DNS of the collision of co-axial vortex rings

The collision of two identical, coaxial vortex rings with opposite sign of circulation at ReΓ = 1000–3000 and slenderness ratios ϵ in the range [0.1477 ⩽ ϵ ⩽ 0.2957] is investigated using an accurate numerical method. First, the linear stability of the axi-symmetric collision flow is analyzed numerically by solving the nonlinear, axi-symmetric basic flow and the linearized, 3-d disturbance equations simultaneously. The basic flow is linearly stable for the Reynolds number ReΓ = 1955, but exhibits algebraic growth phases. Then the fully nonlinear equations are solved for the Reynolds numbers ReΓ = 1806.91, ReΓ = 2701.82 and the same but enhanced initial disturbances. It is shown that the two vortex rings mutually expand in diameter with the subsequent formation of instabilities along the circumference of the resultant, compound vortex ring.

► Numerical simulation of the collision of coaxial vortex rings at ReΓ = 1000–3000.
► Linear stability of the axi-symmetric collision flow.
► Full Navier–Stokes simulations for two Reynolds numbers.
► Results show mutual expansion and break up in agreement with experiments.