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 |
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Format: | Artikel |
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. |
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ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/jfm.2019.957 |