Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4):046317. doi: 10.1103/PhysRevE.81.046317. Epub 2010 Apr 26.

Oscillating pendulum decay by emission of vortex rings.

Physical review. E, Statistical, nonlinear, and soft matter physics

Diogo Bolster, Robert E Hershberger, Russell J Donnelly

PMID: 20481837 DOI: 10.1103/PhysRevE.81.046317

Abstract

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.

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