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Pattern formation on an ice surface

Published online by Cambridge University Press:  23 June 2025

Zhihua Wang Open the ORCID record for Zhihua Wang [Opens in a new window] ,
Kwing-So Choi Open the ORCID record for Kwing-So Choi [Opens in a new window] ,
Shuguang Li Open the ORCID record for Shuguang Li [Opens in a new window] ,
Chao Sun Open the ORCID record for Chao Sun [Opens in a new window]  and
Xuerui Mao Open the ORCID record for Xuerui Mao [Opens in a new window]
Zhihua Wang
Affiliation:
Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD, UK
Kwing-So Choi
Affiliation:
Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD, UK
Shuguang Li
Affiliation:
Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD, UK
Chao Sun
Affiliation:
Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
Xuerui Mao*
Affiliation:
Beijing Institute of Technology (Zhuhai), Zhuhai 519087, PR China School of Interdisciplinary Science, Beijing Institute of Technology, Beijing 100081, PR China
*
Corresponding author: Xuerui Mao, maoxuerui@sina.com
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Abstract

A linear stability model based on a phase-field method is established to study the formation of ripples on the ice surface. The pattern on horizontal ice surfaces, e.g. glaciers and frozen lakes, is found to be originating from a gravity-driven instability by studying ice–water–air flows with a range of water and ice thicknesses. Contrary to gravity, surface tension and viscosity act to suppress the instability. The results demonstrate that a larger value of either water thickness or ice thickness corresponds to a longer dominant wavelength of the pattern, and a favourable wavelength of 90 mm is predicted, in agreement with observations from nature. Furthermore, the profiles of the most unstable perturbations are found to be with two peaks at the ice–water and water–air interfaces whose ratio decreases exponentially with the water thickness and wavenumber.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Nonlinear Dynamical Systems: Pattern formation Phase change: Morphological instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1013 , 25 June 2025 , A35
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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