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: 2.31). 04/2010; 81(4 Pt 2):046317. DOI: 10.1103/PhysRevE.81.046317 Source: PubMed

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**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.01/2015; 764:5-25. - [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. · 2.33 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The simple pendulum remains one of the most fundamental systems studied in physics. It is commonly used as a model to illustrate a broad variety of mechanisms in a wide range of areas. However, in spite of this popularity, subtle behaviours still remain to be discovered and to be explored when the pendulum is strongly coupled to fluid mechanics. This is for instance illustrated in recent studies by Neill, Livelybrooks & Donnelly (Am. J. Phys., vol. 75, 2007, pp. 226–229) and Bolster, Hershberger & Donnelly (Phys. Rev. E, vol. 81, 2010, pp. 1–6) which highlight the impact on a simple spherical pendulum of vortex shedding and added mass effects. In the present work we show that the equilibrium of a pendular disk facing a flow exhibits bi-stability and hysteresis. We give a simple interpretation of this behaviour in terms of a two-potential-well description, only requiring to know the angular dependence of the normal drag coefficient of an inclined plate. We investigate the influence of turbulence on the equilibrium of the pendulum in general and on the observed bi-stability in particular. Our results have potentially important fundamental and practical consequences: (i) they extend the attractiveness of the pendulum as a model to investigate generic questions related to bi-stable stochastic processes, (ii) they highlight important fluid dynamic mechanisms, including turbulent drag enhancement and fluid–structure interaction issues.Journal of Fluid Mechanics 08/2013; 728. · 2.29 Impact Factor

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