Surface Shear and Persistent Wave Groups

Abstract

We investigate the interaction of waves with surface flows by considering the full set of conserved quantities, subtle but important surface elevation changes induced by wave packets and by directly considering the necessary forces to prevent packet spreading in the deep water limit. Narrow surface shear flows are shown to exert strong localizing and stabilizing forces on wavepackets to maintain their strength and amplify their intensity even in the linear regime. Subtle packet scale nonlinear elevation changes from wave motion are crucial here and it suggest that popular notions of wave stress and action are naive. Quantitative bounds on the surface shear flow necessary to stabilize packets of any wave amplitude are given. One implication of this mechanism is that rogue wave stabilization must be due to a purely nonperturbative process