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Oblique wave scattering by an impermeable ocean-bed of variable depth in a two-layer fluid with ice-cover

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Abstract

Within the framework of linearized theory, obliquely incident water wave scattering by an uneven ocean-bed in the form of a small bottom undulation in a two-layer fluid, where the upper layer has a thin ice-cover while the lower one has the undulation, is investigated here. In such a two-layer fluid, there exist two modes of time-harmonic waves—the one with lower wave number propagating just below the ice-cover and the one with higher wave number along the interface. An incident wave of a particular mode gets reflected and transmitted by the bottom undulations into waves of both the modes. Assuming irrotational motion, a perturbation technique is employed to solve the first-order corrections to the velocity potentials in the two-layer fluid by using Fourier transform appropriately and also to calculate the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom undulation. For a sinusoidal bottom topography, these coefficients are depicted graphically against the wave number. It is observed that when the oblique wave is incident on the ice-cover surface, we always find energy transfer to the interface, but for interfacial oblique incident waves, there are parameter ranges for which no energy transfer to the ice-cover surface is possible.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Chemical Technology, Matunga, Mumbai, 400 019, India

    S. Mohapatra

  2. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781 039, India

    S. N. Bora

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  1. S. Mohapatra
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  2. S. N. Bora
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Correspondence to S. N. Bora.

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Mohapatra, S., Bora, S.N. Oblique wave scattering by an impermeable ocean-bed of variable depth in a two-layer fluid with ice-cover. Z. Angew. Math. Phys. 63, 879–903 (2012). https://doi.org/10.1007/s00033-012-0210-3

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  • DOI: https://doi.org/10.1007/s00033-012-0210-3

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