  We calculate static solutions of the 'GOY' shell model of turbulence and do a
linear stability analysis. The asymptotic limit of large Reynolds numbers is
analyzed. A phase diagram is presented which shows the range of stability of
the static solution. We see an unexpected oscillatory dependence of the
stability range upon $\lg \nu $, where $\nu$ is the viscosity. This effect
depends upon the discrete structure of the shell model and goes to zero as the
separation between the shells is brought to zero. These findings show how
viscous effects play a role in determining inertial properties of shell models
and give some hints for understanding the effects of viscous dissipation upon
real turbulence.
