Spiral Instability of Fanning Swirling Jets

The goal of this paper is to study the axisymmetric and helical instabilities occurring in leading-edge vortices of aircraft and at a vortex-wall collision. Simple but pithy models considered are swirling jets of viscous incompressible fluid fanning along a mid-fluid or rigid plane. For large Reynolds numbers, the jets are boundary layers with all three velocity components being non-zero and strongly depending on streamwise and normal coordinates. For these highly non-parallel flows, the variable transformation is found allowing an exact reduction of the linear stability problem to a system of ordinary differential equations. Although the approach is valid only for steady disturbances, it allows one to find the instability occurring at rather small Reynolds numbers and causing the rotational symmetry breaking of primary regimes. In addition, there is the axisymmetric instability leading to hysteretic separation from and attachment to the rigid wall. The approach allows analytical (in limiting cases) and numerical solutions which show secondary regimes developing due to the instability and transition.