Linear stability analysis of ice growth under supercooled water film driven by a laminar airflow

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.