Open Access
March 2010 On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model
Boris Levant, Fabio Ramos, Edriss S. Titi
Commun. Math. Sci. 8(1): 277-293 (March 2010).


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.


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Boris Levant. Fabio Ramos. Edriss S. Titi. "On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model." Commun. Math. Sci. 8 (1) 277 - 293, March 2010.


Published: March 2010
First available in Project Euclid: 23 February 2010

zbMATH: 1188.35135
MathSciNet: MR2655910

Primary: 35Q30 , 35Q35 , 76F20 , 76F55

Keywords: dynamic models , Navier-Stokes equations , Navier-Stokes-Voight equations , Navier-Stokes-Voigt equations , regularization of the Navier-Stokes equations , Shell models , Turbulence models , viscoelastic models

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 1 • March 2010
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