TY - JOUR

T1 - Analytical study of wave diffraction and radiation by a submerged sphere in infinite water depth

AU - Liu, Ying Yi

AU - Teng, Bin

AU - Cong, Pei Wen

AU - Liu, Chang Feng

AU - Gou, Ying

N1 - Funding Information:
The authors gratefully acknowledge the financial support provided by National Natural Science Foundation of China (Grant Nos. 11072052 , 50921001 ), and the financial support provided by the National Basic Research Program of China (973-Program) (Grant No. 2011CB013703 ). The authors would also like to thank Dr. S.N. Bora of IIT for his kindly supply of documentations and Dr. Chong-Jun Li of DUT for his useful suggestions of some mathematics techniques. The authors are also grateful to the referees for their valuable comments.

PY - 2012/9/1

Y1 - 2012/9/1

N2 - The wave diffraction and radiation of a submerged sphere in deep water are studied using the multipole method within the frame of linear wave theory. By expressing the velocity potential in spherical harmonics and formulating the problems into truncating and solving M sets of linear equation systems, simple analytical expressions are derived for the hydrodynamic characteristics. A novel analytical expression for the multipoles coefficient is derived to accelerate the numerical implementation. A similar procedure of Wu et al. (1994) and Rahman (2001) is used to condense the expression for the total wave potentials at the sphere surface in the diffraction problem. Results obtained by present model precisely coincide with other numerical schemes, and converge very rapidly with the increase of the truncation parameter that generally the number of series terms N=4 and M=0,1 are sufficient to an accuracy of 3 decimals. A further analysis shows that for large submergences, the surge and the heave exciting forces approach equal. In the mean time, there exists an exact relationship a11-0.5=(a00-0.5)/2 between the surge and the heave added mass, and b11=b00/2 between the surge and the heave damping, where j=0 and j=1 correspond to the heave and surge motion, respectively. Extensive numerical results involving convergence of the multipole method, exciting forces and hydrodynamic coefficients for various parameters are also presented.

AB - The wave diffraction and radiation of a submerged sphere in deep water are studied using the multipole method within the frame of linear wave theory. By expressing the velocity potential in spherical harmonics and formulating the problems into truncating and solving M sets of linear equation systems, simple analytical expressions are derived for the hydrodynamic characteristics. A novel analytical expression for the multipoles coefficient is derived to accelerate the numerical implementation. A similar procedure of Wu et al. (1994) and Rahman (2001) is used to condense the expression for the total wave potentials at the sphere surface in the diffraction problem. Results obtained by present model precisely coincide with other numerical schemes, and converge very rapidly with the increase of the truncation parameter that generally the number of series terms N=4 and M=0,1 are sufficient to an accuracy of 3 decimals. A further analysis shows that for large submergences, the surge and the heave exciting forces approach equal. In the mean time, there exists an exact relationship a11-0.5=(a00-0.5)/2 between the surge and the heave added mass, and b11=b00/2 between the surge and the heave damping, where j=0 and j=1 correspond to the heave and surge motion, respectively. Extensive numerical results involving convergence of the multipole method, exciting forces and hydrodynamic coefficients for various parameters are also presented.

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U2 - 10.1016/j.oceaneng.2012.05.004

DO - 10.1016/j.oceaneng.2012.05.004

M3 - Article

AN - SCOPUS:84862902366

VL - 51

SP - 129

EP - 141

JO - Ocean Engineering

JF - Ocean Engineering

SN - 0029-8018

ER -