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On the coupled time-harmonic motion of a freely floating body and water covered by brash ice

Published online by Cambridge University Press:  14 April 2016

Nikolay Kuznetsov  and
Oleg Motygin
Nikolay Kuznetsov*
Affiliation:
Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol’shoy pr. 61, St Petersburg 199178, Russian Federation
Oleg Motygin
Affiliation:
Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol’shoy pr. 61, St Petersburg 199178, Russian Federation
*
†Email address for correspondence: nikolay.g.kuznetsov@gmail.com
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Abstract

A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 174 - 186
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Copyright
© 2016 Cambridge University Press 

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References

Gabov, S. A. & Sveshnikov, A. G. 1991 Problems in the dynamics of flotation liquids. J. Sov. Math. 54, 979–1041.Google Scholar
Hariprasad, C. 2011 Brash ice. In Encyclopedia of Snow, Ice and Glaciers (ed. Singh, V. P., Singh, P. & Haritashya, U. K.), pp. 103–104. Springer.Google Scholar
John, F. 1949 On the motion of floating bodies, I. Commun. Pure Appl. Math. 2, 13–57.Google Scholar
John, F. 1950 On the motion of floating bodies, II. Commun. Pure Appl. Math. 3, 45–101.CrossRefGoogle Scholar
Kuznetsov, N. 2011 On the problem of time-harmonic water waves in the presence of a freely-floating structure. St. Petersburg Math. J. 22, 985–995.Google Scholar
Kuznetsov, N. 2015 Two-dimensional water waves in the presence of a freely floating body: trapped modes and conditions for their absence. J. Fluid Mech. 779, 684–700.Google Scholar
Kuznetsov, N., Maz’ya, V. & Vainberg, B. 2002 Linear Water Waves: A Mathematical Approach. Cambridge University Press.Google Scholar
Kuznetsov, N. & Motygin, O. 2011 On the coupled time-harmonic motion of water and a body freely floating in it. J. Fluid Mech. 679, 616–627.Google Scholar
Kuznetsov, N. & Motygin, O. 2012 On the coupled time-harmonic motion of deep water and a freely floating body: trapped modes and uniqueness theorems. J. Fluid Mech. 703, 142–162.CrossRefGoogle Scholar
Kuznetsov, N. & Motygin, O. 2015 Freely floating structures trapping time-harmonic water waves. Q. J. Mech. Appl. Maths 68, 173–193.Google Scholar
Linton, C. M. & McIver, P. 2001 Handbook of Mathematical Techniques for Wave/Structure Interactions. Chapman & Hall/CRC.Google Scholar
Mandal, B. N. & Kundu, K. 1986 A note on the singularities in the theory of water waves with an inertial surface. J. Austral. Math. Soc. B 28, 271–278.Google Scholar
Mellor, M. 1980 Ship resistance in thick brash ice. Cold Reg. Sci. Technol. 3, 305–321.CrossRefGoogle Scholar
Peters, A. S. 1950 The effect of a floating mat on water waves. Commun. Pure Appl. Maths 3, 319–354.CrossRefGoogle Scholar
Rhodes-Robinson, P. F. 1984 On the generation of water waves at an inertial surface. J. Austral. Math. Soc. B 25, 366–383.Google Scholar
Starosolszky, Ö. 1977 Multilingual Ice Terminology. Research Centre for Water Resources.Google Scholar