  Shell models of turbulence have a finite-time blowup in the inviscid limit,
i.e., the enstrophy diverges while the single-shell velocities stay finite. The
signature of this blowup is represented by self-similar instantonic structures
traveling coherently through the inertial range. These solutions might
influence the energy transfer and the anomalous scaling properties empirically
observed for the forced and viscous models. In this paper we present a study of
the instantonic solutions for a set of four shell models of turbulence based on
the exact decomposition of the Navier-Stokes equations in helical eigenstates.
We find that depending on the helical structure of each model, instantons are
chaotic or regular. Some instantonic solutions tend to recover mirror symmetry
for scales small enough. Models that have anomalous scaling develop regular non
chaotic instantons. Conversely, models that have non anomalous scaling in the
stationary regime are those that have chaotic instantons. The direction of the
energy carried by each single instanton tends to coincide with the direction of
the energy cascade in the stationary regime. Finally, we find that whenever the
small-scale stationary statistics is intermittent, the instanton is less steep
than the dimensional Kolmogorov scaling, independently of whether or not it is
chaotic. Our findings further support the idea that instantons might be crucial
to describe some aspects of the multi-scale anomalous statistics of shell
models.
