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Azimuthal instability of a vortex ring computed by a vortex sheet panel method

A Lagrangian panel method is presented for vortex sheet motion in three-dimensional (3D) flow. The sheet is represented by a set of quadrilateral panels having a tree structure. The panels have active particles that carry circulation and passive particles used for adaptive refinement. The Biot–Savart kernel is regularized and the velocity is evaluated by a treecode. The method is applied to compute the azimuthal instability of a vortex ring, starting from a perturbed circular disc vortex sheet initial condition. Details of the core dynamics are clarified by tracking material lines on the sheet surface. Results are presented showing the following sequence of events: spiral roll-up of the sheet into a ring, wavy deformation of the ring axis, first collapse of the vortex core in each wavelength, second collapse of the vortex core out of phase with the first collapse, formation of loops wrapped around the core and radial ejection of ringlets. The collapse of the vortex core is correlated with converging axial flow.