Core dynamics of a strained vortex column: Linear instability, nonlinear evolution and transition

The instability and transition in a vortex column embedded in a plane shear perpendicular to its axis is studied via direct numerical simulations. We focus on the evolution of varicose modes (i.e. core dynamics, CD) on the column. Standing wave oscillations of vorticity, damped in the absence of shear, amplify exponentially at a rate that increases with increasing shear. The instability has a shortwave character, a low-shear cutoff at a given Re, and a low-Re cutoff at a given shear; the instability results from resonant forcing of perturbation vorticity that occurs when the CD frequency matches the angular velocity of vortex fluid, causing sustained stretching of perturbation vorticity and hence cumulative CD growth. Nonlinear CD generates strong meridional flow-whose peak velocity even exceeds vortex azimuthal velocity-and is responsible for causing transition to turbulence via two distinct mechanisms: (i) generation and subsequent roll-up of intense vorticity sheaths, and (ii) folding and reconnection of core vortex filaments. Cascade to small scales occurs in parallel with backscatter (Le. anticascade) by the pairing of rolled up vortices. The result is a fully turbulent flow, containing small-scale structures (which themselves may, as Re increases, generate finer scale vortices via selfsimilar CD). Although CD instability has a smaller growth rate than bending waves, it generates vorticity intermittency faster, which underlines its significance in transitional and turbulent flows.