Analytical Solution of Diffraction by a Composite Cylinders Above a Special Bottom Undulation in Uniform Water
DOI:
https://doi.org/10.26713/cma.v13i2.1801Keywords:
Diffraction, Uniform depth, Virtual boundary, Exciting forces, Analytical solutionAbstract
We consider the co-axial cylindrical structure as a composite submerged solid cylinder above a special bottom undulation, i.e., a circular plate at the impermeable horizontal bottom. We consider the diffraction problem of the proposed structure in water of finite depth. This diffraction problem can be expressed as a wave energy converter. The variables of separation and eigenfunction expansion methods are utilized to determine the analytical solutions for the diffraction problem in their identified sub-domains. By using the methods of expansion of eigenfunction and the orthogonality of Bessel functions to the expression of the diffracted velocity potentials. We achieve a system of linear equations after suitably truncated to the obtain infinite series. This work may be helpful to the wave designer to design appropriate device so that one can extract maximum wave energy. The created wave energy may be used in many applications of conventional energy.
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References
M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, New York (1965), URL: https://personal.math.ubc.ca/~cbm/aands/abramowitz_and_stegun.pdf.
D.D. Bhatta and M. Rahman, On the scattering and radiation problem for a cylinder in water of finite depth, International Journal of Engineering Science 41 (2003), 931 – 967, DOI: 10.1016/S0020-7225(02)00381-6.
C.J.R. Garrett, Wave forces on a circular dock, Journal of Fluid Mechanics 46(1) (1971), 129 – 139, DOI: 10.1017/S0022112071000430.
M. Hassan and S.N. Bora, Exciting forces for a pair of coaxial hollow cylinder and bottom-mounted cylinder in water of finite depth, Ocean Engineering 50 (2012), 38 – 43, DOI: 10.1016/j.oceaneng.2012.05.013.
R.C. MacCamy and R.A. Fuchs, Wave Forces on Piles: A Diffraction Theory, Technical Memorandum No. 69, US Army Beach Erosion Board, Corps of Engineers, p. 17 (1954), URL: https://apps.dtic.mil/sti/pdfs/AD0699406.pdf.
M. Rahman and D.D. Bhatta, Second order wave forces on a pair of cylinders, Canadian Applied Mathematics Quarterly 1(3) (1993), 343 – 382, DOI: ref.
Y.M. Shen, Y.H. Zhang and Y.G. You, On the radiation and diffraction of linear water waves by a rectangular structure over a sill, Part I. Infinite domain of finite water depth, Ocean Engineering 32(8-9) (2005), 1073 – 1097, DOI: 10.1016/j.oceaneng.2004.07.011.
P. Siddorn and R.E. Taylor, Diffraction and independent radiation by an array of floating cylinders, Ocean Engineering 35(13) (2008), 1289 – 1303, DOI: 10.1016/j.oceaneng.2008.06.003.
B.J. Wu, Y.H. Zhang, Y.G. You, D.S. Jie and Y. Chen, On diffraction and radiation problem for two cylinders in water of finite depth, Ocean Engineering 33(5-6) (2006), 679 – 704, DOI: 10.1016/j.oceaneng.2005.05.011.
B.J. Wu, Y.M. Zhang, Y.G. You, X.Y. Sun and Y. Chen, On diffraction and radiation problem for a cylinder over a caisson in water of finite depth, International Journal of Engineering Science 42(11-12) (2004), 1193 – 1213, DOI: 10.1016%2Fj.ijengsci.2003.12.006.
Y.H. Zhang, Y.M. Shen, Y.G. You, B.J. Wu and L. Rong, Hydrodynamic properties of two vertical truncated cylinders in waves, Ocean Engineering 32(3-4) (2005), 241 – 271, DOI: 10.1016/j.oceaneng.2004.09.002.
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