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Citation:
　Dilip Das and B. N. Mandal.Construction of Wave-free Potential in the Linearized Theory of Water Waves[J].Journal of Marine Science and Application,2010,(4):347-354.
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Construction of Wave-free Potential in the Linearized Theory of Water Waves

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Title:
Construction of Wave-free Potential in the Linearized Theory of Water Waves
Author(s):
Dilip Das and B. N. Mandal
Affilations:
Author(s):
Dilip Das and B. N. Mandal
1. Shibpur Dhinbundhoo Institution (College), Department of Mathematics, 412/1 G. T. Road, Howrah-711102, India 2. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India
Keywords:
wave-free potential;  free surface;  surface tension;  ice-cover;  Laplace equation;  Helmholz equation
分类号:
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DOI:
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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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Last Update: 2011-04-29