Influence of shear-flow vorticity on wave-current interaction. Part 1: Surface gravity waves without surface tension effect

Abstract: Propagation of surface waves on a background shear flow with constant vorticity is studied and compared against the case when the background flow is uniform in depth. For a shear flow with the linear vertical profile, the dispersion relation of surface gravity waves is minutely analyzed for a fluid of finite depth. Under the assumption that the background flow gradually varies in the horizontal direction, the primary attention is paid to the wave blocking phenomenon; the effect of vorticity on this phenomenon is studied in details. The conditions of wave blocking are obtained and categorized for different values of the governing dimensionless parameters.