Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations

Abstract

We study the inviscid mechanisms governing the three-dimensional evolution of an axisymmetric jet by means of vortex filament simulations. The spatially periodic calculations provide a detailed picture of the processes leading to the concentration, reorientation, and stretching of the vorticity. In the purely axisymmetric case, a wavy perturbation in the streamwise direction leads to the formation of vortex rings connected by braid regions, which become depleted of vorticity. The curvature of the jet shear layer leads to a loss of symmetry as compared to a plane shear layer, and the position of the free stagnation point forming in the braid region is shifted towards the jet axis. As a result, the upstream neighbourhood of a vortex ring is depleted of vorticity at a faster rate than the downstream side. When the jet is also subjected to a sinusoidal perturbation in the azimuthal direction, it develops regions of counter-rotating streamwise vorticity, whose sign is determined by a competition between global and local induction effects. In a way very similar to plane shear layers, the streamwise braid vorticity collapses into counter-rotating round vortex tubes under the influence of the extensional strain. In addition, the cores of the vortex rings develop a wavy dislocation. As expected, the vortex ring evolution depends on the ratio R/θ of the jet radius and the jet shear-layer thickness. When forced with a certain azimuthal wavenumber, a jet corresponding to R/θ = 22.6 develops vortex rings that slowly rotate around their unperturbed centreline, thus preventing a vortex ring instability from growing. For R/θ = 11.3, on the other hand, we observe an exponentially growing ring waviness, indicating a vortex ring instability. Comparison with stability theory yields poor agreement for the wavenumber, but better agreement for the growth rate. The growth of the momentum thickness is much more dramatic in the second case. Furthermore, it is found that the rate at which streamwise vorticity develops is strongly affected by the ratio of the streamwise and azimuthal perturbation amplitudes.