Turbulent transition of helical vortices destabilized by short-wave instability*

Helical vortices appear in devices which possess rotating wings. It is important to understand the dynamics of helical vortices because they affect the performance of the devices. Helical vortices are subject to several types of instability. Among them the elliptic and curvature instabilities, both of which are short-wave instabilities, are of particular interest since they can lead to turbulent transition of the helical vortices. We study the time evolution of a helical vortex disturbed by an unstable mode of the elliptic instability by direct numerical simulation. The incompressible Navier-Stokes equations in the cylindrical coordinate system are solved numerically by a high-precision method. For low Reynolds numbers, the instability saturates as the vortex core grows by viscous diffusion to lose resonance condition for the elliptic instability; then another mode of the elliptic instability grows and saturates. For large Reynolds numbers, the first instability causes turbulent transition of the vortex core; then the turbulence decays gradually. In both cases, the helical vortex is eventually destroyed by interaction between the adjacent spirals.