32 



WAVE DIMENSIONS 



seas from which it has been derived, or even faster if its length has 

 increased during the period of time since it altered from sea into swell; 

 and there are reasons for thinking that this may happen (p. 66). 



It is commonly stated that the velocity of a free wave (i. e., of one 

 that is kept advancing by gravity alone) is proportional to the square 

 root of its length, 7 with the velocity in knots equal to about 1.3 times 

 the square root of the length in feet. And observations on waves at 

 sea agree closely enough with this to show that the formula is ;i close 

 approximation for waves of ordinary shape. 



Actually the velocity depends somewhat on the steepness of a wave, 

 as well, in that higher waves of a given length run a little faster than 

 lower. But this effect is so small that it can be ignored for ordinary 

 waves unless in shoal water (p. 104). (For the complete equation, 

 taking account of steepness, see O'Brien and others, 1942, p. 21, 

 equation 19.) 



The facts that the velocity of a wave in deep water is chiefly depend- 

 ent upon its length, but hardly at all upon its height, and that swells 

 reminiscent of previous storms run at the greatest velocities of all, 

 because of their great lengths (p. 66), make it as misleading to corre- 

 late the velocities of waves as a whole with the strength of the wind 

 as it is to attempt similar correlations for their steepness (p. 29), 

 unless their stage of development is known. Any such correlation 

 must therefore take account of the length of time during which the 

 waves in question have been subject to a wind of any given strength 

 if they are to be of any significance whatever. This has been at- 

 tempted in the following table, adapted and simplified from a recent 

 theoretical analysis of the subject. 



Table 15. — Theoretical wave periods {italic), in seconds, and wave velocities (bold- 

 face), in knots, in relation to the strength and duration of the wind 1 



[Based on H. O. Pub. No. 604] 



1 The theoretical relationships bet ween v elocit y, per iod, and length, for waves of small steepness, is ex- 

 pressed in the basic equations T=-»/-^ L, C=-J^- L, and L=^- T\ where T is the period, C the velocity, 



L the length, g the acceleration of gravity, and v the constant 3.14 (Krummel, 1911, and various subsequent 

 authors). 



7 According to a simplified equation C=-W Y r L ' where Cis the velocity, g the acceleration of gravity, t 

 the relation between the circumference of a circle and its diameter (approximately 3.14), and L the length; 

 or. taking the average value of g as 32.172 feet per second, C (in knots) equals about 1.34 ->/•£• See also Foot- 

 note to Table 15. 



