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

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

2009-01-05

arxiv.org/abs/0901.0474v1

Physics

Fluid Dynamics

24 pages, 7 figures, In honor of Professor Andrew Majda in his 60th birthday

Scientific paper

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.

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