Nakazono, Takefumi (Kagoshima University) | Kunitake, Masato (Miyazaki University) | Kondo, Fumiyoshi (Miyazaki University) | Inagaki, Hitone (Kagoshima University) | Nakazawa, Takao (Miyazaki University) | Kikumura, Tadayoshi (Ready-Mixed Concrete Association of Miyazaki) | Saito, Masaki (Crown Engineering Co. Ltd.) | Kakuda, Itsuro (Nihon Suiko Consultant Co. Ltd.)
Shin, Jong-Gye (Dept. of Naval Architecture and Ocean Engineering, Seoul National University) | Kim, Won-Don (Dept. of Naval Architecture and Ocean Engineering, Seoul National University) | Lee, Jang-Hyun (Dept. of Naval Architecture and Ocean Engineering, Seoul National University)
The nonlinear effects of the steady flow on wave diffraction-radiation at low forward speed are analyzed via a new theoretical method. The method is based on a decomposition of the time-harmonic potential into linear and nonlinear components. The linear time-harmonic potential satisfies the classical linearized free-surface condition while the nonlinear potential takes into account nonlinear interactions between the local steady flow and the linear time-harmonic potential. Both the linear and nonlinear potentials are evaluated by using the source method which involves the Green function of wave diffraction-radiation at small forward speed given in Noblesse and Chen (1995). Within the approximation of order 0 (τ), the present method leads to a consistent solution of the time-harmonic potential. The limitation of application to bodies of large size by the previous analysis based on a perturbation expansion, due to secular terms, is removed. The present method gives correctly fluid kinematics at any point in the fluid domain, in addition to first-order, second-order loadings, and wave drift dampings. It is shown that the nonlinear effects of the steady flow at the free surface give substantial contribution to above quantities.
Nonlinear effects are significant in the vicinity of floating bodies, as is convincingly shown in some recent studies by using hybrid calculation methods based on zonal coupling of an inner nonlinear and/or viscous flow with an outer linear potential flow. Even within potential theory, nonlinear interactions between the (unsteady) time-harmonic flow and the local steady flow are important for blunt bodies, as shown in Faltinsen (1994). A body advancing at constant speed in regular waves generates a steady Kelvin pattern plus several systems of linear time- harmonic waves. The general interaction between the steady flow and the time-harmonic flows may be solved by using a zonal approach, which needs considerable effort in solving numerical problems associated with higher-order derivatives of the velocity potential and in required CPU time.