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Ring-like ripples on the surface of icicles are an example of morphologicalinstability of the ice-water interface during ice growth under supercooledwater film flow. The surface of icicles is typically covered with ripples ofabout 1 cm in wavelength, and the wavelength appears to be almost independentof external temperature, icicle radius, and volumetric water flow rate. Oneside of the water layer consists of the water-air surface and growing ice isthe other. This is one of the more complicated moving phase boundary problemswith two interfaces. A recent theoretical work [K. Ueno, Phys. Rev. E 68,(2003) 021603] to address the underlying instability that produces ripples isbased on the assumption of the absence of airflow around icicles. In thispaper, we extend the previous theoretical framework to include a naturalconvection airflow ahead of the water-air surface and consider whether theeffect of natural convection airflow on the wavelength of ripples produced onan ice surface is essential or not.

Morphological instability of the solid-liquid interface in crystal growth under supercooled liquid film flow and natural convection airflow