  We perform direct numerical simulations of planar jets of non-Newtonian
fluids at low Reynolds number, in typical laminar conditions for a Newtonian
fluid. We select three different non-Newtonian fluid models characterized by
shear-thinning (Carreau), viscoelasticity (Oldroyd-B) and shear-thinning and
viscoelasticity together (Giesekus), and perform a thorough analysis of the
resulting flow statistics. We observe that, as the Weissenberg number is
increased, the jet transitions from a laminar flow at low Weissenberg number,
to a turbulent flow at high Weissenberg number. We show that the different
non-Newtonian features and their combination give rise to rather different
flowing regimes, originating from the competition of viscous, elastic and
inertial effects. We observe that both viscoelasticity and shear-thinning can
develop the instability and the consequent transition to a turbulent flowing
regime; however, the purely viscoelastic Oldroyd-B fluid exhibits the onset of
disordered fluid motions at a lower Weissenberg number than what observed for
the purely shear-thinning Carreau fluid. When the two effects are both present,
an intermediate condition is found, suggesting that, in this case, the
shear-thinning feature is acting against the fluid elasticity. Despite the
qualitative differences observed in the flowing regime, the bulk statistics,
namely the centerline velocity and jet thickness, follow almost the same
power-law scalings obtained for laminar and turbulent Newtonian planar jets.
