Effects of dual wavenumber dispersion solutions on a nonlinear monochromatic wave-current field

An analytical solution for quadratic nonlinear wave-current interactions is derived using a perturbation method. In contrast to existing formulations, it accounts for dual wavenumber solutions of the linear problem for a single frequency and their nonlinear interactions. It is demonstrated that even a small amount of energy present on the second solution will introduce significant quantitative and qualitative differences in the surface elevation. These differences include a shorter wavelength component moving with a lower wave celerity, nonlinear spatial focusing, and a mean water level that varies in space. The second solution is also shown to produce a mechanism which may easily result in localized violations of wave breaking criteria. These weakly nonlinear effects are expected to be relevant to a variety of engineering applications and physical processes.