Icy stars reveal the secret of their patterns
Jul 2, 2007
Some physicists gaze at the stars in the sky, but Victor Tsai of Harvard University and John Wettlaufer of Yale University in the US gaze at the stars on frozen lakes. Such star patterns often surround holes in ice, but the origin of their shape has always been a mystery. Now, by modelling their formation, the researchers have discovered that the shape is governed by the properties of the snow that covers the ice (Phys. Rev. E 75 066105).
Wettlaufer was first inspired to investigate star patterns when he and his wife were looking out of an aeroplane window landing in Chicago and noticed a frozen lake peppered with the distinct shapes. "We were absolutely struck," he said. "My wife is from Sweden and she knew these as the harbingers of dangerous ice skating, but had never seen so many."
The star patterns are formed when a hole in a recently-frozen lake allows water to swell up from beneath and spread over the snow-covered surface, leaving dark "fingers" of melted ice stemming from a central point. Previously, physicists had suspected that the fingers form because of a domino effect: the water starts flowing in one direction, causing the snow to melt faster in that region and thus helping the water to flow faster. But no-one has ever constructed a model to see if this idea is correct.
Tsai and Wettlaufer began by assuming that the rate of flow of the water is dependent on how compacted – and thus how porous – the snow is. They then created a model that also took into account parameters including the driving pressure and heat content of the water and how fast heat could transfer by diffusion.
The US pair found that all these parameters govern the number of unstable regions in which fingers would form. In particular, more porous snow coupled with a higher driving pressure would result in more fingers.
Tsai and Wettlaufer performed tests in the lab to see if their model matched real-world data by pumping water at a temperature of 1 °C through a dish of slush held below freezing. Although they were not able to change how porous the slush was, they changed other parameters included in their model such as the size of the initial hole. After 14 test runs, they could conclude that their model did not perfectly predict the number of holes, but was right 95% of the time.
Wettlaufer told Physics Web that their study could be relevant in many other processes involving instabilities, such as the fate of floating ice in polar oceans. "We hope that…more people notice wintertime lakes with a different eye to these stars," he said. "I know I will always have a camera on hand."
About the author
Jon Cartwright is a reporter for Physics Web