Long-Wave Generation Due to the Refraction of Short-Wave Groups over a Shear Current

Abstract

The generation of long waves by short-wave groups propagating over a shear current is studied. The incident wave groups consist of two co-linear short waves with slightly different frequencies. These short waves are refracted by the shear currents. For certain angles of incidence caustics may exist and the short waves are reflected back by the shear current. Similarly, caustics could also appear in the wave envelope, which propagates in a different direction from that of the short waves. In the present paper, the treatment of caustics is not considered. In the region where the shear current vanishes, the short-wave groups are accompanied by locked long waves that propagate with the wave envelope of short waves at their group velocity. In the shear current region, the refraction effects not only separate the propagation directions of the short waves and the wave envelope but also generate free long waves, which propagate at the speed of.gh. The free long waves could also be trapped over the shear current region.