BREAKING BOW AND STERN WAVES: NUMERICAL SIMULATIONS

Ship-generated waves have always fascinated scientists, and played a key role in surface-ship hydrodynamics for contributing to hull resistance, generating sounds and radiating very long narrow wakes remotely visible. Some of these phenomena originate abeam the ship through extensive breaking of diverging bow and stern waves, forming a wake. In this paper we summarize and extend our recent research activity aimed to understand the complex fluid dynamics involved in bow- and stern-wave radiation, including wave breaking. The analysis is limited to practical slender ships, with a sharp stem, for which basic insight can be achieved by an approximate quasi three-dimensional model based on the idea that longitudinal gradients of relevant flow quantities are small compared with vertical and transverse gradients. A historical recollection of slender-body theory for ship hydrodynamics is given by Maruo (1989), Tulin and Wu (1996), Fontaine and Tulin (2001). In this framework, two methods have been developed at the OEL. One based on a potential flow model, where the velocity field is given through the Laplace equation solved by a Boundary Element Method (BEM), and the evolution in time is obtained by integration of free-surface boundary conditions. Specific details of the latest code are documented in Landrini and Colagrossi (2001 a). The method has the advantage of high resolution, sufficient to capture breaking, and to trace jet overturning up to the impact against the underlying free surface. Post-breaking evolution is studied by a gridless method, called SPH and developed by Monaghan and co-authors (see e.g. Monaghan (1988)), which we applied to breaking waves since the previous Workshop. In this case, Euler equations for a weakly compressible fluid have been considered. Further developments led to a code named SPlasH, applied to a variety of free-surface problems, and presented in Tulin and Landrini (2000), Colagrossi et al. (2000). A detailed description of the algorithm is given in Landrini et al. (2001 b)