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

TL;DR

This paper investigates the statistical properties of the Navier-Stokes-Voigt model, showing it can reduce simulation stiffness in turbulent flows with minimal impact on large-scale dynamics.

Contribution

It combines heuristic analysis with shell model simulations to explore the NSV model's effects on turbulence statistics and regularization benefits.

Findings

Exhibits multiscaling inertial range at large regularization parameters

Displays low intermittency in the dissipation range

Potentially reduces stiffness in turbulent flow simulations

Abstract

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.