Turbulence without the Viscous Tilting of Vorticity

Vortex stretching is a fundamental aspect of Navier-Stokes turbulence and is commonly compared to the stretching of infinitesimal material lines. The essential difference between the stretching of infinitesimal material lines and vortex lines is the explicit role of viscosity in the directional realignment of the latter process. This "viscous tilting" of vorticity is known to produce important differences in the alignment, and thus stretching, behavior of vorticity compared to infinitesimal material lines. In this study, direct numerical simulations (DNS) of isotropic turbulence are performed with and without viscous tilting. To facilitate the artificial removal of viscous tilting in DNS, the Navier-Stokes equations are solved in their vorticity form together with the Biot–Savart reconstruction of velocity. Then, the viscous Laplacian term in the vorticity equation is projected parallel to the local vorticity so that it directly impacts the magnitude only, not the orientation of the vorticity's unit vector. The DNS results reveal dramatic deviations from Navier-Stokes turbulence when viscous tilting is removed, which will be explored in this presentation.