A FRACTAL-FRACTIONAL TSUNAMI MODEL CONSIDERING NEAR-SHORE FRACTAL BOUNDARY

Yan Wang, Weifan Hou (), Khaled Gepreel and Hongju Li
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Yan Wang: School of Science, Tianjin University of Commerce, Tianjin 300134, P. R. China†Tianjin Yi-Sheng Offshore Engineering Co. Ltd., Tianjin 300400, P. R. China
Weifan Hou: ��Basic Department, Shaanxi Institute of Fashion Engineering, Shaanxi 712000, P. R. China
Khaled Gepreel: �Department of Mathematics, College of Science, Taif University, Taif, Saudi Arabia
Hongju Li: ��Tianjin Yi-Sheng Offshore Engineering Co. Ltd., Tianjin 300400, P. R. China¶Tianjin Tianwei Chemical Engineering Co. Ltd., Tianjin 300400, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-6

Abstract: Every fluid problem is greatly affected by its boundary conditions, especially the near-shore seabed could produce an irrevocable harm when a tsunami wave is approaching, and a real-life mathematical model could stave off the worst effect. This paper assumes that the unsmooth seabed is a fractal surface, and fractal-fractional governing equations are established according to physical laws in the fractal space. The geometrical potential theory is used to explain the force produced by the wave surface, and Kong-He friction law is applied to further figuring out the local and memory properties of the friction along the fractal boundary. This paper aims at studying tsunami waves in a fractal space, rendering a reliable mathematical model for both prediction of the tsunami motion and the coastal protection.

Keywords: Two-Scale Fractal Theory; Fractal Soliton Theory; Fractal Derivative; Mass Conservation in the Fractal Space; Navier-Stokes Equations in a Fractal Space; He-Liu Fractal Dimensions (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500403

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