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Water wave propagation over multiple porous barriers with variable porosity in the presence of an ice cover

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Abstract

A semi-analytical method is applied to investigate the propagation of flexural wave over multiple bottom-standing porous barriers with variable porosity beneath an ice cover under the assumption of linearised theory of water waves. Eigenfunction expansion method is used to express the velocity potential explicitly in terms of non-orthogonal eigenfunctions. Utilizing mode coupling relations satisfied by aforesaid eigenfunctions, the boundary value problem is reduced to a set of coupled Fredholm-type integral equations. These integral equations are solved by multi-term Galerkin’s method involving the Chebychev polynomials (multiplied by proper weights) as basis functions . The reflection and transmission coefficients, hydrodynamic forces and dissipated wave energy at the barriers are presented both analytically and graphically. A notable effect of the porosity of barriers and flexural rigidity of the ice cover on wave propagation is recorded. Bragg resonance of the flexural gravity waves due to the presence of four vertical porous barriers is observed and shown graphically. Efficiency of the present study is confirmed through a good agreement of the present results and the existing results available in the literature.

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Acknowledgements

The authors thank the reviewers for their comments and suggestions to improve the article in the present form. This work is completely supported by Higher Education, Science and Technology and Bio-Technology, Government of West Bengal Memo no: 14(Sanc.)/ST/P/S&T/16G-38/2017.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata, 700 009, India

    Biman Sarkar & Soumen De

  2. Dr. B. C. Roy Engineering College, Durgapur, 713206, India

    Sandip Paul

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  1. Biman Sarkar
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  2. Sandip Paul
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  3. Soumen De
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Correspondence to Soumen De.

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Sarkar, B., Paul, S. & De, S. Water wave propagation over multiple porous barriers with variable porosity in the presence of an ice cover. Meccanica 56, 1771–1788 (2021). https://doi.org/10.1007/s11012-021-01341-3

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