STEEPNESS 



29 



Table 12. — The average steepness of waves, expressed as the ratios of their lengths to 

 their heights (boldface, to nearest whole number) and of their heights to their lengths 

 (italics) , for winds of different strengths and durations 



[Based on tables 4 and 15] 



Observations taken at sea cannot be expected to yield any general 

 rule for the ratio of the lengths of ocean waves to their heights, be- 

 cause low waves may either still be very young — hence, relatively short 

 and steep — or they may represent very old swells, in which case they 

 may be many times as long, relative to their heights. The ratios of 

 length to height among the 2- to 5-foot waves, for example, that are 

 listed in one of the most extensive tabulations yet published (Gaillard, 

 1904, p. 79), ranges from 10 : 1 to 125 : 1 (steepness 0.1 to 0.008). In 

 the case of very high waves, however, the ratio of length to height 

 is never as great as this last, for the fact that they still continue rela- 

 tively high shows that their proportions have not altered very greatly 

 since the wind commenced to die down. Thus, the largest ratio of 

 length to height for waves of 15 feet and higher (34 cases) that is in- 

 cluded in the tabulation cited is 45.6 : 1 (steepness 0.022). And while 

 the smallest ratio there listed is 10:1 (steepness 0.1), it is certain 

 that waves sometimes are as steep as 7 : 1, when they become unstable. 



Since it is 1 among old — but low — waves that the lengths are greatest 

 relative to the heights, the ratio of length to height would average 

 somewhat greater for low waves than for high, if waves of all stages 

 of growths were combined. But an average of this sort is meaningless 

 in the case of low waves, for the reason just stated, unless indeed the 

 cases that represent waves still in the process of growth can be segre- 

 gated in some way from those that represent old swells. The need for 

 this precaution has been emphasized before, but no attempt to do this 

 appears ever to have been made for any extensive series of data. And 

 the most that we dare offer in this connection is that the ratio of length 

 to height is usually less than 25 : 1 (steepness 0.040) for waves that are 

 still growing in height, or of such as have only recently attained their 

 maximum heights, as appears from the following tabulation for 68 

 published cases falling in this category from different oceans (table 

 13). 



