Communications in Mathematical Sciences

Volume 8 (2010)

Number 1

Special Issue on the Occasion of Andrew Majda’s Sixtieth Birthday: Part I

On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model

Pages: 277 – 293



Boris Levant

Fabio Ramos

Edriss S. Titi


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 phenomeno- logical 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 inter- mittency. 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.


Navier-Stokes-Voigt equations; Navier-Stokes-Voight equations; Navier-Stokes equations; regularization of the Navier-Stokes equations; turbulence models; viscoelastic models; shell models; dynamic models

2010 Mathematics Subject Classification

35Q30, 35Q35, 76F20, 76F55

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