Water wave scattering by an infinite step in the presence of an ice-cover

• Autorzy: Ray S. , De S. , Mandal B. N.

Identyfikatory

DOI

10.2478/ijame-2019-0055

• Języki publikacji: EN

Abstrakty

EN

The classical problem of water wave scattering by an infinite step in deep water with a free surface is extended here with an ice-cover modelled as a thin uniform elastic plate. The step exists between regions of finie and infinite depths and waves are incident either from the infinite or from the finite depth water region. Each problem is reduced to an integral equation involving the horizontal component of velocity across the cut above the step. The integral equation is solved numerically using the Galerkin approximation in terms of simple polynomial multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge of the step. The reflection and transmission coefficients are obtained approximately and their numerical estimates are seen to satisfy the energy identity. These are also depicted graphically against thenon-dimensional frequency parameter for various ice-cover parameters in a number of figures. In the absencje of ice-cover, the results for the free surface are recovered.

Słowa kluczowe

EN

water wave scattering; ice cover; infinite step; integral equation; Galerkin approximation; reflection and transmission coefficients

PL

fala wodna; pokrywa lodowa; aproksymacja Galerkina

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2019
• Tom: Vol. 24, no. 4
• Strony: 157--168
• Opis fizyczny: Bibliogr. 8 poz., wykr.

Twórcy

autor

Ray S.

• Department of Applied Mathematics, University of Calcutta 92, A.P.C. Road, Kolkata- 700009, INDIA

autor

De S.

• Department of Applied Mathematics, University of Calcutta 92, A.P.C. Road, Kolkata- 700009, INDIA

autor

Mandal B. N.

• Physics and Applied Mathematics Unit, Indian Statistical Institute 203, B.T. Road, Kolkata-700 108, INDIA

Bibliografia

• [1] Fox C. and Squire V.A. (1994):On the oblique reflection and transmission of ocean waves at shore fast sea ice. Phil. Trans. R. Soc. London, A347, pp.185-218.
• [2] Hermans A.J. (2004):Interaction of free surface waves with floating flexible strips. J. Engg. Math., vol.49, pp.133-147.
• [3] Gayen R., Mandal B.N. and Chakrabarti A. (2005): Water wave scattering by an ice-strip. J. Engg. Math., vol.53, pp.21-37.
• [4] Newman J.N. (1965): Propagation of water waves over an infinite step. J. Fluid Mech., vol.23, pp.399-415.
• [5] Chung F. and Fox C. (2002): Calculation of wave ice interaction using Wiener-Hopf technique. New Zealand J. Math., vol.31, pp.1-18.
• [6] Havelock T.H. (1929): Forced surface waves on water. Phillos. Mag, vol.8, pp.569-576.
• [7] Manam S.R., Bhattacharjee J. and Sahoo T. (2005): Expansion Formulae in wave structure interaction problems. Proc. R. Soc., A462, pp.263-287.
• [8] Das D., Mandal B.N. and Chakrabarti A. (2008): Energy identities in water wave theory for free surface boundary condition with higher order derivatives. Fluid Dynamics Res., vol.40, pp.253-272.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)