Title: Non-linear Lessons from Axisymmetric Vortex Rings
Speaker: Karim Shariff
Speaker Info: NASA Ames Research Center
Special Note: More current information may be available at Plan-it Purple
The talk will present two types of phenomena, both recognizable to students of nonlinearity, that are exhibited by axisymmetric vortex rings in numerical and laboratory experiments.Date: Friday, May 25, 2001
(1) The first type of phenomenon is reminiscent of inelastic solitons and is illustrated by the following examples:
(a) A perturbed Hill's spherical vortex sheds a tail and returns to Hill's vortex.
(b) The core shapes of two thin rings colliding head-on evolve through a sequence of shapes that happens to be Pierrehumbert's family of _planar_ steadily translating vortex pairs. This continues until the limiting member of the family is reached. Thereafter, the core shapes continue to approximately maintain this shape while continually depositing vorticity into a tail.
(c) Fat rings that collide head-on, flatten but then the vortex cores grow a head in the shape of Pierrehumbert's limiting vortex pair.
(d) When one tries to create a vortex ring at the edge of a pipe by pushing a piston forward, there is a limiting piston stroke length beyond which the vortex ring refuses to grow any larger. It then propagates away leaving a train of smaller rings behind. It is shown (heuristically) that the limiting stroke occurs when the apparatus is no longer able to keep ejecting energy at a rate compatible with the requirement (due to Kelvin) that a steadily translating vortex have maximum energy with respect to impulse preserving isovortical perturbations.
(2) The second phenomenon is the heteroclinic tangle. Some vortex ring motions are periodic in time and therefore create a time periodic velocity field. The motion of fluid particles are solutions to a 2 dof system with a time periodic Hamiltonian.