Dynamics of vortex lines in turbulent flows

We examine the dynamic interplay between vorticity magnitude and vortex line geometry, and its relevance for curbing potential finite-time singularities in incompressible Navier-Stokes flows. We present direct numerical simulations of flows with various low and mid-range Reynolds numbers and different types of forcing, The central conclusion is that the vortex lines in regions of high vorticity tend to be straight and well aligned. Such an organization indicates rbe existence of a self-correcting mechanism that cancels the quadratic nonlinearity inherent in the vorticity equation. We consider several relevant effects, including the observation of straightening of vortex lines by stretching.