Surface instability of icicles

Quantitatively unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1-mm-thick layers of water flow down an icicle. These waves typically have a wavelength of about 1 cm, which is independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper, we show that these waves cannot be obtained by a naive Mullins-Sekerka instability but are caused by a quite different type of surface instability related to thermal diffusion and the hydrodynamic effect of a thin water flow.