Bursting on a vortex tube with initial axial core-size perturbations

Abstract

We simulate and analyze the evolution of a rectilinear vortex tube with initial axial core-size perturbations at circulation-based Reynolds number of 5000. The initial variations in the core size are associated with axial gradients in the azimuthal velocity, which generates azimuthal vorticity. This azimuthal vorticity propagates as twist waves in the axial direction. Varying the initial core-size ratio A shows that the propagation speed of the twist waves varies linearly with A and approaches linear stability results of the long-wave limit of Kelvin waves on rectilinear vortex tubes as A → 1 . The simulations show that when two twist waves of opposite handedness meet the core expands radially, forming a pair of local ringlike structures with opposite-signed azimuthal vorticity through a process termed vortex bursting. An analysis of the vorticity dynamics during bursting reveals that initially the flow behaves qualitatively like a head-on collision of two isolated vortex rings, with the azimuthal vorticity dynamics driving radial growth. During bursting, however, the localized radial expansion of the core is also accompanied by an increase in the radial vorticity component, which ultimately arrests the bursting and reverses the sign of the azimuthal vorticity. Through long-time simulations of the periodic tube, we demonstrate that after the primary bursting event the twist waves reverse their direction and interact again, leading to further bursting events. The evolution of the perturbed tubes is then accompanied by sustained elevated enstrophy levels and thus accelerated energy decay as compared to undisturbed Lamb-Oseen vortices of identical initial circulation and energy. Overall, this work provides the first detailed qualitative and quantitative insights into the mechanisms and evolution of vortex bursting on rectilinear vortex tubes. To further assess the relevance and prevalence of bursting in practical settings, subsequent investigations in the stability and sensitivity of our results to varying Reynolds number, nonrectilinear vortex center lines, and external strain fields are needed.