On the kinematics of short waves in the presence of surface flows of larger scales

Abstract

When the resonance condition is satisfied, i.e. that the local group velocity of short surface waves matches the local velocity associated with 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 short surface waves propagating on long surface waves. By direct numerical resolution of the kinematic equations, some aspects of the reflection or trapping are first examined. Next, the effects of a second long wave on the trajectory of the short waves are considered. It is found that the trajectory is strongly distorted in general. Reflection still occurs, having a larger effect on the variation of the shortwave wavenumber than when only a single long wave is present. The entrapment becomes more sporadic. At short time intervals, a forced Mathieu equation is found to govern the short-wave development. This leads to a discussion on a more general physical context.