Numerical simulation of breaking waves

Abstract

Recent accidents with smaller fishing vessels in breaking waves have focused the interest of naval architects on the dynamics of extreme waves. In the field of ocean engineering there is also a lack of knowledge about what velocities and accelerations to use when calculating the forces from breaking waves on structural members of offshore structures. A number of theories for steady, finite amplitude surface waves are available. In general they are, however, only valid for symmetric, progressive waves. LonguetHiggins and Cokelet 12 have developed a numerical technique for solving the periodic, 2-dimensional, deep water breaking wave problem. This method is based on potential theory and a conformal mapping of the physical plane inside a closed contour in the mapped plane, and the equations of motion are solved in this plane. Then the wave form in the physical plane is found by an inversion of the mapping. Details about the numerical techniques and the time integration procedures are found in the references. In this paper we present a similar method, but with the exceptions that the problem is solved in the physical plane and finite depth is introduced. Except for this, the problem is stated in the same way. The advantage of working in the physical plane is that certain other effects can be included without much modification of the program. Presently we are introducing a floating cylinder into the problem to try to solve the ship motion problem in 2-dimensional breaking waves and a submerged floating or fixed cylinder may quite easily be introduced.