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Propagation of Water Waves in the Presence of Thin Vertical Barrier on the Bottom Undulation

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Mathematics and Computing 2013

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 91))

Abstract

The problem involving diffraction of water waves by submerged thin vertical barrier over irregular bottom is examined using linearized theory of water waves. While formulating the problem mathematically, a mixed boundary value problem (BVP) occurs. The problem is solved using perturbation theory along with least-squares method and Green’s integral theorem. The first order reflection and transmission coefficients are obtained in terms of integrals involving the shape function \(c(x)\) representing the bottom undulation and the solution of the scattering problem by the submerged barrier. A special case of bottom undulation is considered to evaluate the first order reflection and transmission coefficients in detail. The numerical results of these coefficients are shown graphically.

A. Choudhary is grateful to the University Grants Commission (UGC), Government of India, for providing the Junior Research Fellowship for pursuing Ph.D. degree at the Indian Institute of Technology Ropar, India. S. C. Martha thanks the Indian Institute of Technology Ropar, India, for providing all necessary facilities.

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Authors and Affiliations

  1. Indian Institute of Technology Ropar, Nangal Road, Rupnagar, 140001, Punjab, India

    A. Choudhary & S. C. Martha

Authors
  1. A. Choudhary
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  2. S. C. Martha
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Corresponding author

Correspondence to A. Choudhary .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  2. Dept of Computer Science & Engineering, Haldia Institute of Technology, Haldia, India

    Debasis Giri

  3. Ministry of Defence, Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, Delhi, India

    P. K. Saxena

  4. Department of Mathematics, India Institute of Technology, Kharagpur, West Bengal, India

    P. D. Srivastava

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Choudhary, A., Martha, S.C. (2014). Propagation of Water Waves in the Presence of Thin Vertical Barrier on the Bottom Undulation. In: Mohapatra, R., Giri, D., Saxena, P., Srivastava, P. (eds) Mathematics and Computing 2013. Springer Proceedings in Mathematics & Statistics, vol 91. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1952-1_1

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