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Interaction of water waves with small undulations on a porous bed in a two-layer ice-covered fluid

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Abstract

The scattering problem involving water waves by small undulation on the porous ocean-bed in a two-layer fluid, is investigated within the framework of the two-dimensional linear water wave theory where the upper layer is covered by a thin uniform sheet of ice modeled as a thin elastic plate. In such a two-layer fluid there exist waves with two different modes, one with a lower wave number propagate along the ice-cover whilst those with a higher wave number propagate along the interface. An incident wave of a particular wave number gets reflected and transmitted over the bottom undulation into waves of both modes. Perturbation analysis in conjunction with the Fourier transform technique is used to derive the first-order corrections of reflection and transmission coefficients for both the modes due to incident waves of two different modes. One special type of bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are depicted in graphical forms to demonstrate the transformation of wave energy between the two modes and also to illustrate the effects of the ice sheet and the porosity of the undulating bed.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, 140001, Punjab, India

    Srikumar Panda & S. C. Martha

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  1. Srikumar Panda
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  2. S. C. Martha
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Correspondence to S. C. Martha.

Additional information

Foundation item: Supprted by the ISIRD grant (Ref. No. 16-3/10/IITRPR/ Acad/116).

Srikumar Panda received his M. Sc. in Mathematics and Computing from the Indian Institute of Technology, Guwahati, India in 2010. He is now studying as a Ph.D. student at the Indian Institute of Technology, Ropar, India under the CSIR Senior Research Fellowship. His main areas of interest are water wave scattering in a multilayered fluid, nonlinear fluid flow problems and Singular Integral Equations.

Subash Chandra Martha is an Assistant Professor at the Department of Mathematics, Indian Institute of Technology Ropar, India. He received his Ph.D. from the Indian Institute of Technology, Guwahati, India in 2007. He also worked as a NBHM post doctoral fellow at the Indian Institute of Science, Bangalore, India. His main areas of interest are Fluid dynamics, Mathematical modeling on water wave phenomena and Integral Equations.

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Panda, S., Martha, S.C. Interaction of water waves with small undulations on a porous bed in a two-layer ice-covered fluid. J. Marine. Sci. Appl. 12, 381–392 (2013). https://doi.org/10.1007/s11804-013-1208-8

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  • DOI: https://doi.org/10.1007/s11804-013-1208-8

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