  We propose a theoretical model for ice growth under a wind-driven supercooled
water film. The thickness and surface velocity of the water layer are variable
by changing the air stream velocity. For a given water supply rate, linear
stability analysis is carried out to study the morphological instability of the
ice-water interface. In this model, water and air boundary layers are
simultaneously disturbed due to the change in ice shape, and the effect of the
interaction between air and water flows on the growth condition of the
ice-water interface disturbance is taken into account. It is shown that as wind
speed increases, the amplification rate of the disturbance is significantly
affected by variable stresses exerted on the water-air interface by the air
flow as well as restoring forces due to gravity and surface tension. We predict
that an ice pattern of a centimeter scale in wavelength appears and the
wavelength decreases as wind speed increases, and that the ice pattern moves in
the direction opposite to the water flow. The effect of the air stress
disturbance on the heat transfer coefficient at the water-air interface is also
investigated for various wind speeds.
