Evolution of vortex structures in a model of the turbulent trailing vortex

Abstract

We present results obtained from a direct numerical simulation for a model of incompressible trailing vortices consisting of an array of counter-rotating vortices and a superposed axial velocity in a doubly-periodic domain, infinite in the vertical direction. The Reynolds number based on vortex circulation is 1000. It is found that for suffciently strong axial flow, helical instability modes develop on each vortex. This leads to a decrease in the magnitude of the axial flow and subsequent relaminarization of each vortex. At later times, modes corresponding to the more slowly growing co-operative instability become dominant. These produce their own helical structures followed by the rapid growth of small scales, then vorticity cancellation and decay of the vortex array. In the presence of strong axial flow the helical structure persists and the vortices appear more resistant to the breakdown phenomena than for arrays with no axial flow.