Illustrated Physics
physics, drawn
Concept

Flotation — where it appears

The state of a body whose weight is carried wholly by the fluid it displaces rather than by any solid support. At the point where an ice sheet begins to float, its thickness is fixed by flotation at the water's depth times the ratio of the water's density to the ice's.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Where the level goes when a floating ice cube melts. The change in level when a 30 g ice cube floating in a glass 7 cm across has melted completely, against the density of the liquid it floats in (the liquid must be denser than ice, 917 kg/m³, or the cube sinks). In fresh water the level does not move: the meltwater exactly fills the volume the ice displaced. In seawater it rises 0.21 mm and in saturated brine 1.3 mm, because the ice was displacing a denser liquid than it melts into; in castor oil, which is lighter than water and does not mix with it, the level falls 0.32 mm as the meltwater sinks beneath the oil. The change is the meltwater's volume minus the displaced volume, m/ρw − m/ρ, spread over the glass.

The floating ice that still raises the sea

An ice cube melting in a glass of water leaves the level exactly where it was, and the reason is exact: a floating body displaces its own weight, and the meltwater has that weight. The same argument is often used to say that melting sea ice and ice shelves cannot raise the sea. It nearly works. The ice was floating in salt water and melts into fresh, which is lighter, so the meltwater overfills the hole by almost three per cent — and the ice that really fills the sea is the part of a grounded glacier above the thickness at which it would float.

fluids · Buoyancy An ice sheet resting on a bed below the sea. A section along the flow of an ice sheet on the MISMIP benchmark bed, which lies below sea level beyond 480 km from the divide and deepens inland between 974 and 1265 km. Dashed: the height the ice surface would stand at if the ice were just thick enough to touch the bed — 1.11 times the water's depth thick, a ninth of it above the sea. At the rate factor drawn, the balance of snowfall against export has three solutions: grounding lines at 800, 1124, 1376 km. The outer two are stable; the middle one, on the stretch where the bed deepens inland, is not. The ice drawn — its surface a plastic profile, a sketch rather than a solution — rests on the bed out to 1376 km, where it must be 803 m thick to touch it, and floats beyond as a shelf.

The grounding line with nowhere to stop

Where an ice sheet flowing into the sea lifts off its bed and begins to float, buoyancy fixes how thick it is: just thick enough to touch the rock, about 1.1 times the depth of the water. The ice crossing that line goes as the 19/4 power of the thickness, so twice the depth sends out twenty-seven times the ice. On a bed that deepens inland, a grounding line that retreats a little moves into deeper water, exports more, and retreats further. No steady state can sit there, and an ice sheet whose edge reaches such a slope crosses the whole of it.

fluids · Buoyancy

Named alongside it

The objects these essays reach for when they reach for this one.

BuoyancySea levelArchimedes principleDensityGrounding lineHysteresisIce sheetIce shelfInstabilitySalinity

All concepts