Figure 3.6 already showed that real ocean wind waves have an irregular character (not-periodic, not repeating itself in time and space) as opposed to the single sinusoidal signal in Fig. 3.1. The waves are therefore called irregular or random waves. In spite of the seemingly unpredictable (random) way in which the signal fluctuates, if we describe the short-term variations in a statistical way by taking average parameters it appears that the statistics can be considered constant in time (stationary). In order for the averages to be representative of the sea state, the record should be short enough to be statistically stationary (not changing in time). On the other hand the record should be long enough to get reliable averages. At sea 15 to 30 minutes is used, most commonly 20 minutes. On longer timescales the short-term mean values are variable due to variations in mean wind velocity, tidal elevation or tidal currents which change the wave characteristics. Thus wind waves are a random stationary process for timescales up to half an hour. In practice one recording of for instance 20 minutes is done every three hours. This record is thought to be representative for the entire time-period of three hours. The duration of a storm is generally 6 to 8 hours in which the conditions (mean wind speed) are more or less constant.
There are basically two ways to characterise a wave record in terms of its short term statistics:
- Based on direct analysis of the time series and regarding it as a sequence of individual waves each with their own wave height and wave period (wave-by-wave analysis);
- Through a spectral analysis using the fact that the surface can be seen as a summation of an infinite number of sine waves with different heights, periods and directions.
The short-term statistical analysis based on the time series is treated in Sect. 3.4.2. Spectral analysis is dealt with in Sect. 3.4.3. It appears that the short-term distribution of wave heights can be described by a Rayleigh distribution as long as we are dealing with not too steep waves (wave slope \(ak\) small) in deep water. In those conditions the parameters as determined by the wave-by-wave analysis and by the spectral analysis can be related to each other by constant ratios. This is the topic of Sect. 3.4.4.