Nonlinear dispersive wave groups or packets occur in a wide range of natural systems, exhibiting complex behaviors especially in focal zones where there is rapid wave energy concentration and possible wave breaking. In the presence of dispersion, pure plane waves of different wavelengths and directions traveling within a medium have different propagation velocities. Important classes of geophysical wave systems include surface gravity waves, oceanic and atmospheric internal waves, and seismic waves.
We propose a multi-faceted study that will provide a new perspective on wave group dynamics and focusing, towards understanding wave breaking and the mysterious formation of rogue waves, and their relation to the recently discovered crest slowdown phenomenon. In particular, we propose, for the first time, leading edge and highly novel field observations combined with numerical and theoretical studies to investigate the physics of wave groups in the ocean and in linear and nonlinear elastic media. In particular, we will extend these studies forward to understand the role of the slowdown phenomenon and rogue waves in seismic wave systems. The major envisaged outcomes of the proposed research are i) a new perspective on the physics of wave groups and prediction of rogue waves and ii) unveiling of the ‘genetic code’ of oceanic and seismic waves, namely the fundamental space-time structure of a wave group and iv) the groundwork that will provide the basis for the formulation of a unifying theory of the dispersive nonlinear wave motion of geophysical wave systems.