# Pattern formation in crystal growth under parabolic shear flow II

Source: [Pattern formation in crystal growth under parabolic shear flow II](<https://www.sota2.com/research/paper/68fa26712c2a3760193ba0a0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:23:03.993Z

Authors: K. Ueno

Published: 2004-01-28T22:01:17.000Z

## Abstract

Wavy pattern of ice with a specific wavelength occurs during ice growth from a thin layer of undercooled water flowing down the surface of icicles or inclined plane. In the preceding paper \[K. Ueno, Phys. Rev. E {\\bf 68}, 021603 (2003)\], we have found that restoring forces due to gravity and surface tension is a factor for stabilization of morphological instability of the solid-liquid interface. However, the mechanism for the morphological instability and stability of the solid-liquid interface has not been well understood. In the present paper, it is shown that a phase difference between fluctuation of the solid-liquid interface and distribution of heat flux at the deformed solid-liquid interface, which depends on the magnitude of the restoring forces, is a cause of the instability and stability of the interface. This mechanism is completely different from the usual Mullins-Sekerka instability due to diffusion and stabilization due to the Gibbs-Thomson effect.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0401593>)

[PDF](<https://arxiv.org/pdf/cond-mat/0401593.pdf>)