30 



WAVE DIMENSIONS 



If moderately high swells are included under (he heading of "storm 

 waves," as they should be since rough seas are so often running on top 

 of swells, the average ratio is not far from 26: 1 (steepness 0.038). 

 When seas have altered into swells as described on page 0-3, they are 

 often as much as 40 to 100 times as long as high, and swells so old and 

 low that they are recognizable only when they develop into surf along 

 some coastline may even be 1,000 times as long as high. Storm seas 

 and swells varying in steepness from 0.013 to 0.001 have in fact been 

 observed on the south shore of Martha's Vineyard, and probably could 

 be on any other exposed beach to which old swells commonly run. 



Table 13. — Maximum, minimum, and mean steepness of waves of different heights 

 expressed as the ratios of their lengths to their heights (boldface) and of their heights 

 to their lengths (italics) 



[Adapted from Oaillard] 



A further illustration of this general rule is that the average ratios 

 of length to height, among 179 published French observations, were 

 17: 1 for waves shorter than 100 feet, hence still comparatively young; 

 21 : 1 for those of 100 to 200 feet, hence older; 25 : 1 for those of 200 to 

 300 feet ; and 27 : 1 for those of 300 to 400 feet. 



Since, as the waves grow, length and height increase, at different 

 relative rates, the steepness of growing waves is a measure of their 

 development, for younger waves are steeper than older ones. It 

 has also been found that the age of a wave that is growing under the 

 influence of the wind may be satisfactorily expressed as the ratio of 

 wave velocity to wind velocity. The relationship between wave age 

 and wave steepness for growing waves is shown in table 14. 



The relationship between the heights of waves and their lengths, 

 whether arrived at from measurements at sea or from a theoretical 

 analysis, fails in one very striking respect, for neither method of 

 calculation would suggest that waves are ever less than about 10 times 

 as long as high (steepness 0.1), whereas it is certain that at least the 

 tops of their crests frequently rise to the angle of instability (steepness 

 0.14), else waves would not break as they so commonly do in windy 

 weather. The discrepancy arises from the fact that the theoretical 

 treatment concerns an average condition. 



