  Helicity is the scalar product between velocity and vorticity and, just like
energy, its integral is an in-viscid invariant of the three-dimensional
incompressible Navier-Stokes equations. However, space-and time-discretization
methods typically corrupt this property, leading to violation of the inviscid
conservation principles. This work investigates the discrete helicity
conservation properties of spectral and finite-differencing methods, in
relation to the form employed for the convective term. Effects due to
Runge-Kutta time-advancement schemes are also taken into consideration in the
analysis. The theoretical results are proved against inviscid numerical
simulations, while a scale-dependent analysis of energy, helicity and their
non-linear transfers is performed to further characterize the discretization
errors of the different forms in forced helical turbulence simulations.
