Settling disks in a linearly stratified fluid

We consider the unbounded settling dynamics of a circular disk of diameter $d$ and finite thickness $h$ evolving with a vertical speed $U$ in a linearly stratified fluid of kinematic viscosity $\unicode[STIX]{x1D708}$ and diffusivity $\unicode[STIX]{x1D705}$ of the stratifying agent, at moderate Rey...

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Veröffentlicht in:Journal of fluid mechanics 2020-02, Vol.885, Article A2
Hauptverfasser: Mercier, M. J., Wang, S., Péméja, J., Ern, P., Ardekani, A. M.
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Sprache:eng
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Zusammenfassung:We consider the unbounded settling dynamics of a circular disk of diameter $d$ and finite thickness $h$ evolving with a vertical speed $U$ in a linearly stratified fluid of kinematic viscosity $\unicode[STIX]{x1D708}$ and diffusivity $\unicode[STIX]{x1D705}$ of the stratifying agent, at moderate Reynolds numbers ( $Re=Ud/\unicode[STIX]{x1D708}$ ). The influence of the disk geometry (diameter $d$ and aspect ratio $\unicode[STIX]{x1D712}=d/h$ ) and of the stratified environment (buoyancy frequency $N$ , viscosity and diffusivity) are experimentally and numerically investigated. Three regimes for the settling dynamics have been identified for a disk reaching its gravitational equilibrium level. The disk first falls broadside-on, experiencing an enhanced drag force that can be linked to the stratification. A second regime corresponds to a change of stability for the disk orientation, from broadside-on to edgewise settling. This occurs when the non-dimensional velocity $U/\sqrt{\unicode[STIX]{x1D708}N}$ becomes smaller than some threshold value. Uncertainties in identifying the threshold value is discussed in terms of disk quality. It differs from the same problem in a homogeneous fluid which is associated with a fixed orientation (at its initial value) in the Stokes regime and a broadside-on settling orientation at low, but finite Reynolds numbers. Finally, the third regime corresponds to the disk returning to its broadside orientation after stopping at its neutrally buoyant level.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.957