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Effect of bottom topography on wave scattering by multiple porous barriers

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Abstract

Scattering of obliquely incident surface gravity waves by multiple porous barriers is studied in the presence of step type varying bottom topography. The bottom bed consists of a finite interval of uneven geometry which is connected by two semi-infinite intervals of uniform water depths. An array of porous barriers are located on water of uniform depth on the lee side of bottom variations. Using small amplitude wave theory and Darcy’s law for flow past porous structure, the physical problem is converted into a boundary value problem which is handled for solution using coupled eigenfunction expansion in uniform bottom regions and modified mild-slope equation in varying bottom region. Further, certain jump conditions are used for the conservation of mass flux at slope discontinuities in bottom profile. To understand the effect of variations in bottom topography on wave scattering by multiple porous barriers, physical quantities such as reflection and transmission coefficients, wave forces on the barriers are computed and analyzed for different values of depth ratio, varying bottom parameter, porous-effect parameter, incident wave angle, spacing between the barriers and slope length of varying bottom. In the presence of ripple bottom bed, effect of multiple porous barriers on Bragg scattering is analyzed. Certain drift in Bragg reflection is noticed due to propagation of oblique incident waves over step type ripple beds.

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Acknowledgements

The authors thank the reviewers for their valuable comments to improve the presentation of this paper. Saista Tabssum expresses her gratitude to CTS, IIT Kharagpur for giving support under visitors program during which the revised manuscript was finalized.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, 826004, India

    R. B. Kaligatla & S. Tabssum

  2. Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    T. Sahoo

Authors
  1. R. B. Kaligatla
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  2. S. Tabssum
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  3. T. Sahoo
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Correspondence to R. B. Kaligatla.

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Kaligatla, R.B., Tabssum, S. & Sahoo, T. Effect of bottom topography on wave scattering by multiple porous barriers. Meccanica 53, 887–903 (2018). https://doi.org/10.1007/s11012-017-0790-2

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  • DOI: https://doi.org/10.1007/s11012-017-0790-2

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