The evolution of subharmonic edge wavepackets on a sloping beach

A study is made of the temporal and spatial development of subharmonic edge wavepackets which are resonantly excited by a wavetrain normally incident and reflected on a mildly sloping beach. The nonlinear evolution equations of the wavepacket envelopes are solved numerically for a variety of initial conditions. It is shown that, under certain conditions, large-scale modulations of edge waves are generated and undergo a recurrence phenomenon. These findings lend support to the belief that modulational instabilities of edge wavepackets could be related to certain long-period oscillatory phenomena observed on natural beaches.