Skip to main content
×
×
Home

On the coupled time-harmonic motion of water and a body freely floating in it

  • NIKOLAY KUZNETSOV (a1) and OLEG MOTYGIN (a1)
Abstract

We consider a spectral problem that describes the time-harmonic small-amplitude motion of the mechanical system that consists of a three-dimensional water layer of constant depth and a body (either surface-piercing or totally submerged), freely floating in it. This coupled boundary-value problem contains a spectral parameter – the frequency of oscillations – in the boundary conditions as well as in the equations governing the body motion. It is proved that the total energy of the water motion is finite and the equipartition of energy of the whole system is established. Under certain restrictions on body's geometry the problem is proved to have only a trivial solution for sufficiently large values of the frequency. The uniqueness frequencies are estimated from below.

Copyright
Corresponding author
Email address for correspondence: nikolay.g.kuznetsov@gmail.com
References
Hide All
Beale, J. T. 1977 Eigenfunction expansions for objects floating in an open sea. Commun. Pure Appl. Math. 30, 283313.
Evans, D. V. & Porter, R. 2007 Wave-free motions of isolated bodies and the existence of motion-trapped modes. J. Fluid Mech. 584, 225234.
Fitzgerald, C. J. & McIver, P. 2010 Passive trapped modes in the water-wave problem for a floating structure. J. Fluid Mech. 657, 456477.
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. 2010 On the problem of time-harmonic water waves in the presence of a freely-floating structure. Algebra Analiz. 22 (6), 185199.
Kuznetsov, N. G. 2008 On uniqueness of a solution to the plane problem on interaction of surface waves with obstacle. J. Math. Sci. 150, 18601868.
Kuznetsov, N., Maz'ya, V. & Vainberg, B. 2002 Linear Water Waves: A Mathematical Approach. Cambridge University Press.
Linton, C. M. & McIver, P. 2007 Embedded trapped modes in water waves and acoustics. Wave Motion 45, 1629.
McIver, P. & McIver, M. 2006 Trapped modes in the water-wave problem for a freely-floating structure. J. Fluid Mech. 558, 5367.
McIver, P. & McIver, M. 2007 Motion trapping structures in the three-dimensional water-wave problem. J. Engng Math. 58, 6775.
Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005 Theory and Applications of Ocean Surface Waves. Part 1: Linear Aspects. World Scientific.
Nazarov, S. A. 2011 Incomplete comparison principle in problems about surface waves trapped by fixed and freely floating bodies. J. Math. Sci. 175, 309348.
Nazarov, S. A. & Videman, J. H. 2011 Trapping of water waves by freely floating structures in a channel. Proc. R. Soc. Lond. A (submitted).
Newman, J. N. 2008 Trapping of water waves by moored bodies. J. Engng Math. 62, 303314.
Porter, R. & Evans, D. V. 2008 Examples of trapped modes in the presence of freely floating structures. J. Fluid Mech. 606, 189207.
Porter, R. & Evans, D. V. 2009 Water-wave trapping by floating circular cylinders. J. Fluid Mech. 633, 311325.
Weck, N. 1990 On a boundary value problem in the theory of linear water-waves. Math. Meth. Appl. Sci. 12, 393404.
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? *
×
MathJax

JFM classification

Metrics

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