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Oblique flexural gravity-wave scattering due to changes in bottom topography

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Abstract

Oblique flexural gravity-wave scattering due to an abrupt change in water depth in the presence of a compressive force is investigated based on the linearized water-wave theory in the case of finite water depth and shallow-water approximation. Using the results for a single step, wide-spacing approximation is used to analyze wave transformation by multiple steps and submerged block. An energy relation for oblique flexural gravity-wave scattering due to a change in bottom topography is derived using the argument of wave energy flux and is used to check the accuracy of the computation. The changes in water depth significantly contribute to the change in the scattering coefficients. In the case of oblique wave scattering, critical angles are observed in certain cases. Further, a resonating pattern in the reflection coefficients is observed due to change in the water depth irrespective of the presence of a compressive force in the case of a submerged block.

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Authors and Affiliations

  1. Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology, 721 302, Kharagpur, India

    D. Karmakar & T. Sahoo

  2. Centre for Marine Technology and Engineering, Technical University of Lisbon, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    J. Bhattacharjee

Authors
  1. D. Karmakar
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  2. J. Bhattacharjee
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  3. T. Sahoo
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Correspondence to T. Sahoo.

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Karmakar, D., Bhattacharjee, J. & Sahoo, T. Oblique flexural gravity-wave scattering due to changes in bottom topography. J Eng Math 66, 325–341 (2010). https://doi.org/10.1007/s10665-009-9297-8

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  • DOI: https://doi.org/10.1007/s10665-009-9297-8

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