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Settling disks in a linearly stratified fluid

Published online by Cambridge University Press:  17 December 2019

M. J. Mercier Open the ORCID record for M. J. Mercier [Opens in a new window] ,
S. Wang Open the ORCID record for S. Wang [Opens in a new window] ,
J. Péméja ,
P. Ern Open the ORCID record for P. Ern [Opens in a new window]  and
A. M. Ardekani Open the ORCID record for A. M. Ardekani [Opens in a new window]
M. J. Mercier*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France
S. Wang*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
J. Péméja
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France
P. Ern
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France
A. M. Ardekani
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
*
†Email address for correspondence: [email protected]
‡Present address: Davidson School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, IN 47907, USA.
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Abstract

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.

JFM classification

Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A2
Copyright
© 2019 Cambridge University Press

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