1. A wave will break if the particle speed exceeds the propagation speed of the wave. If the speed is above a certain threshold then the water curls over and forms a tunnel. Otherwise, the water will slide down the front of the wave.
2. A wave will break if the wave becomes too steep. If the amplitude becomes too great for the wavelength and depth, then gravity will force the water to fall over itself. This theory also requires that the particle speed exceed the propagation speed.

It should be noted that after the wave breaks the water no longer follows the equations set forth earlier. After breaking, the particles do not move separately around ellipses, but rather the water has a total movement, with speed being controlled by the wave's ending propagation speed, gravity and turbulence.

Our model shows water moving as it would at a beach. Again, the important aspects to notice are that the wavelength decreases with depth and the amplitude increases. The model stops where the wave would break.

Java applet: beach waves