Numerical simulation of capillary gravity waves excited by an obstacle in shallow water

Capillary gravity waves excited by an obstacle are investigated by numerical simulations. Under the resonant condition for which large-amplitude solitary waves are generated, solutions of the Euler equations show that the capillary effects induce the generation of short waves both upstream of the solitary waves and downstream of the obstacle. Overall characteristics of these waves agree with the weakly nonlinear theory, although the theory overestimates the wavelength of the upstream short waves.