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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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Thin disks falling in air
We experimentally investigate the settling of millimetre-sized thin disks in quiescent air. The range of physical parameters is chosen to be relevant to plate crystals settling in the atmosphere: the diameter-to-thickness aspect ratio is $$\chi =25\unicode{x2013}60$$ , the Reynolds numbers based on the disk diameter and fall speed are $Re=O(10^2)$ and the inertia ratio is $I^*=O(1)$ . Thousands of trajectories are reconstructed for each disk type by planar high-speed imaging, using the method developed by Baker & Coletti ( J. Fluid Mech. , vol. 943, 2022, A27). Most disks either fall straight vertically with their maximum projected area normal to gravity or tumble while drifting laterally at an angle $$<20^\circ$$ . Two of the three disk sizes considered exhibit bimodal behaviour, with both non-tumbling and tumbling modes occurring with significant probabilities, which stresses the need for a statistical characterization of the process. The smaller disks (1 mm in diameter, $Re=96$ ) have a stronger tendency to tumble than the larger disks (3 mm in diameter, $Re=360$ ), at odds with the diffused notion that $Re=100$ is a threshold below which falling disks remain horizontal. Larger fall speeds (and, thus, smaller drag coefficients) are found with respect to existing correlations based on experiments in liquids, demonstrating the role of the density ratio in setting the vertical velocity. The data supports a simple scaling of the rotational frequency based on the equilibrium between drag and gravity, which remains to be tested in further studies where disk thickness and density ratio are varied.
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- Award ID(s):
- 1822192
- PAR ID:
- 10447102
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 962
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.209
