Turbulence Without the Viscous Tilting of Vorticity

Abstract

Vortex stretching is a fundamental aspect of Navier-Stokes turbulence and is commonly understood in analogy to the stretching of infinitesimal material lines. However, the parallel alignment of material lines and vorticity cannot be maintained due to the role of viscosity in the directional realignment of vorticity. In Navier-Stokes turbulence, the result is relatively modest quantitative differences in the alignment and stretching rates of vorticity compared to material lines. In this study, the qualitative effect of viscous tilting of vorticity is demonstrated directly by surgically removing it from direct numerical simulations of isotropic turbulence. The result is a drastic change to the fundamental structure of the flow, including a substantial deviation from the -5/3 inertial range scaling of the energy spectrum brought about by the infiltration and prevalence of viscous effects beyond the smallest scales. These observations demonstrate that the viscous tilting of vorticity is an essential characteristic of fluid turbulence. By extension, the same may be said of the difference in orientation and stretching rates for vorticity and infinitesimal material lines.