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Water wave propagation over an infinite trench

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Propagation of water waves over an infinite trench is examined here assuming linear theory where waves are incident from the direction of either negative infinity or positive infinity. For each case, the problem is reduced to solving coupled weakly singular integral equations of first kind involving horizontal component of velocity above the two edges of the trench. The integral equations are solved employing Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions at the corners of the trench. The numerical estimates for reflection and transmission coefficients are depicted graphically against the wave number for different distance between the trenches and also for different heights of the asymmetric trench.

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Acknowledgements

The authors thank the reviewers for their comments and suggestions to revise the paper in its present from. SR thanks CSIR (File No. 09/028(1018)/2017-EMR-I), New Delhi, for providing financial assistance.

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Authors and Affiliations

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

    Swagata Ray & Soumen De

  2. Physics and Applied Mathematics Unit Indian Statistical Institute, 203, B.T. Road, Kolkata, 700 108, India

    B. N. Mandal

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  1. Swagata Ray
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Ray, S., De, S. & Mandal, B.N. Water wave propagation over an infinite trench. Z. Angew. Math. Phys. 73, 46 (2022). https://doi.org/10.1007/s00033-022-01682-3

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  • DOI: https://doi.org/10.1007/s00033-022-01682-3

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