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A Fractal-Fractional Tsunami Model Considering Near-Shore Fractal Boundary

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yan Wang & Weifan Hou & Khaled Gepreel & Hongju Li, 2024. "A Fractal-Fractional Tsunami Model Considering Near-Shore Fractal Boundary," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-6.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24500403
    DOI: 10.1142/S0218348X24500403
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