Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (5): 635-644.doi: https://doi.org/10.1007/s10483-011-1445-7

• Articles • 上一篇    下一篇

Scattering of water waves by thin vertical plate submerged below ice-cover surface

 P. MAITI1, P.RAKSHIT2, S. BANERJEA1   

  1. 1. Department of Mathematics, Jadavpur University, Kolkata 700032, India;
    2. Deshapran Birendranath Institution For Boys, 198-B S.P. Mukherjee Road, Kolkata 700026, India
  • 收稿日期:2010-10-28 修回日期:2011-03-22 出版日期:2011-04-27 发布日期:2011-05-01

Scattering of water waves by thin vertical plate submerged below ice-cover surface

 P. MAITI1, P.RAKSHIT2, S. BANERJEA1   

  • Received:2010-10-28 Revised:2011-03-22 Online:2011-04-27 Published:2011-05-01

摘要: The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green’s integral theorem in terms of difference of potential functions across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.

Abstract: The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green’s integral theorem in terms of difference of potential functions across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.

中图分类号: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals