Robert E. Hershberger

Dynamics of thin vortex rings

As part of a long-range study of vortex rings, their dynamics, interactions with boundaries and with each other, we present the results of experiments on thin core rings generated by a piston gun in water. We characterize the dynamics of these rings by means of the traditional equations for such rings in an inviscid fluid suitably modifying them to be applicable to a viscous fluid. We develop expressions for the radius, core size, circulation and bubble dimensions of these rings. We report the direct measurement of the impulse of a vortex ring by means of a physical pendulum.

Dynamic similarity, the dimensionless science

Dimensional analysis, a framework for drawing physical parallels between systems of disparate scale, affords key insights into natural phenomena too expansive and too energetic to replicate in the lab.