Vortexring

Vortexring, commonly called a vortex ring, is a torus-shaped patch of fluid within which vorticity is concentrated and which propagates through surrounding fluid. The ring has a major radius R, the distance from the torus center to the centerline of its tube, and a tube radius a. The strength of the ring is quantified by its circulation Γ.

Formation can occur when a finite slug of fluid is impulsively ejected through a circular orifice, by piston-like motion of a boundary, or by fragmentation of a jet. Common physical realizations include smoke rings produced by exhalation or trained demonstrations, as well as underwater toroidal vortices shed by propulsors. The ring translates along its axis with a speed that depends on Γ and the geometry.

Dynamics: For a slender core (a much smaller than R), the self-induced axial velocity is approximately U ≈ Γ/(4πR) [ln(8R/a) − 0.558]. The ring may deform, interact with other rings, or undergo leapfrogging in multi-ring configurations. Viscosity causes diffusion of vorticity and gradual decay of the ring's strength over time.

Importance: Vortex rings serve as a canonical example in fluid dynamics for studying coherent structures, vorticity transport, and jet or plume entrainment. They appear in natural flows and engineered systems, including propulsion concepts, flow visualization techniques, and various laboratory experiments.