Abstract
Evaluation of hydrodynamic coefficients and loads on submerged or floating bodies is of great significance in designing these structures. Some special regular-shaped geometries such as those of cylindrical (circular, elliptic) and spherical (hemisphere, sphere, spheroid) structures are usually considered to obtain analytical solutions to wave diffraction and radiation problems. The work presented here is the result of water-wave interaction with submerged spheres. Analytical expressions for various hydrodynamic coefficients and loads due to the diffraction of water waves by a submerged sphere are obtained. The exciting force components due to surge and heave motions are derived by solving the diffraction problem. Theory of multipole expansions is used to express the velocity potentials in terms of an infinite series of associated Legendre polynomials with unknown coefficients and the orthogonality of the polynomials is utilized to simplify the expressions. Since the infinite series appearing in various expressions have excellent truncation properties, they are evaluated by considering only a finite number of terms. Gaussian quadrature is used to evaluate the integrals. Numerical estimates for the analytical expressions for the hydrodynamic coefficients and loads are presented for various depth to radius ratios. Consideration of more values for depth makes it easy to compare the results with those available. The results obtained match closely with those obtained earlier by Wang and Wu and their coworkers
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bora S N 2002 Exciting forces due to diffraction of water waves on a sphere in finite depth water.WSEAS Trans. Math. 1: 180–185
Havelock T H 1931 The wave resistance of a spheroid.Proc. R. Soc. London A131: 275–284
Havelock T H 1955 Waves due to a floating sphere making periodic heaving oscillations.Proc. R. Soc. London A231: 1–7
Hulme A 1982 The wave forces acting on a floating hemisphere undergoing forced periodic oscillations.J. Fluid Mech. 121: 443–463
McLachlan N W 1941Bessel functions for engineers (Oxford: University Press)
Thorne R C 1953 Multipole expansions in the theory of surface waves.Proc. Cambr. Philos. Soc. 49: 707–716
Wang S 1986 Motions of a spherical submarine in waves.Ocean Eng. 13: 249–271
Wu G X 1994 Hydrodynamic forces on a submerged sphere undergoing large amplitude motion.J. Ship Res. 38:272–277
Wu G X, Taylor E R 1987 The exciting force on a submerged spheroid in regular waves.J. Fluid Mech. 182:411–426
Wu G X, Taylor E R 1988 Radiation and diffraction of water waves by a submerged sphere at forward speed.Proc. R. Soc. London A417: 433–461
Wu G X, Taylor E R 1989 On the radiation and diffraction of surface waves by submerged spheroids.J. Ship Res. 33: 84–92
Wu G X, Taylor E R 1990 The hydrodynamic forces on a submerged sphere moving in a circular path.Proc. R. Soc. London A428: 215–227
Wu G X, Witz J A, Ma Q, Brown D T 1994 Analysis of wave induced forces acting on a submerged sphere in finite water depth.Appl. Ocean Res. 16: 353–361
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bora, S.N. Hydrodynamic coefficients for water-wave diffraction by spherical structures. Sadhana 29, 617–628 (2004). https://doi.org/10.1007/BF02901476
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02901476