simeq 0.02$, provided that $\alpha \gtrsim 1.1$. On the other
hand, in the momentum conservation limit, which is valid when the push by the
internal pressure of the SN remnant is negligible, we find $\alpha_SNe \lesssim
6\times10^{-4}$.
