We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale sugar and salt slabs attached to a buoy are observed to move rapidly in water with speeds up to 5 mm/s determined by the inclination angle and orientation of the dissolving surfaces. While symmetric boats drift slowly, asymmetric boats are observed to accelerate rapidly along a line before reaching a terminal velocity when their drag matches the thrust generated by dissolution. By visualizing the flow around the body, we show that the boat velocity is always directed opposite to the horizontal component of the density current. We derive the thrust acting on the body from its measured kinematics and show that the propulsion mechanism is consistent with the unbalanced momentum generated by the attached density current. We obtain an analytical formula for the body speed depending on geometry and material properties and show that it captures the observed trends reasonably. Our analysis shows that the gravity current sets the scale of the body speed consistent with our observations, and we estimate that speeds can grow slowly as the cube root of the length of the inclined dissolving surface. The dynamics of dissolving solids demonstrated here applies equally well to solids undergoing phase change and may enhance the drift of melting icebergs, besides unraveling a primal strategy by which to achieve locomotion in active matter.
Arctic icebergs, unconstrained sea ice floes, oil slicks, mangrove drifters, lost cargo containers, and other flotsam are known to move at 2%–4% of the prevailing wind velocity relative to the water, despite vast differences in the material properties, shapes, and sizes of objects. Here, we revisit the roles of density, aspect ratio, and skin and form drag in determining how an object is driven by winds and water currents. Idealized theoretical considerations show that although substantial differences exist for end members of the parameter space (either very thin or thick and very light or dense objects), most realistic cases of floating objects drift at approximately 3% of the free-stream wind velocity (measured outside an object’s surface boundary layer) relative to the water. This relationship, known as a long-standing rule of thumb for the drift of various types of floating objects, arises from the square root of the ratio of the density of air to that of water. We support our theoretical findings with flume experiments using floating objects with a range of densities and shapes.
more » « less- Award ID(s):
- 1643445
- NSF-PAR ID:
- 10367028
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 52
- Issue:
- 5
- ISSN:
- 0022-3670
- Page Range / eLocation ID:
- p. 907-916
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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