Non-linear interaction of water waves with submerged obstacles

The interaction of two-dimensional water waves with a fixed submerged cylinder is studied using a finite difference scheme with boundary-fitted co-ordinates. A mixed Eulerian–Lagrangian (MEL) formulation is used to satisfy the fully non-linear free surface conditions. The diffraction of small-amplitude water waves by a cylinder is examined for various wavelengths and amplitudes of the incident wave. Fourier analyses of the incident and diffracted waves are performed to determine their spectra. An example of a large-amplitude wave breaking over a cylinder is also studied. The non-linear numerical solutions are compared with those of experiments and linear theory where appropriate.