Morphological instability of the solid-liquid interface occuring in a crystal
growing from an undercooled thin liquid being bounded on one side by a free
surface and flowing down inclined plane is investigated by a linear stability
analysis under shear flow. It is found that restoring forces due to gravity and
surface tension is important factor for stabilization of the solid-liquid
interface on long length scales. This is a new stabilizing effect different
from the Gibbs-Thomson effect. A particular long wavelength mode of about 1 cm
of wavy pattern observed on the surface of icicles covered with thin layer of
flowing water is obtained from the dispersion relation including the effect of
flow and restoring forces.Comment: 30 pages, 4 figure
