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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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Interaction between an inclined gravity current and a pycnocline in a two-layer stratification
A series of laboratory experiments were conducted to investigate the characteristics of a dense gravity current flowing down an inclined slope into a quiescent two-layer stratification. The presence of the pycnocline causes the gravity current to split and intrude into the ambient at two distinct levels of neutral buoyancy, as opposed to the classical description of gravity currents in stratified media as being either a pure underflow or interflow. The splitting behaviour is observed to be dependent on the Richardson number ( $$Ri_{\unicode[STIX]{x1D70C}}$$ ) of the gravity current, formulated as the ratio of the excess density and the ambient stratification. For low $$Ri_{\unicode[STIX]{x1D70C}}$$ , underflow is more dominant, while at higher $$Ri_{\unicode[STIX]{x1D70C}}$$ interflow is more dominant. As $$Ri_{\unicode[STIX]{x1D70C}}$$ increases, however, we find that the splitting behaviour eventually becomes independent of $$Ri_{\unicode[STIX]{x1D70C}}$$ . Additionally, we have also identified two different types of waves that form on the pycnocline in response to the intrusion of the gravity current. An underflow-dominated regime causes a pycnocline displacement where the speed of the wave crest is locked to the gravity current, whereas an interflow-dominated regime launches an internal wave that moves much faster than the gravity current head or interfacial intrusion.
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- Award ID(s):
- 1634389
- PAR ID:
- 10184626
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 887
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2020.9
