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Scalloped iceberg sculptures occur due to the weirdness of water ctm magazine


You would think that understanding something as common as melting ice would be relatively easy. But water is a peculiar substance, and that makes it very hard to predict how ice will melt. A lot of that unpredictability has been attributed to water flowing around the ice (as seen in sea currents flowing around icebergs, for example).

Still, understanding melting is required to better predict things like the breakup of sea ice. So a group of physicists turned the fluid dynamics up to 11 and have shown that melting ice is weird, even when there are no currents.

It only does that to annoy you

The rules that govern the Universe are relatively simple. However, to ensure that the Universe is sufficiently maddening, those simple rules were crafted to produce fluid dynamics and water. Fluid dynamics is the study of how fluids flow.

A typical fluid dynamics course is an exercise in humility. The main takeaway is that everything you ever learned about solving equations is the equivalent of doing carpentry with a chocolate hammer in the tropics. When you do manage to bend the equations to your will and cram them into a computer, you get the most astonishingly beautiful results, and what we are about to see is no different.

Water, like any other fluid, gets denser as it cools, except for the last few degrees (4°C is when water hits peak density), where it gets less dense until it freezes. Hence, water is denser than ice, and we have beautiful floating ice floes.

This strange behavior leads to odd situations where cold water first sinks but then—because it cools below 4°C—starts to rise again due to decreasing density. This process can lead to cold water welling up in a reversed convective flow. But in other places, warm water wells to the surface, also due to convective flows. If dry fluid dynamics doesn’t boggle your mind, just add water.

So a brave set of researchers set out to understand the natural ice sculptures hidden beneath icebergs.

Sculpting ice

To understand how ice melts, the researchers combined experimental observations and modeling. They put large, clear ice cylinders at 0°C into a water tank held at a fixed temperature. Then they observed how melting proceeded.

To understand the shapes that form, you must consider the temperature gradient between the water and the ice. When the water temperature is relatively high (8°C), the water hits peak density a few millimeters from the surface of the ice. The heavy water falls, dragging some of the surrounding water with it. The process creates an entrained flow downward along the surface of the ice cylinder, leading to a needle-like point hanging in the ice.

On the other hand, if the water is quite cold (less than 4°C), the water at the surface of the ice is less dense than the surrounding water and flows upward, creating an identical needle pointing up. The researchers’ numerical and experimental results show that these needles can be extremely sharp, reaching the limit of the measurements. The agreement between experiment and calculation is amazing.

Neither warm nor cold

The intermediate case is where things get interesting. Near the surface of the ice, the water is less dense and tries to rise. Farther away from the surface, the water is denser and tries to fall. This leads to a kind of circulating flow. Normally, this type of flow is unstable and will break up. However, the viscosity (how sticky a fluid is) of the water damps the instability. The end result is that the circulating flow stabilizes at a diameter that depends on local temperature.

Thanks to the stabilization, the water flow digs out a scalloped pattern in the ice, with wide scallops near the top and narrow, deep scallops near the bottom. Every pattern is unique, but they all have the same characteristic shapes, and they occur independently of any external water flow or global convection.

And they’re beautiful.

Physical Review Letters, 2022, DOI: 10.1103/PhysRevLett.128.044502 (About DOIs)



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