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Unsteady three-dimensional sources in deep water with an elastic cover and their applications

Published online by Cambridge University Press:  01 August 2013

Izolda V. Sturova
Izolda V. Sturova*
Affiliation:
Lavrentyev Institute of Hydrodynamics, av. Lavrentyev 15, 630090 Novosibirsk, Russia
*
†Email address for correspondence: sturova@hydro.nsc.ru
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Abstract

The velocity potential is derived for a transient source of arbitrary strength undergoing arbitrary three-dimensional motion. The initially quiescent fluid of infinite depth is assumed to be inviscid, incompressible and homogeneous. The upper surface of the fluid is covered by a thin layer of elastic material of uniform density with lateral stress. The linearized initial boundary-value problem is formulated within the framework of the potential-flow theory, and the Laplace transform technique is employed to obtain the solution. The potential of a time-harmonic source with forward speed is obtained as a particular case. The far-field wave motion at long time is determined via the method of stationary phase. The problems of radiation (surge, sway and heave) of the flexural–gravity waves by a submerged sphere advancing at constant forward speed are investigated. The method of multipole expansions is used. Numerical results are obtained for the wave-making resistance and lift, added-mass and damping coefficients. The effects of an ice sheet and broken ice on the hydrodynamic loads are discussed in detail.

JFM classification

Waves/Free-surface Flows: Elastic waves Geophysical and Geological Flows: Ice sheets Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 730 , 10 September 2013 , pp. 392 - 418
Copyright
©2013 Cambridge University Press 

