By Norguet F. (Ed)

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Additional resources for Fonctions de Plusieurs Variables Complexes III: Sa(c)Minaire Franaois Norguet

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The coastal wave height mentioned in a weather report is usually the significant wave height; sometimes an estimate of the expected maximum waves will be added. However, the early investigators could have used the average wave height or one of many other “statistical” measures to describe a group of waves. If waves recorded at a given location were sorted, the record would have a set of wave heights ranging from small to large. To obtain the significant wave height from these sorted data, you would take the average of the largest onethird of the heights.

Surfers’ old advice to look for the seventh wave has some truth. This figure illustrates how waves travel in groups. Whether the seventh wave is the largest is certainly open 28 CHAPTER 1 Figure 5 Simulated variation of water surface with time at a given location, showing the “groupiness” of the waves. Time increases from left to right. WAVES 29 to question, but it is evident here that the height of the waves in each group grows to a maximum and then decreases. A musician reading this might notice that there appears to be a “beat” in the wave record.

In a very simplified sense, an observer looking down on a group of ocean waves sees, as a first approximation, what looks like an irregular corrugated surface with different distances between the peaks of the corrugations. Thus, the observer would see a range of wave lengths, and if the observer were at one location and watched these waves pass by he would observe a range of intervals of time between crests or periods. Generally, what at first appears to be a random distribution of wave amplitude and wave length (or wave period) in an observation of a group of ocean waves results in a relatively peaked spectrum.

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