A spotlight with an adjustable beam width sweeps along the shore. Its light is the long ocean waves that are born in the surf zone and spread in both directions: toward the beach and out to the open sea. Previously, this spotlight was considered a point source, but the actual breaking zone, where short waves break, has a finite width, and it changes as the wave front advances and retreats.
The scientists split the forcing into the contribution of breaking and bound waves. Bound waves are long waves that travel together with groups of short waves, like a cloud's shadow running across the ground. Breaking, on the other hand, acts as a source that does not stay put: it migrates shoreward as waves roll in and retreats as they recede. And here the width of the source begins to play the role of a filter. Light from different points of the spotlight reaches the observer with different phases, and high frequencies cancel each other out, like ripples from two stones thrown into the water.
The motion of the source adds an effect familiar to everyone from an ambulance siren: as it approaches, the pitch is higher; as it recedes, lower. For a shore-based observer, waves heading toward the beach are compressed, while those going out to sea are stretched. Numerical experiments on beaches with slopes from 1:10 to 1:50 confirmed: the wider the source footprint, the stronger the attenuation of the upper part of the spectrum.
The breaking depth, that is, the location where the wave breaks, controls how efficiently the forcing is converted into surface oscillations. If the depth is small, the source acts like a loudspeaker pressed against a wall: the sound goes in one direction. If the depth is large, it radiates in all directions, and less energy reaches the shore.
The spotlight sweeping along the shore is now seen not as a point but as a broad band of light. And its width determines which waves reach the beach and which dissipate at sea. This knowledge helps predict flooding and wave impact on port structures, which can resonate with infragravity waves.
Infragravity waves have periods from 20 to 250 seconds, comparable to the time it takes for a person to take several breaths. These waves can cause water level oscillations in harbors, leading to resonance that rocks moored vessels.