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Bulge evolution on shallow water

Published online by Cambridge University Press:  16 June 2025

Shuo-Jun Teng ,
Jun-Hua Pan Open the ORCID record for Jun-Hua Pan [Opens in a new window]  and
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]
Shuo-Jun Teng
Affiliation:
Sino-Danish College, University of Chinese Academy of Sciences, Beijing 101408, PR China
Jun-Hua Pan
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics and University of Chinese Academy of Sciences, Beijing 100190, PR China
Ming-Jiu Ni*
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics and University of Chinese Academy of Sciences, Beijing 100190, PR China
*
Corresponding author: Ming-Jiu Ni, mjni@ucas.ac.cn
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Abstract

The phenomenon of bulge evolution under the action of gravity on shallow water is prevalent both in natural occurrences and engineering industries. However, despite its ubiquity, its physical process remains largely unexplored. The evolution of bulge contains two fundamental physical processes: collapse and propagation. The collapse process can be further divided into two sub-processes: squeezing process and diffusion process. Based on the weakly nonlinear shallow water assumption with the classical perturbation method, the governing equations controlling the surface elevations in the diffusion process and the propagation process have been theoretically derived, where a bulge-induced surface pressure is modeled for the propagation process. Moreover, their scaling laws for the decay of wave height are also established, which have been validated by direct numerical simulation results. The derived scaling laws for wave height attenuation of bulge evolution provide profound insights, which hold the potential to applications in the engineering industry.

JFM classification

Geophysical and Geological Flows: Shallow water flows Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1013 , 25 June 2025 , A15
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

These authors contributed equally to this work and should be considered co-first authors.

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