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