The Shape of Melting Ice

A team of mathematicians and physicists has discovered how ice formations are shaped by external forces, such as water temperature. “The shapes and patterning of ice are sensitive indicators of the environmental conditions at which it melted, allowing us to ‘read’ the shape to infer factors such as the ambient water temperature,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and one of the authors of the study. At very cold temperatures—those under about 5 degrees C—the pieces take on the shape of a spike or “pinnacle” pointing downward—similar to an icicle, but perfectly smooth (with no ripples). For temperatures above approximately 7 degrees C, the same basic shape forms, but upside down—a spike pointing upward. For in between temperatures, the ice has wavy and rippled patterns melted into its surface. Similar patterns, called “scallops,” are found on icebergs and other ice surfaces in nature. (This video shows ice melting into water a