  The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid has
been recently proposed as a regularization of the 3D Navier-Stokes equations
for the purpose of direct numerical simulations. In this work we investigate
its statistical properties by employing phenomenological heuristic arguments,
in combination with Sabra shell model simulations of the analogue of the NSV
model. For large values of the regularizing parameter, compared to the
Kolmogorov length scale, simulations exhibit multiscaling inertial range, and
the dissipation range displaying low intermittency. These facts provide
evidence that the NSV regularization may reduce the stiffness of direct
numerical simulations of turbulent flows, with a small impact on the energy
containing scales.
