Distribution of ocean waves by Rayleigh

[Dbe.098]

I heard that the analysis of wave measurements close to shore verifies that as long as wave amplitudes are small with respect to mean depth a Rayleigh distribution remains satisfactory of wave heights, but how ?

 

[tech99]

I heard that the analysis of wave measurements close to shore verifies that as long as wave amplitudes are small with respect to mean depth a Rayleigh distribution remains satisfactory of wave heights, but how ?

The Rayleigh Distribution occurs when there are many sources of waves arriving at the observer and combining. Each one must make only a small contribution to the total. The waves have arbitrary phase and amplitude, but the total "sending" power is constant.