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References

Born, M. & Wolf, E. 1964 Principles of Optics. Pergamon.Google Scholar
Bukatov, A. E. 1980 Influence of a longitudinally compressed elastic plate on the non-stationary wave motion of a homogeneous liquid. Fluid Dyn. 15, 687–693.CrossRefGoogle Scholar
Bukatov, A. E. & Cherkesov, L. V. 1977 Unsteady oscillations of an elastic plate floating on the surface of the liquid stream. Sov. Appl. Mech. 13, 103–107.Google Scholar
Bukatov, A. E. & Yaroshenko, A. A. 1986 Evolution of three-dimensional gravitationally warped waves during the movement of a pressure zone of variable intensity. J. Appl. Mech. Tech. Phys. 27, 676–682.Google Scholar
Bukatov, A. E. & Zharkov, V. V. 1997 Formation of the ice cover’s flexural oscillations by action of surface and internal ship waves – Part I. Surface waves. Intl J. Offshore Polar Engng 7, 1–12.Google Scholar
Chowdhury, R. G. & Mandal, B. N. 2006 Motion due to fundamental singularities of finite depth water with an elastic solid cover. Fluid Dyn. Res. 38, 224–240.Google Scholar
Das, D. & Mandal, B. N. 2006 Oblique wave scattering by a circular cylinder submerged beneath an ice-cover. Intl J. Engng Sci. 44, 166–179.Google Scholar
Das, D. & Mandal, B. N. 2007 Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover. Intl J. Engng Sci. 45, 842–872.Google Scholar
Das, D. & Mandal, B. N. 2008 Water wave radiation by a sphere submerged in water with an ice-cover. Arch. Appl. Mech. 78, 649–661.CrossRefGoogle Scholar
Das, D. & Mandal, B. N. 2010 Wave radiation by a sphere submerged in a two-layer ocean with an ice-cover. Appl. Ocean Res. 32, 358–366.CrossRefGoogle Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series, and Products. Academic Press.Google Scholar
Il’ichev, A. T., Savin, A. A. & Savin, A. S. 2012 Formation of a wave on an ice-sheet above the dipole, moving in a fluid. Dokl. Phys. 57, 202–205.CrossRefGoogle Scholar
Kheysin, D. Ye. 1967 Dynamics of Floating Ice Cover. Gidrometeoizdat, Leningrad (in Russian). Technical translation FSTC-HT-23-485-69, US Army Foreign Science and Technology Center.Google Scholar
Korotkin, A. I. 2009 Added Masses of Ship Structures, Fluid Mechanics and Its Applications, vol. 88. Springer.CrossRefGoogle Scholar
Kozin, V. M., Chizhumov, S. D. & Zemlyak, V. L. 2010 Influence of ice conditions on the effectiveness of the resonant method of breaking ice cover by submarines. J. Appl. Mech. Tech. Phys. 51, 398–404.Google Scholar
Lu, D. Q. & Dai, S. Q. 2006 Generation of transient waves by impulsive disturbances in an inviscid fluid with an ice-cover. Arch. Appl. Mech. 76, 49–63.Google Scholar
Lu, D. Q. & Dai, S. Q. 2008a Flexural– and capillary–gravity waves due to fundamental singularities in an inviscid fluid of finite depth. Intl J. Engng Sci. 46, 1183–1193.CrossRefGoogle Scholar
Lu, D. Q. & Dai, S. Q. 2008b Generation of unsteady waves by concentrated disturbances in an inviscid fluid with an inertial surface. Acta Mech. Sin. 24, 267–275.CrossRefGoogle Scholar
Mohapatra, S. & Bora, S. N. 2010 Radiation of water waves by a sphere in an ice-covered two-layer fluid of finite depth. J. Adv. Res. Appl Math. 2, 46–63.CrossRefGoogle Scholar
Mohapatra, S. & Bora, S. N. 2012 Exciting forces due to interaction of water waves with a submerged sphere in an ice-covered two-layer fluid of finite depth. Appl. Ocean Res. 34, 187–197.Google Scholar
Pogorelova, A. V., Kozin, V. M. & Zemlyak, V. L. 2012 Motion of a slender body in a fluid under a floating plate. J. Appl. Mech. Tech. Phys. 53, 27–37.CrossRefGoogle Scholar
Savin, A. A. & Savin, A. S. 2012 Ice cover perturbation by a dipole in motion within a liquid. Fluid Dyn. 47, 139–146.Google Scholar
Schulkes, R. M. S. M., Hosking, R. J. & Sneyd, A. D. 1987 Waves due to a steadily moving source on a floating ice plate. Part 2. J. Fluid Mech. 180, 297–318.Google Scholar
Squire, V. A. 2008 Synergies between VLFS hydroelasticity and sea-ice research. Intl J. Offshore Polar Engng 18, 241–253.Google Scholar
Squire, V. A., Hosking, R. J., Kerr, A. D. & Langhorne, P. J. 1996 Moving Loads on Ice Plates. Kluwer.CrossRefGoogle Scholar
Sturova, I. V. 2011 Hydrodynamic loads acting on an oscillating cylinder submerged in a stratified fluid with ice cover. J. Appl. Mech. Tech. Phys. 52, 415–426.CrossRefGoogle Scholar
Sturova, I. V. 2012 The motion of a submerged sphere in a liquid under an ice sheet. J. Appl. Math. Mech. 76, 293–301.CrossRefGoogle Scholar
Wang, S. 1986 Motions of a spherical submarine in waves. Ocean Engng 13, 249–271.CrossRefGoogle Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik, vol. 9, pp. 446–778. Springer.Google Scholar
Wu, G. X. 1995 Radiation and diffraction by a submerged sphere advancing in water waves of finite depth. Proc. R. Soc. Lond. A 448, 29–54.Google Scholar
Wu, G. X. & Eatock Taylor, R. 1988 Radiation and diffraction of water waves by a submerged sphere at forward speed. Proc. R. Soc. Lond. A 417, 433–461.Google Scholar
Yeung, R. W. & Kim, J. W. 1998 Structural drag and deformation of a moving load on a floating plate. In Proceedings of 2nd International Conference on Hydroelasticity in Marine Technology, Fukuoka, Japan, pp. 77–88.Google Scholar