Genesis and Evolution of Vortex Bursting
Stout, Eric N
“Vortex bursting” has been described to denote abrupt radial expansions of vortex columns without any quantitative discussion. Being mainly a consequence of the vortex radius variation, it is addressed here via Direct Numerical Simulations with two different initial radius variations (β, the ratio of maximum to minimum core radii) at Reynolds number (Re≡Γ_0 \/ν= circulation/viscosity) of 5,000. Radius variations inherently lead to vortex line coiling, forming coaxial rings of azimuthal vorticity (ω_θ) which axially advect to collide and form vortex dipoles. For β=2, the dipole’s outward advection is arrested by a counter-dipole, resulting from the former’s meridional flow tilting the column’s axial vorticity (ω_z). For β=5, in contrast, the dipole erupts as a burst – hence the dipole eruption is defined as vortex bursting. Higher Re's produce complex three-dimensional bursting dynamics involving additional vortex line coiling/uncoiling within the column’s core, as well as dipoles’ leapfrogging and erupting to larger radii. Modeling the dipole’s interaction with the counter-dipole, a criterion for the dipole ω_θ necessary to cause bursting is derived: ω_θ^2>(4/π V/r ω_z ), with ω_z evaluated at the radius (r) where the circulation (in the collision plane) is 90% of its maximum. Further inviscid analysis yields a threshold of β^min=1.55 needed to cause bursting. A parametric search confirms this β^min to be the asymptotic limit at high Re’s. Thus, vortex bursting is defined, its dynamics elucidated, and a criterion for its occurrence derived.