Vortex Motions

Discrete vortex methods

Vortex methods provide a powerful Lagrangian tool to numerically simulate vortex-dominated flows. Despite the inviscid nature of vortex methods, the significant physics are still well captured as vorticity is shed due to a high angle of attack. 

Axisymmetric buoyant vortex rings

When the core of a ring is thin, we formulate the equation of motion using momentum balance for vortex filaments. For a fat ring, we use axisymmetric contour dynamics to study the time evolution of axisymmetric vortex rings when the fluid inside the ring is less dense than that of its ambient. The contour dynamics formulation can be found in [1] and some numerical results in [3].

Motion of vortex filaments with buoyancy

We used Moore and Saffman’s momentum balance for vortex filaments to construct their self-induced velocity. Buoyancy was introduced into the formulation and numerical study was carried out for both vortex rings and knots in an inviscid, incompressible flow. Examples of buoyant vortex rings in real observations can also be found here and here (YouTube video). The mathematical model is published in [2].