Breakpoint Forcing Revisited: Phase Between Forcing and Response

Using the breakpoint forcing model, for long wave generation in the surf zone, expressions for the phase difference between the breakpoint-forced long waves and the incident short wave groups are obtained. Contrary to assumptions made in previous studies, the breakpoint-forced long waves and incident wave groups are not in phase and outgoing breakpoint-forced long waves and incident wave groups are not out of phase. The phase between the breakpoint-forced long wave and the incident wave group is shown to depend on beach geometry and wave group parameters. The breakpoint-forced incoming long wave lags behind the wave group, by a phase smaller than /2. The phase lag decreases as the beach slope decreases and the group frequency increases, approaching approximately /16 within reasonable limits of the parameter space. The phase between the breakpoint-forced outgoing long wave and the wave group is between /2 and and it increases as the beach slope decreases and the group frequency increases, approaching 15/16 within reasonable limits of the parameter space. The phase between the standing long wave (composed of the incoming long wave and its reflection) and the incident wave group tends to zero when the wave group is long compared to the surf zone width. These results clarify the phase relationships in the breakpoint forcing model and provide a new base for the identification of breakpoint forcing signal from observations, laboratory experiments and numerical modeling.