Chapter 3 



THE CONTOURS OF WAVES; THE EFFECTS OF CURRENTS AND OF 

 SHOAL WATER; THE MEASUREMENT OF WAVES 



The Profiles and Surface Contours of Waves 



The theoretical profile of a free surface wave of oscillation (i. e., 

 of one that is no longer being driven by the wind but is running on its 

 own momentum, p. 69) is very nearly the shape of a trochoid. That 

 is to say, it follows the curve that would be outlined by the motion 

 of a point within a disc, if the disc were rolled along the underside 

 of a level surface (fig. 9) . In a curve of this kind the crest is slightly 



Figuke y. — Profile of a wave of trochoid form 20 times as long from crest to 

 crest as it is high from crest to trough. 



steeper and narrower than the trough, i. e., the mean level of the 

 water is a little lower than midway between crest and trough, a 

 phenomenon which has some importance in relation to harbor con- 

 struction but is not of practical interest in relation to ocean waves. 



Storm waves still being built up by the wind are usually between 14 

 times and 24 times as long (from crest to crest) as they are high, so 

 that their average slopes from crest to trough would range from 1 in 

 7 (8°) to 1 in 12 (5°) if the profile of the wave from trough to crest 

 were a straight line. But it is actually concave in the trough and 

 convex on the crest, so that the slope is somewhat steeper near the top 

 of the latter. 



In the case of comparatively long waves, this curvature is so gentle 

 that its effect is very small. If, for example, a wave were 100 feet 

 long and 5 feet high (a common ratio of length to height), its slope 

 would average only about 7° to 8°, along a distance of 15 feet of the 

 steepest part of the actual curve, contrasted with about 5° (or 1 in 

 10) along a direct line from the bottom of the trough to the top of the 



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