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Sca.tering of wa.er wa.es by thin vertica. pla.e submerged below ice-cover surfa.e

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a.plied Ma.hema.ics a.d Mecha.ics(English Edition) 2011年第5期32卷 635-644页

作者： P.Ma.TI P.Ra.SHIT S.banerjea Depa.tment of Ma.hema.ics Ja.a.pur University Desha.ra. Birendra.a.h Institution For Boys

The present pa.er is concerned with sca.tering of wa.er wa.es from a.vertica. pla.e, modeled a. a. ela.tic pla.e, submerged in deep wa.er covered with a.thin uniform sheet of ice. The problem is formula.ed in terms of a.hypersingula. integra. equa.ion by a.suita.le a.plica.ion of Green＇s integra. theorem in terms of difference of potentia. functicns a.ross the ba.rier. This integra. equa.ion is solved by a.colloca.ion method using a.finite series involving Chebyshev polynomia.s. Reflection a.d tra.smission coefficients a.e obta.ned numerica.ly a.d presented gra.hica.ly for va.ious va.ues of the wa.e number a.d ice-cover pa.a.eter.

关键词： sca.tering problem ice-cover surfa.e hypersingula. integra. equa.ion Green's integra. theorem reflection a.d tra.smission coefficients

Wa.e Motion in a. Ice Covered Ocea. Due to Sma.l Oscilla.ions of a.Submerged Thin Vertica. Pla.e

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Journa. of Ma.ine Science a.d a.plica.ion 2015年第4期14卷 355-365页

作者： Pa.a.ita.Ma.ti Puspendu Ra.shit Sudeshna.banerjea Depa.tment of Ma.hema.ics Jadavpur University Kolkata 700032 India Depa.tment of Ma.hema.ics J. K. College Purulia West Bengal 723101 India

In this pa.er we study the problem of genera.ion of surfa.e wa.es produced due to a. rolling of the pla.e a.d b） presence of a.line source in front of a.fixed vertica. pla.e. The a.plitudes of ra.ia.ed wa.es a. la.ge dista.ce from the pla.e, in both ca.es, a.e obta.ned by a.suita.le a.plica.ion of Green＇s integra. theorem. These a.e then studied gra.hica.ly for va.ious va.ues of the ice cover pa.a.eter.

关键词： ice covered ocea. sma.l oscilla.ions thin pla.e wa.e motion wa.e a.plitude line source Green's integra. theorem

Effect of Bottom Undula.ion on the Wa.es Genera.ed Due to Rolling of a.Pla.e

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Journa. of Ma.ine Science a.d a.plica.ion 2011年第1期10卷 7-16页

作者： Puspendu Ra.shit Sudeshna.banerjea Desha.ra. Birendra.a.h Institution for Boys Depa.tment of Ma.hema.ics Jadavpur University

In the present pa.er, the effect of a.sma.l bottom tmdula.ion of the sea.bed in the form of periodic bed form on the surfa.e wa.es genera.ed due to a.rolling oscilla.ion of a.vertica. ba.rier either pa.tia.ly immersed or completely submerged in wa.er of non uniform finite depth is investiga.ed. a.simplified perturba.ion technique involving a.non dimensiona. pa.a.eter cha.a.terizing the sma.lness of the bottom deforma.ion is a.plied to reduce the given bounda.y va.ue problem to two independent bounda.y va.ue problems upto first order. The first bounda.y va.ue problem corresponds to the problem of wa.er wa.e genera.ion due to rolling oscilla.ion of a.vertica. ba.rier either pa.tia.ly immersed or completely submerged in wa.er of uniform finite depth. This is a.well known problem whose solution is a.a.la.le in the litera.ure. From the second bounda.y va.ue problem, the first order correction to the wa.e a.plitude a. infinity is eva.ua.ed in terms of the sha.e function cha.a.terizing the bottom undula.ion, by employing Green＇s integra. theorem. For a.pa.ch of sinusoida. ripples a. the sea.bottom, the first order correction to the wa.e a.plitude a. infinity for both the configura.ion of the ba.rier is then eva.ua.ed numerica.ly a.d illustra.ed gra.hica.ly for va.ious va.ues of the wa.e number. It is observed tha. resona.t intera.tion of the wa.e genera.ed, with the sinusoida. bottom undula.ion occurs when the ra.io of twice the wa.elength of the sinusoida. ripple to the wa.e length of wa.es genera.ed, a.proa.hes unity. a.so it is found tha. the resona.ce increa.es a. the length of the ba.rier increa.es.

关键词： bottom undula.ion rolling oscilla.ion pa.tia.ly immersed ba.rier submerged pla.e a.ticle