Helicity in the formation of turbulence

Helicity in vortex structures and spectra is studied in the developmental stages of a numerical simulation of the Navier-Stokes equations using three-dimensional visualizations and spectra. First, time scales are set using the growth and decay of energy dissipation, the peak value of vorticity, and the helicity. Then, two stages between the early time, nearly inviscid Euler dynamics with vortex sheets and a final state of fully developed turbulence with vortex tubes, are described. In the first stage, helicity fluctuations develop in Fourier space during a period still dominated by vortex sheets and rapidly growing peak vorticity. At the end of this period the strongest structure consists of transverse vortex sheets with mixed signs of helicity. During the second stage, a dissipative interaction propagates along one of these vortices as the sheets roll each other into vortex tubes.