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 Rajdeep Maiti,Uma Basu,B. N. Mandal.Oblique Wave-free Potentials for Water Waves in Constant Finite Depth[J].Journal of Marine Science and Application,2015,(2):126-137.[doi:10.1007/s11804-015-1299-5]
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Oblique Wave-free Potentials for Water Waves in Constant Finite Depth


Oblique Wave-free Potentials for Water Waves in Constant Finite Depth
Rajdeep Maiti Uma Basu and B. N. Mandal
Rajdeep Maiti1; Uma Basu1; B. N. Mandal2
1. Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India;
2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700035, India
wave-free potentials modified Helmholtz equation free surface surface tension ice-cover water wave
In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform finite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.


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Received date: 2014-8-19          Accepted date:2014-12-22
Corresponding author: S. Bhattacharyya        E-mail:somnath@maths.iitkgp.ernet.in
Last Update: 2016-06-23