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Scientists discover how water temperature affects the shape of melting ice

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These photographs show the different forms of melted ice that form for cold (4 degrees C), intermediate (5.6 degrees C), and warmer (8 degrees C) ambient water temperatures. Credit: Courtesy of NYU Applied Mathematics Lab

A team of mathematicians and physicists has discovered how ice formations are shaped by external forces, such as water temperature. His recently published research may offer another way to assess the factors that melt ice.

“The shapes and patterns of ice are sensitive indicators of the environmental conditions in which it melted, allowing us to ‘read’ the shape to infer factors such as ambient water temperature,” says Leif Ristroph. , associate professor at[{” attribute=””>New York University’s Courant Institute of Mathematical Sciences and one of the authors of the paper, which appears in the journal Physical Review Letters.

“Our work helps to understand how melting induces unusual flow patterns that in turn affect melting, which is one of the many complexities affecting the ice on our planet,” adds author Alexandra Zidovska, an associate professor in NYU’s Department of Physics.

The paper’s other authors were Scott Weady, an NYU graduate student, and Josh Tong, an undergraduate in NYU’s College of Arts and Science at the time of the study.

At NYU’s Applied Mathematics Laboratory and Soft Matter Research Center, researchers studied, through a series of experiments, the melting of ice in water and, in particular, how the temperature of the water affects the shapes and eventual patterns of the ice. To do this, they created ultra-pure ice, free of bubbles and other impurities. The team recorded the melting of ice submerged in water tanks in a “cold room”, which is similar to a refrigerator-chamber whose temperature is controlled and varied.

“We focused on cold temperatures, from 0 to 10 degrees Celsius– at which ice in natural waters typically melts, and we found a surprising variety of shapes that formed,” says Ristroph, who directs the Applied Mathematics Laboratory.

Specifically, at very cold temperatures – those below about 5 degrees Celsius – the pieces take on the shape of a point or “pinnacle” pointing downwards – similar to an ice cube, but perfectly smooth (without ripples) . For temperatures above about 7 degrees Celsius, the same basic shape is formed, but upside down – an upward pointing tip. Between temperatures, the ice has melted wavy and wavy patterns on its surface. Similar patterns, called “scallops,” are found on icebergs and other ice surfaces in nature.

These differences in shape are due to changes in water flows, which are determined by their temperatures.

“The melting causes temperature gradients in the water near the ice, which causes the liquid in different places to have different densities,” Weady explains. “This generates flows due to gravity – with heavier liquid sinking and lighter fluid rising – and such flows along the surface lead to different melting rates at different places and therefore to changes in form.”

“What is strange in physics is that liquid water has a very unusual temperature dependence of density, in particular a density maximum at around 4 degrees Celsius,” he adds. “This ‘density anomaly’ makes water unique from other fluids.”

Research shows that this property is responsible for producing very different flow rates, depending on the precise value of the water temperature. Low-temperature descending pinnacles are associated with upflows, while rising pinnacles have downflows. The scalloped patterns form because upflows very near the surface interact with downflows farther away, destabilizing into eddies that carve pits in the ice.

“Our findings help explain some characteristic shapes of ice observed in nature, in particular the so-called pinnacle morphology of icebergs which consists of sharp points or arrows and the so-called scallops which consist of undulating patterns of pits.” , notes Ristroph.

“The broader context of this work relates to Earth’s climate change and the increasing rate of ice melt on our planet,” he continues. “It is important to better understand the detailed physics and mathematics of melting on a smaller scale, as they are key components of larger scale climate models.”

Reference: “Anomalous Convective Flows Carve Pinnacles and Scallops in Melting Ice” by Scott Weady, Joshua Tong, Alexandra Zidovska and Leif Ristroph, January 28, 2022, Physical examination letters.
DOI: 10.1103/PhysRevLett.128.044502

The research was supported by grants from the National Science Foundation (PHY-1554880, CBET-1805506, DMS-1646339).