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The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid hasbeen recently proposed as a regularization of the 3D Navier-Stokes equationsfor the purpose of direct numerical simulations. In this work we investigateits statistical properties by employing phenomenological heuristic arguments,in combination with Sabra shell model simulations of the analogue of the NSVmodel. For large values of the regularizing parameter, compared to theKolmogorov length scale, simulations exhibit multiscaling inertial range, andthe dissipation range displaying low intermittency. These facts provideevidence that the NSV regularization may reduce the stiffness of directnumerical simulations of turbulent flows, with a small impact on the energycontaining scales.

On the Statistical Properties of the 3D Incompressible Navier-Stokes-Voigt Model