54 WAVES 



same velocity, its height would be 0.82 as great as previously and 

 its length 1.28 as great. Thus a contrary current affects the heights 

 of waves much more in proportion than a following current does, a 

 matter of importance in connection with tide rips. For example, the 

 steepness of the 100-foot wave would very shortly he increased by 

 about 2.07 if it ran into a contrary current of 2 knots, and by 1.35 if it 

 ran into a contrary current of only 1 knot. The result is that when 

 moderately steep waves run into contrary currents, the increase in 

 their heights, combined with the decrease in their lengths, may ren- 

 der them so much steeper still as to cause a violently breaking sea. 

 Thus, a head current of 2.2 knots would soon cause a wave that was 

 5 feet high and 100 feet long, to start with, to steepen to the breaking 

 point. 



The effects of currents on the heights of waves are the greater, the 

 shorter the waves and the lower the wave velocities, because the dif- 

 ference between the speed of the current and the original velocities 

 of the waves is less then. If, for example, the wave just men- 

 tioned, as encountering a head current of 2 knots, were only 50 feet 

 long, the ratio of velocity of current to that of the wave would be ; 

 about 0.21. in which case the effect of the current would be to increase 

 the height of the wave by about 1.9 or nearly to double it, if the wave 

 did not break. And for the same reason, the decrease in height in a 

 following current is greater for a short wave of low velocity than for 

 a long one. 



The surface currents that are of concern to the seaman, as they 

 affect the shapes of waves, may be classified as '"wind drifts," as 

 "ocean currents," and as "tidal currents." It is not necessary for our 

 present purposes to discuss the basic causes for larger ocean currents. 



The frictional drag of a wind blowing in a constant direction for 

 more than a brief period soon sets a wind drift in motion, the velocity 

 of which varies according to the strength and duration of the wind, 

 entirely apart from any velocity of mass transport by the waves 

 (p. 6). And drifts of this sort are often so strong that they must 

 be taken seriously into account in navigation, especially in coastwise 

 waters where a slight error in one's dead reckoning may have serious 

 results. In most cases, however, the velocities of wind drifts average 

 only about 1.5 to 2 percent as great as that of the wind, 14 which is not 

 enough for them to have any great effect on the shapes of the waves 

 that may be running either with them, or even against them. The 

 drift, for example, set up by a 20-mile wind would average only about 

 0.3 to 0.4 knot, which is only about 0.03 of the velocity of the waves that 

 winds of that same strength should, theoretically, generate after blow- 

 ing for a period of 10 hours. Even if the current were directly con- 



14 Based on a very large number of observations by the U. S. Coast and Geodetic Survey. 



