10 



PHYSICAL NATURE OF WIND WAVES 



orbit remains the same. Theoretically (and this is supported by 

 laboratory observations) this decrease in the size of the orbits is in 

 geometric progression as the depth increases in arithmetic proportion, 

 the diameters of the orbits decreasing by approximately one-half, 

 with each additional increase in depth equal to one-ninth of the length 

 of the wave (table 2) . 



Table 2. — Diameters of orbital motion, relative to the diameter at the surface, with 



increasing depth 



[According to the equation Ild = U<t>e~ iw -f, where Ih is the diameter of the orhit, H<t> the heightof the wave, 



d the mean depth of the particle, L the wave length, e a constant equal to 2.72, and ■* the constant 3.14. 

 (From Johnson)] 



Depth below mean sea level in fractions 

 of wave length 







Propor- 

 tionate 

 diameter 

 of orbit 



Depth below mean sea level in fractions 

 of wave length 



S 

 H 

 % 

 H 



Propor- 

 tionate 

 diameter 

 of orbit 



H* 



Mi* 



^12 



The orbits calculated by this ratio, for a wave 16 feet high and 

 360 feet long, for example, which would be 16 feet in diameter at the 

 surface, would be 8 feet in diameter at a depth of 40 feet, 2 feet at 

 a depth of 120 feet, and only 0.059 foot in diameter at 320 feet, and 

 so on. Even for a wave 40 feet high, the orbits circled by each particle 

 would be less than an inch in diameter at a depth of 360 feet. And 

 the velocities with which the water particles circle their orbits 

 decrease in a corresponding ratio as the depth increases, because the 

 period occupied by them in so doing is dependent solely on the time 

 required for the passage of two successive crests past a given point 

 and so continues the same no matter what the depth. For example, the 

 orbital velocity of the particles in a wave 10 feet high and 360 feet 

 long from crest to crest, which would be about 3.9 feet per second at 

 the surface, would be about 0.8 foot per second at a depth of 90 feet, 

 0.17 foot per second at 180 feet, and 0.04 foot per second at 270 feet. 

 The effects of choppy seas 6 to 8 feet high, such as are common when 

 the wind is rising, would not be great enough to be of any practical 

 importance deeper than 40 to 50 feet, or those of waves 100 to 200 feet 

 long deeper than say 50 to 100 feet, while wave action is wholly negli- 

 gible, even from the theoretical standpoint, at depths greater than 

 the length of the waves in question. The most interesting illustra- 

 tion, from the navigational standpoint, of the decrease in wave action 

 as the depth increases is afforded by the operation of submarines, for 

 these seldom roll or pitch appreciably when submerged deeper than 

 90 feet. It is for this reason that it is easy to take pendulum measure- 



