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.

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.

We have studied oscillation of a pendulum in water using spherical bobs. By measuring the loss in potential energy, we estimate the drag coefficient on the sphere and compare to data from liquid-helium experiments. The drag coefficients compare very favorably illustrating the true scaling behavior of this phenomenon. We also studied the decay of amplitude of the pendulum over time. As observed previously, at small amplitudes, the drag on the bob is given by the linear Stokes drag and the decay is exponential. For larger amplitudes, the pendulum bob sheds vortex rings as it reverses direction. The momentum imparted to these vortex rings results in an additional discrete drag on the bob. We present experiments and a theoretical estimate of this vortex-ring-induced drag. We analytically derive an estimate for a critical amplitude beyond which vortex ring shedding will occur as well as an estimate of the radius of the ring as a function of amplitude.

We discuss the possibility of capturing carbon dioxide from the flue gas of a coal-fired electrical power plant by cryogenically desublimating the carbon dioxide and then preparing it for transport in a pipeline to a sequestration site. Various other means have been proposed to accomplish the same goal. The problem discussed here is to estimate the "energy penalty" or "parasitic energy loss,' defined as the fraction of electrical output that will be needed to provide the refrigeration and that will then not be deliverable. We compute the energy loss (7.9-9.2% at 1 atm) based on perfect Carnot efficiency and estimate the achievable parasitic energy loss (22-26% at 1 atm) by incorporating the published coefficient of performance values for appropriately sized refrigeration or liquefaction cycles at the relevant temperatures. The analyses at 1 atm represent a starting point for future analyses using elevated pressures.

We study experimentally the slowing of viscous vortex rings. In particular we do so using the concept of drag coefficient, which is a bulk coefficient which aims to capture the various mechanisms of slowing that can occur. At early times of flight the ring slows at a certain rate. After some time, instabilities (which we refer to as Kelvin waves) begin to form on the ring and there is a transient increase in the measured drag coefficient. After this brief transient the rings enter another regime with constant drag coefficient, which is larger than the early time one. In particular, our data illustrate that there appears to be a direct link between the number of waves that form on the ring and the relative increase in drag coefficient.