Scaling analysis of wave profiles

In the field of wind-wave interaction, scaling features for both wind and waves are often found experimentally. Several theoretical explanations of the scaling law for wind speed and sea surface wave height have been advocated, while a theoretical consideration for the significant wave height (Hs) is still lacking. In this work, we considered a long-term (more than 20 years) and high sampling frequency (about 0.78 Hz) wave profile data collected by buoys provided by Coastal Data Information Program (CDIP). The scaling features for Hs and for the absolute value of the wave profile are evident in the sense of the Fourier power spectrum. The same scaling features were obtained for frequencies below 10^-4 Hz, with a scaling exponent close to 3. While the spectrum for wave profile shows a plain-like distribution under the frequency around 0.02 Hz due to the band pass filter. Furthermore, measured Hs is well overlapped with the absolute value of the wave profiles, which indicates that the amplitude modulation is still preserved after band pass filtering, and that might be the reason for the existence for the scaling features for Hs.