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Wave scattering by undulating bed topography in a two-layer ocean

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Abstract

The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape function. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    P. Maiti

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India

    B. N. Mandal

  3. Department of Applied Mathematics, Calcutta University, Kolkata, 700009, India

    U. Basu

Authors
  1. P. Maiti
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  2. B. N. Mandal
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  3. U. Basu
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Corresponding author

Correspondence to B. N. Mandal.

Additional information

P. MAITI was born in 1974. She is a research associate(CSIR) in the Department of Mathematics, Jadavpur University, Kolkata, India. Her current research interests include water wave problems.

B.N. MANDAL was born in 1943. He is a NASI Platinum Jubilee senior scientist in the Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India. His current research interests include water wave problems and associated mathematical techniques, integral equations, integral expansions, etc.

U. BASU was born in 1949. She is a professor in the Department Applied Mathematics, Calcutta University, India. Her current research interests include water wave problems, continuum mechanics, etc.

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Maiti, P., Mandal, B.N. & Basu, U. Wave scattering by undulating bed topography in a two-layer ocean. J. Marine. Sci. Appl. 8, 183–195 (2009). https://doi.org/10.1007/s11804-009-8063-7

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  • DOI: https://doi.org/10.1007/s11804-009-8063-7

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