Icicle Instability

No two snowflakes are alike, according to common wisdom. Icicles, on the other hand, are all alike--that is, the ripples that embellish the surfaces of most icicles are similar regardless of variations in air temperature, humidity, icicle thickness, or growth rate.

An icicle grows when thin sheets of water flow down the icicle shaft. A portion of the flowing water freezes and the rest drips from the icicle tip. But the ice that's left behind doesn't build up uniformly; instead, it is selectively deposited at certain locations.

As a result, icicles are covered in ring-like ripples extending along their lengths, which always measure about 1 cm from peak to peak.

Researchers at Hokkaido University's Institute of Low Temperature Sciences in Japan (Naohisa Ogawa and Yoshinori Furukawa: ogawa@particle.sci.hokudai.ac.jp, frkw@lowtem.hokudai.ac.jp) have developed a theoretical model that explains the surprisingly universal structure of icicles.

According to the new model, two effects are important as an icicle grows. The first effect is the Laplace instability, which is related to the latent heat released from an icicle's surface and dispersed into the air through the thin water layer. The instability arises because heat is more rapidly lost from the convex surfaces than that from the concave surfaces, which makes ice build up faster on an icicle's convex protrusions than on the concave indentations, thus amplifying ripples.

The second factor is the fluid effect. Flow in the thin water layer decreases the temperature distribution along the layer, making it uniform and thus inhibiting the Laplace instability.

As it happens, these two competing effects ensure that all icicle ripples have the same wavelength, although the ripple height can vary from one icicle to another. The theory also predicts that the ripples should migrate down an icicle at about half the speed that the icicle grows--a prediction the researchers hope will soon be verified experimentally.

In addition the researchers expect that their model should be helpful in explaining the structures of mineral stalagmites commonly found in limestone caves. (N. Ogawa and Y. Furukawa, Physical Review E, October 2002)