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Construction of wave-free potential in the linearized theory of water waves

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Abstract

Various water wave problems involving an infinitely long horizontal cylinder floating on the surface water were investigated in the literature of linearized theory of water waves employing a general multipole expansion for the wave potential. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation (for non-oblique waves in two dimensions) or two-dimensional Helmholz equation (for oblique waves) satisfying the free surface condition and decaying rapidly away from the point of singularity. The method of constructing these wave-free potentials is presented here in a systematic manner for a number of situations such as deep water with a free surface, neglecting or taking into account the effect of surface tension, or with an ice-cover modelled as a thin elastic plate floating on water.

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Authors and Affiliations

  1. Department of Mathematics, Shibpur Dhinbundhoo Institution (College), 412/1 G. T. Road, Howrah, 711102, India

    Dilip Das

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700 108, India

    B. N. Mandal

Authors
  1. Dilip Das
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  2. B. N. Mandal
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Correspondence to B. N. Mandal.

Additional information

Foundation item: Partially Supported by a NASI Senior Scientist Fellowship to BNM and a DST Research Project no. SR/S4/MS: 521/08.

Dilip Das was born in 1981. He is working as an Assistant Professor in the Department of Mathematics, Shibpur Dinobundhoo Institution (College), Howrah, West Bengal, India. His 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.

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Das, D., Mandal, B.N. Construction of wave-free potential in the linearized theory of water waves. J. Marine. Sci. Appl. 9, 347–354 (2010). https://doi.org/10.1007/s11804-010-1019-0

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  • DOI: https://doi.org/10.1007/s11804-010-1019-0

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