Abstract
The influence of exponentially sheared currents on unidirectional bichromatic waves in deep water is investigated by the HAM. The governing equations contain four coupled PDEs, including a nonlinear vorticity transport equation and two nonlinear free-surface conditions on the unknown wave elevation. No constrain is made for the primary wave amplitudes, and the current owns a exponential type profile along the vertical line. Convergent solutions are obtained with the help of convergence-control parameter. It is found that a critical characteristic current profile slope exists for each parts of phase velocity caused by nonlinear interaction, under/above which the mean flow vorticity increases/decreases the corresponding part of phase velocity. This work indicates that the HAM is a powerful tool for complicated coupled nonlinear PDEs, which deserves more attention for further development.