  Non-positive definite, global inviscid invariants similar to helicity are
discussed for two types of shell models and evidence for a new role for
helicity in Navier-Stokes turbulence is presented. It is suggested that the
extra invariants play the role of triggering the intermittent cascade of energy
to small scales characterized by pulses. These invariants also determine where
a transition to chaos appears. New analysis of numerical experiments with
existing models is suggested and a new class of shell-models where the
dynamical interactions of a second quadratic invariant are closer to those of
helicity in the Navier-Stokes equations is introduced. The place of the popular
GOY model within this class is discussed.
