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

Fractals Pub Date : 2024-02-28 DOI:10.1142/s0218348x24500403
YAN WANG, WEIFAN HOU, KHALED GEPREEL, HONGJU LI
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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.

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考虑近岸分形边界的分形-分形海啸模型
每一个流体问题都会受到其边界条件的极大影响,尤其是近岸海床在海啸来临时可能会产生无法挽回的危害,而现实中的数学模型可以避免最坏的影响。本文假定不光滑的海底是一个分形面,并根据分形空间的物理规律建立了分形-分形控制方程。利用几何势理论解释波浪表面产生的力,并应用孔和摩擦定律进一步阐明分形边界摩擦的局部性和记忆性。本文旨在研究分形空间中的海啸波,为预测海啸运动和海岸保护提供可靠的数学模型。
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