Roughness characteristics of an ice surface grown in the presence of a supercooled water film driven by gravity and wind drag

A theoretical model is proposed to explain the roughness characteristics of an ice surface grown from a gravity and wind-driven supercooled water film flowing over an inclined plane. The effects of the water supply rate, plane slope and air stream velocity on the spacing and height of ice surface roughness are investigated from a new type of morphological instability of the ice-water interface. The proposed macro-scale morphological instability under a supercooled water film is quite different from the micro-scale one which results in dendritic growth. It was found that ice surface roughness spacing depends mainly on water layer thickness, and that surface roughness height is very sensitive to the convective heat transfer rate at the water-air interface. The present model takes into account the interaction between air and water flows through the boundary conditions at the water-air interface. This leads us to a major finding that tangential and normal shear stress disturbances due to airflow at the water-air interface play a crucial role not only on the convective heat transfer rate at the disturbed water-air interface but also on the height of the ice surface roughness. This is confirmed by comparison of the amplification rate of the ice-water interface disturbance predicted by the model with the roughness height observed experimentally.