Article

Oscillating pendulum decay by emission of vortex rings

Department of Civil Engineering an Geological Sciences, University of Notre Dame, Notre Dame, Indiana 46556, USA.
Physical Review E (Impact Factor: 2.33). 04/2010; 81(4 Pt 2):046317. DOI: 10.1103/PhysRevE.81.046317
Source: PubMed

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.

0 Followers
 · 
206 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The flow around a tethered cylinder subjected to an incoming flow transverse to its main axis and confined in a channel is investigated by means of global stability analysis of the full coupled body–fluid problem. When the cylinder is strongly confined (ratio of cylinder diameter to cell height, D/H = 0.66) we retrieve the confinement-induced instability (CIV) discovered by Semin et al. (J. Fluid Mech., vol. 690, 2011, pp. 345–365), which sets in at a Reynolds number below the vortex-induced vibration threshold. For a moderately confined case (D/H = 0.3), a new steady static instability is discovered, referred to as confinement-induced divergence (CID). This instability saturates into an asymmetric steady solution through a supercritical pitchfork bifurcation. In addition, the CIV and CID instabilities are studied via a reduced model obtained by considering a quasi-static response of the fluid, allowing for tracing back the physical mechanisms responsible for the instabilities.
    Journal of Fluid Mechanics 02/2015; 764:5-25. DOI:10.1017/jfm.2014.670 · 2.29 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider vortex rings moving in a Bose-Einstein condensate. By numerically solving the Gross-Pitaevskii equation, we show that if the circular shape of the ring is perturbed by helical Kelvin waves of given amplitude and azimuthal wave number, the translational self-induced velocity of the vortex ring is reduced; at large amplitude, the vortex ring halts.
    Physical Review A 04/2011; 83(4):045601-045601. DOI:10.1103/PHYSREVA.83.045601 · 2.99 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Passing a fluid through a grid is a well-known mechanism used to study the properties of turbulence. Oscillating a horizontal grid vertically in a tank has also been used extensively and is considered to be a source of almost homogenous isotropic turbulence. When the oscillating grid is turned on a turbulent flow is induced. A front translates into the experimental tank, behind which the flow is highly turbulent. Long predicted that the growth of such a front would grow diffusively as the square root of time (i.e., d∼sqrt[t]) and Dickinson and Long presented experimental evidence for the diffusive result at a low mesh Reynolds number of 555. This paper revisits these experiments and attempts a set of two models for the advancing front in both square and round tanks. We do not observe significant differences between runs in square and round tanks. The experiments in water reach mesh Reynolds numbers of order 30000. Using some data from superfluid helium experiments we are able to explore mesh Reynolds numbers to about 43000. We find the power law for the advancing front decreases weakly with the mesh Reynolds number. Using a very long tank we find that the turbulent front stops completely at a certain depth and attempt a simple explanation for that behavior. We study the propagation of the turbulent front into tubes of different diameters inserted into the main tank. We show that these tubes exclude wavelengths much larger than the tube diameter. We explore the variation of the position of the steady-state boundary H on tube diameter D and find that H=cD with c∼2. We suggest this may be explained by saturation of the energy-containing length scale ℓ_{e}. We also report on the effect of plugging up just one hole of the grid. Finally, we recall some earlier oscillating grid experiments in superfluid ^{4}He in the light of the present results.
    Physical Review E 05/2014; 89(5-1):053016. DOI:10.1103/PhysRevE.89.053016 · 2.33 Impact Factor

Preview

Download
2 Downloads
Available from