Helical vortices: Quasiequilibrium states and their time evolution

International audienceThe time evolution of a viscous helical vortex is investigated by direct numerical simulations of the Navier– Stokes equations where helical symmetry is enforced. Using conservation laws in the framework of helical symmetry, we elaborate an initial condition consisting in a finite core vortex, the time evolution of which leads to a generic quasi-equilibrium state independent of the initial core size. Numerical results at different helical pitch values provide an accurate characterization in time for such helical states, for which specific techniques have been introduced: helix radius, angular velocity, streamfunction/velocity/vorticity relationships, core properties (size, self-similarity and ellipticity). Viscosity is shown to be at the origin of a small helical velocity component which we relate to the helical vorticity component. Finally, changes in time of the flow topology are studied using the helical streamfunction and three-dimensional Lagrangian orbits