Finite-source filtering and Doppler modulation of infragravity waves generated by breakpoint forcing
Infragravity waves generated in the surf zone contribute substantially to nearshore water-level variability, with group-scale variations in wave breaking generating free long waves through breakpoint forcing. Existing interpretations of this mechanism rely largely on an idealised moving-breakpoint picture in which breaking is tied to a local saturation relation, leaving unresolved how the finite extent and evolution of a realistic breaking region control the radiated waves. We first derive a local decomposition of the wave-induced forcing into breakpoint and bound wave forcing, separating the two contributions within the same evolving short-wave field. We then describe the breakpoint-forcing field as a finite, evolving source through its integrated strength, centroid, cross-shore width, and shape. This representation shows that finite source extent produces spatial interference, as phase differences between contributions emitted from different positions attenuate the high-frequency part of the infragravity response and shift this attenuation toward lower frequencies as the source widens. Source migration produces a directional Doppler shift by modifying the arrival times of successive emissions, with shoreward motion compressing arrivals at a shoreward observer and stretching them at a seaward observer. Breaking depth controls both the conversion of this forcing into surface elevation and the celerities governing these propagation-time effects. Controlled numerical experiments across a range of plane-beach slopes reproduce the predicted signatures: broader source footprints strengthen upper-band attenuation on both branches. The diagnosed migration history, with breaking strongest during shoreward motion, partly offsets that attenuation shoreward and reinforces it seaward.