A numerical continuation approach for computing water waves of large wave height

We analyse an algorithm for the calculation of travelling water waves in flows with constant and variable vorticity. The algorithm is based on numerical continuation techniques, which are suitably adapted to the water wave problem. Numerical examples illustrate the performance of the algorithm for flows of constant vorticity, where the results are compared with the literature. We observe agreement with already existing results, but we also have some new qualitative and quantitative results considering the characteristics of the water waves both for constant and variable vorticity.