Evaluation of the modi ed 3D free-surface Greenʹʹs function for potential ow in a numerical towing tank

What is derived in this paper is the potential ow around the marine structures in the numerical towing tank. The Greenʹs formula and image method is employed to solve the boundary value problem. The Greenʹs function satises the Laplace equation and the boundary conditions on the bottom, walls and free surface. The Greenʹs function consists of three parts. The rst part is correlated with spatial spacing between the source and a eld point. The second part consists of the free surface disturbance. The radiation condition is dealt with in the third part to ensure that the waves vanish upstream of the source. An innite series is obtained for each part of the Greenʹs function using the image method. Eects of the numerical towing tankʹs width and depth on the solution are investigated, and the ow patterns due to the presence of a singularity with constant strength in the uniform ow are computed. Uniform motion of a submerged sphere and ellipsoid are simulated and compared with the analytical solutions and other numerical results. Wave proles are computed for a sphere and an ellipsoid to show the eect of the tank width on the solution.