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Wave scattering by a circular cylinder over a porous bed

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Abstract

The dispersion of waves over a permeable seabed due to the presence of a vertically floating rigid circular cylinder is investigated under the assumptions of the linearized water wave theory and small-amplitude surface waves. Using the radiation condition and boundary conditions, the unknown potentials for the free-surface region and for the region covered by the cylinder are determined. The velocity potentials of the incident and scattered waves are expanded using the Bessel and Hankel functions for each region in the problem. The eigenfunction expansion technique is employed to solve the resulting boundary value problem. The effectiveness of the study is accessed by demonstrating the wave forces on the circular cylinder and the flow distribution along with the temporal simulation of the flow for different parameters. It is shown that the presence of a floating circular cylinder over the porous seabed reduces the amplitude of a surface wave on the leeside of the structure significantly. It is also illustrated that the radius and height of the cylinder play a significant role in reducing the wave forces on the cylinder and, hence, in creating a calm region in the leeside of the structure. The proposed setup has the potential to help design offshore structures that are capable of reducing the impact of the wave forces on the coastal structures, which can then safely be used for various marine operations.

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Acknowledgements

A.K.K. gratefully acknowledges the financial support from the Council of Scientific and Industrial Research (CSIR) [09/1022(12263)/2021-EMR-I]. A.K.K. and V.K.G. also express their gratitude to the DST-FIST Project SR/FST/MS I/2018/26 for their support toward the Bhaskaracharya Mathematics Laboratory and Brahmagupta Mathematics Library that have been used to carry out this work. H.B. gratefully acknowledges the financial support from SERB, Department of Science and Technology, Government of India, through the “CRG" project, Award No. CRG/2022/006698.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Indore, Indore, 453552, India

    Aman Kumar Kushwaha & Vinay Kumar Gupta

  2. Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai, 603203, India

    Harekrushna Behera

  3. Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung, 202301, Taiwan

    Harekrushna Behera

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  1. Aman Kumar Kushwaha
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Contributions

A.K.K. contributed to Coding, Writing-original draft, Formal analysis, Replying to reviewers’ comments. H.B. contributed to Conceptualization, Coding, Writing-review and editing, Replying to reviewers’ comments. V.K.G. contributed to Writing-review and editing, Replying to reviewers’ comments, Supervision.

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Correspondence to Harekrushna Behera.

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Kushwaha, A.K., Behera, H. & Gupta, V.K. Wave scattering by a circular cylinder over a porous bed. Arch Appl Mech 94, 555–570 (2024). https://doi.org/10.1007/s00419-023-02536-8

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