ON THE KINEMATICS OF SHORT WAVES IN THE PRESENCE OF SURFACE FLOWS OF LARGER SCALES

When the resonance condition is satisfied, i.e. that the local group v elocity of short surface waves matches the local velocity associated w ith a larger-scale surface flow, it is known that the short waves are reflected or trapped by the flow. A typical example is the case of sho rt surface waves propagating on long surface waves. By direct numerica l resolution of the kinematic equations, some aspects of the reflectio n or trapping are first examined. Next, the effects of a second long w ave on the trajectory of the short waves are considered. It is found t hat the trajectory is strongly distorted in general. Reflection still occurs, having a larger effect on the variation of the short-wave wave number than when only a single long wave is present. The entrapment be comes more sporadic. At short time intervals, a forced Mathieu equatio n is found to govern the short-wave development. This leads to a discu ssion on a more general physical context.