Numerical investigations of two-dimensional irrotational water waves over finite depth with uniform current

We investigate large amplitude steady water waves in the presence of underlying uniform current with using a numerical continuation method. The two branches of traveling wave solutions, whose existence has been proved recently by Basu [On the existence of two-dimensional irrotational water waves over finite depth with uniform current. Appl Anal. 2018;97(14):2523-2532.] for a parameter or are computed numerically. The numerical results for the case have not been previously reported in the literature. The properties of the waves and flows in this solution branch are discussed as comparison to those in the case of .