The crest pours forward

A breaking wave

As the water gets even shallower, the depth under the crest and the depth under the trough become very different. The crest, sitting over deeper water, moves faster than the trough and tries to overtake it. When the wave is about 0.8 times as tall as the water is deep, its front can no longer hold and the crest pours forward. In this scene the wave breaks at 2.9 m high in water 3.8 m deep.

Why?It is not that “the bottom drags while the top runs ahead”. In shallow water, deeper water means faster waves, and the water under a crest is deeper than under a trough by the height of the wave. So the crest pulls ahead.

Learn more0.78 is the value McCowan calculated in 1894. On real beaches the ratio changes with the slope of the seabed and the shape of the waves. On gentle beaches the crest spills down the front; on steep beaches it curls over and plunges. The leaning crest and the foam on screen are a rough sketch, not a calculation.

Height ÷ water depth when breaking

0.78

calculated from the textbook equations for water waves (linear wave theory)