An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged body

An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave-body interaction problem into body and free-surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free-surface problem satisfies modified nonlinear free-surface boundary conditions. It is then shown that the nonlinear free-surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free-surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo-spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright (c) 2007 John Wiley & Sons, Ltd.