  We investigate the fixed points of a shell model for the turbulent advection
of passive scalars introduced Jensen, Paladin and Vulpiani. The passive scalar
field is driven by the velocity field of the popular GOY shell model. The
scaling behavior of the static solutions is found to differ significantly from
Obukhov-Corrsin scaling theta_n ~ k_n^(-1/3) which is only recovered in the
limit where the diffusivity vanishes, D -> 0. From the eigenvalue spectrum we
show that any perturbation in the scalar will always damp out, i.e. the
eigenvalues of the scalar are negative and are decoupled from the eigenvalues
of the velocity. Furthermore we estimate Lyapunov exponents and the
intermittency parameters using a definition proposed by Benzi et al. The full
model is as chaotic as the GOY model, measured by the maximal Lyapunov
exponent, but is more intermittent.
