Semi-analytical solution for second-order wave diffraction by a truncated circular cylinder in monochromatic waves

Abstract

A complete semi-analytical solution is given for second-order diffraction of monochromatic waves by a truncated vertical circular cylinder in water of uniform finite depth. The methodology presented in detail elsewhere (Eatock Taylor & Huang 1996) is adopted to find a particular solution which exactly satisfies the governing equation, the inhomogeneous free-surface condition and the seabed condition. In order to satisfy the boundary condition on the cylinder bottom, the fluid domain around the cylinder is divided into two regions. First- and second-order velocity potentials are described separately in the two regions and matched on the interface by the pressure and normal-velocity continuity conditions. Based on the formulation, the second-order wave field in the vicinity of the cylinder and the corresponding wave forces and overturning moments on the cylinder are studied in detail. Numerical results for the double frequency forces obtained by using the present semi-analytical approach are compared with those computed with a higher-order boundary element method (Eatock Taylor & Chau 1992). As well as the exact solution, an approximate solution is also given for the second-order potential and the corresponding forces. Numerical results show that the approximate solution possesses excellent accuracy for the total second-order heave force over a wide range of conditions. When kb > 1.2 (where k, b are the incident wavenumber and the draught of the cylinder respectively), the accuracy for total second-order surge force and pitch moment is also satisfactory. These results could lead to the development of very efficient solutions and corresponding algorithms for the analysis of second-order wave diffraction by more complicated structures such as tension leg platforms. Numerical results based on the present solution show that in many cases, both the first- and the second-order-free surface elevation in the vicinity of a truncated cylinder is very close to that of a bottom-seated cylinder. For waves with larger amplitudes, the maximum free-surface elevation around a vertical cylinder predicted with the second-order theory can significantly exceed that given by linear theory. There is also a considerable difference in the location of the maximum elevation predicted by the linear and nonlinear theories.

Study on Wave Run-Up Phenomenon over Vertical Cylinder

“…또한 고정된 원형실린더에 작용하는 산란파 이론을 적용하여 Diffraction 퍼텐셜을 구하고 이를 실린더 표면에서의 경계조건을 적용하면 식 (3)과 같이 표현된다 (Mei et al, 2005;Garrett, 1971;Walker and Eatock Taylor, 2005;Maniar and Newman, 1997;Huang and Eatock Taylor, 1996).…”

Determination of the Heave and Pitch Motions of a Floating Cylinder by Analytical Solution of its Diffraction Problem and Examination of the Effects of Geometric Parameters on its Dynamics in Regular Waves

“…Wu et al [16] explored the diffraction and radiation problem for a cylinder over a caisson in water of finite depth and presented the calculated results of hydrodynamic coefficients, wave forces and hydrodynamic effect of the caisson on the hydrodynamics of the cylinder. In order to achieve findings close to the experiment results, a second-order diffraction problem for truncated cylinder in finite depth water was investigated by Huang and Eatock Taylor [17] and Mavrakos and Chatjigeorgiou [18] and diffraction forces due to second-order potential was calculated. In this paper, we have considered the diffraction problem of a floating vertical circular cylinder.…”

Low-Frequency Responses of Nonlinearly Moored Vessels in Random Waves: Coupled Surge, Pitch and Heave Motions

“…and f R have been derived. To simplify the analysis, the scattered potential due to the truncated cylinder can be approximated by that of a bottom-seated cylinder (Huang & Eatock Taylor 1996;Sarkar & Eatock Taylor 1998) in calculating all the second-order forces. The validity of this approximation, which signi"cantly simpli"es the derivation of analytical expressions for the various terms, has been justi"ed for the truncated cylinder by comparing results with those obtained using a numerical approach.…”

“…The expression for the scattered potential of a wave with amplitude a and frequency is given by (Huang & Eatock Taylor 1996) Q "…”