Abstract
A particular hydro-elastic model is considered to examine a radiation problem involving an immersed sphere in an infinitely extended ice-covered sea, where the lower surface is enveloped by a flexible base surface. Both the flexible base surface and floating ice-plate are modelled as thin elastic plates with different configurations and are based on the Euler–Bernoulli beam equation. The appearance of surface tension at the surface below the floating ice-plate is ignored. Under such circumstance, two different modes of propagating waves appear in the fluid for any particular frequency. One of the modes with lower wavenumber propagates along the surface beneath the ice-plate and the other with higher wavenumber propagates along the elastic base surface. The method of multipole expansions is used to calculate the solutions of the heave and sway radiation problems involving a submerged sphere in an ice-covered fluid. Furthermore, this procedure gives rise to an infinite system of linear equations, which can be solved computationally by any regular method. The added-mass as well as damping coefficients in case of heave as well as sway motions are calculated, and displayed graphically in various submergence depths of the oscillating sphere and elastic specifications of both the flexible base surface as well as the floating ice-plate.
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Bora SN (1997) The interaction of water waves with submerged spheres and circular cylinders. PhD thesis, Technical University of Nova Scotia, Halifax, Canada
Cadby JR, Linton CM (2000) Three-dimensional water-wave scattering in two-layer fluids. J Fluid Mech 423:155–173
Chakrabarti A, Mohapatra S (2013) Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth. J Mar Sci Appl 12:325–333
Das D, Mandal BN (2008) Water wave radiation by a sphere submerged in water with an ice-cover. Arch Appl Mech 78:649–661
Evans DV (1976) A theory for wave-power absorption by oscillating bodies. J Fluid Mech 77:1–25
Evans DV, Linton CM (1989) Active devices for the reduction of wave intensity. Appl Ocean Res 11:26–32
Gray EP (1978) Scattering of a surface wave by a submerged sphere. J Eng Math 12:15–41
Havelock TH (1955) Waves due to a floating sphere making periodic heaving oscillations. Proc R Soc Lond 231:1–7
Hulme A (1982) The wave forces acting on a floating hemisphere undergoing forced periodic oscillations. J Fluid Mech 121:443–463
Linton CM (1991) Radiation and diffraction of water waves by a submerged sphere in finite depth. Ocean Eng 18:61–74
Milgram JH, Halkyard JE (1971) Wave forces on large objects in the sea. J Ship Res 15:115–124
Mohapatra S, Bora SN (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
Mohapatra SC, Sahoo T (2011) Surface gravity wave interaction with elastic bottom. Appl Ocean Res 33:31–40
Mohapatra S, Bora SN (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
Mohapatra S (2017) Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth. Z Angew Math Phys 68:91. https://doi.org/10.1007/s00033-017-0837-1
Newman JN (1977) Marine hydrodynamics. The MIT Press, Cambridge, England
Sarangi MR, Mohapatra S (2018) Investigation on the effects of versatile deformating bed on a water wave diffraction problem. Ocean Eng 164:377–387
Sarangi MR, Mohapatra S (2019) Hydro-elastic wave proliferation over an impermeable seabed with bottom deformation. Geophys Astrophys Fluid Dyn 113:303–325
Squire VA (2007) Of ocean waves and sea-ice revisited. Cold Reg Sci Technol 49:110–133
Srokosz MA (1979) The submerged sphere as an absorber of wave power. J Fluid Mech 95:717–741
Sturova IV (2013) Unsteady three-dimensional sources in deep water with an elastic cover and their applications. J Fluid Mech 730:392–418
Thorne RC (1953) Multipole expansions in the theory of surface waves. Proc Camb Philos Soc 49:707–716
Tkacheva LA (2015) Oscillations of a cylinderical body submerged in a fluid with ice-cover. J Appl Mech Tech Phys 56:1084–1095
Ursell F (1949) On the heaving motion of a circular cylinder on the surface of a fluid. Q J Mech Appl Math 2:218–231
Ursell F (1950) Surface waves on deep water in the presence of a submerged circular cylinder-I. Proc Camb Philos Soc 46:141–152
Wang S (1986) Motions of a spherical submarine in waves. Ocean Eng 13:249–271
Acknowledgements
The authors would like to acknowledge and thank Prof. Swaroop Nandan Bora, Indian Institute of Technology Guwahati, India for his invaluable discussions to accomplish the preparation of the manuscript. The authors are very much indebted to the learned reviewers for their suggestions and constructive comments, which enabled the authors in carrying out the desired revision of the manuscript.
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This work is partially supported by Department of Science and Technology (DST), India through a research project No. SB/FTP/MS003/2013 (S. Mohapatra).
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Das, L., Mohapatra, S. Effects of flexible bottom on radiation of water waves by a sphere submerged beneath an ice-cover. Meccanica 54, 985–999 (2019). https://doi.org/10.1007/s11012-019-00998-1
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DOI: https://doi.org/10.1007/s11012-019-00998-1