Pierson and Moskowitz (1964) laid the foundation for all future discussion of ocean wave spectra. Moskowitz’s wave observations were self-similar; when plotted in dimensionless form they all fitted a single curve – the Pierson and Moskowitz spectrum. The variance density in the high frequency tail of this spectrum was deemed to be inversely proportional to the fifth power of the frequency, i.e. to be a power law spectrum with an index of -5. It was recognised that if the index were smaller in magnitude, say 4.5 or 4, waves “would break and dissipate energy”. Isn’t that the point? Isn’t that what happens in a wind sea?Wave breaking involves increases in turbulent entropy. This shapes the wind sea spectrum.
When Moskowitz’s own data are re-plotted using logarithmic scales it is clear that the index is not -5. The index is actually -3!
This is “the Fluid Catastrophe”, the failure of the Fluid Dynamics to accommodate the granular, stochastic nature of real fluids which means it cannot deal with turbulent phenomena such as breaking waves.
A paper by Reid(1992) describing experimental evidence for the role of wave breaking in the evolution of wind sea spectra can be found here.