The wave spectrum is the term that describes mathematically the distribution of wave energy with frequency and direction. The wave spectrum consists of a range of frequencies.

Remember that ocean waves are composed of a multitude of sine waves, each having a different frequency. For purposes of explanation, these frequencies are arranged in ascending order from left to right, ranging from the low-valued frequencies on the left to the high-valued frequencies on the right, as illustrated in figure 6-3.

A particular range of frequencies, for instance, from 0.05 to 0.10 does not, however, represent only six different frequencies of sine waves, but an infinite number of sine waves whose frequencies range between 0.05 and 0.10. Each sine wave contains a certain amount of energy, and the energy of all the sine waves added together is equal to the total energy present in the ocean waves. The total energy present in the ocean waves is not distributed equally throughout the range of frequencies; instead, in every spectrum, the energy is concentrated around a particular frequency (fmax), that corresponds to a certain wind speed. For instance, for a wind speed of 10 knots (kt) fcnax is 0.248; for 20 kt, 0.124; for 30 kt, 0.0825; for 40 kt, 0.0619. For more

Figure 6-3.-A typical frequency range of a wave spectrum. 

information refer to the publication Practical Methods for Observing and Forecasting Ocean Waves (H.O. Publication 603), which gives the complete range of fu values and the corresponding periods for wind speeds, starting from 10 kt, at 2-kt intervals, Notice that the frequency decreases as the wind speed increases, This suggests that the higher wind speeds produce higher ocean waves. The table mentioned above can be graphed for each wind speed, An example of such a graph can also be found in H.O. publication 603.

It is difficult to work with actual energy values of these sine waves; for this reason the square of the wave amplitude has been substituted for energy. This value is proportional to wave energy.

The square of the wave amplitude plotted against frequency for a single value of wind speed constitutes the spectrum of waves. Thus, a graph of the spectrum is needed for each wind speed, and the energy associated with each sine wave can be determined from these graphs. Each wind speed produces a particular spectrum; and the higher the wind speed, the larger the spectrum.

LEARNING OBJECTIVES: Describe the generation and growth of sea waves. Explain the formation of fully developed seas. Recognize the factors associated with nonfully developed seas, and determine and analyze features associated with sea waves. Define sea wave terms and describe an objective method of forecasting sea waves.

Since sea waves are in the generating area, forecasting of them will be most important when units are deployed in areas close to storm centers. Problems encountered in providing these forecasts will include accurately predicting the storm track and the intensity of the winds that develop the sea waves. Now lets look at the generation and growth of sea waves.

When the wind starts to blow over a relatively calm stretch of water, the sea surface becomes covered with tiny ripples. These ripples increase in height and decrease in frequency value as long as the wind continues to blow or until a maximum of energy has been imparted to the water for that particular wind speed. These tiny waves are being formed over the entire length and breadth of the fetch. The waves formed near the windward edge of the fetch move through the entire fetch and continue to grow in height and period, so that the waves formed at the leeward edge of the fetch are superimposed on the waves that have come from the windward edge and middle of the fetch. This description illustrates that at the windward edge of the fetch the wave spectrum is small; at the leeward edge of the fetch the spectrum is large.

These waves are generated and grow because of the energy transfer from the wind to the wave. The energy is transferred to the waves by the pushing and dragging forces of the wind. Since the speed of the generated waves is continually increasing, these waves will eventually be traveling at nearly the speed of the wind. When this happens the energy transfer from the wind to the wave ceases, When waves begin to travel faster than the wind, they meet with resistance and lose energy because they are then doing work against the wind. This then explains the limitation of wave height and frequency that a particular wind speed may create.

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