Fixed points, stability, and intermittency in a shell model for advection of passive scalars

We investigate the fixed points of a shell model for the turbulent advectio n of passive scalars introduced in Jensen, Paladin, and Vulpiani [Phys. Rev . A 45, 7214 (1992)]. The passive scalar field is driven by the velocity fi eld of the popular Gledzer-Ohkitani-Yamada (GOY) shell model. The sealing b ehavior of the static solutions is found to differ significantly from Obukh ov-Corrsin scaling theta(n)similar to k(n)(-1/3), which is only recovered i n the limit where the diffusivity vanishes, D-->0. From the eigenvalue spec trum 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 eig envalues of the velocity. We estimate Lyapunov exponents and the intermitte ncy parameters using a definition proposed by Benzi, Paladin, Parisi, and V ulpiani [J. Phys. A 18, 2157 (1985)]. The full model is found to be as chao tic as the GOY model, measured by the maximal Lyapunov exponent, but is mor e intermittent.