Skip to main content Accesibility Help

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

  • Nikolay Kuznetsov (a1) and Oleg Motygin (a1)

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.

Corresponding author
Email address for correspondence:
Hide All
Gabov, S. A. & Sveshnikov, A. G. 1991 Problems in the dynamics of flotation liquids. J. Sov. Math. 54, 9791041.
Hariprasad, C. 2011 Brash ice. In Encyclopedia of Snow, Ice and Glaciers (ed. Singh, V. P., Singh, P. & Haritashya, U. K.), pp. 103104. Springer.
John, F. 1949 On the motion of floating bodies, I. Commun. Pure Appl. Math. 2, 1357.
John, F. 1950 On the motion of floating bodies, II. Commun. Pure Appl. Math. 3, 45101.
Kuznetsov, N. 2011 On the problem of time-harmonic water waves in the presence of a freely-floating structure. St. Petersburg Math. J. 22, 985995.
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, 684700.
Kuznetsov, N., Maz’ya, V. & Vainberg, B. 2002 Linear Water Waves: A Mathematical Approach. Cambridge University Press.
Kuznetsov, N. & Motygin, O. 2011 On the coupled time-harmonic motion of water and a body freely floating in it. J. Fluid Mech. 679, 616627.
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, 142162.
Kuznetsov, N. & Motygin, O. 2015 Freely floating structures trapping time-harmonic water waves. Q. J. Mech. Appl. Maths 68, 173193.
Linton, C. M. & McIver, P. 2001 Handbook of Mathematical Techniques for Wave/Structure Interactions. Chapman & Hall/CRC.
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, 271278.
Mellor, M. 1980 Ship resistance in thick brash ice. Cold Reg. Sci. Technol. 3, 305321.
Peters, A. S. 1950 The effect of a floating mat on water waves. Commun. Pure Appl. Maths 3, 319354.
Rhodes-Robinson, P. F. 1984 On the generation of water waves at an inertial surface. J. Austral. Math. Soc. B 25, 366383.
Starosolszky, Ö. 1977 Multilingual Ice Terminology. Research Centre for Water Resources.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed