Impact of the inherent separation of scales in the Navier–Stokes- αβ equations

We study the effect of the length scales α and β in the Navier–Stokes-αβ equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier–Stokes-α and Navier–Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for β<α. The vorticity structures predicted by the Navier–Stokes-αβ equations also improve as β decreases away from α. However, optimal choices for α and β depend not only on the problem of interest but also on the grid resolution.