Distribution of ocean waves by Rayleigh

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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 ?
 
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Dbe.098 said:
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.