C 2 /C n 2 = C/C n . tanh 2 77 d/L = L/L tanh 2 77d/L< 



therefore, we have#- 



C/C = L/L 



C/C Q - L/Lq = tanh 2 77" d/L (U) 



The wave length changes with depth,, and so it is inconvenient to u§e d/L 

 as a parameter., The most convenient term to measure is the period, since 

 it is a constant o Thus, L may be computed easily because L Q = g_ ^2; 

 therefore, it is most convenient to use the parameter d/L 277 



d/L x L/Lq s d A 3 and k/Lo = tanh 2 77 d/L 



At any value of d/L, L/Lq can be had from L/L = tanh 2 77 d/L, and by 

 multiplying d/L x L/Lq, d/L can be obtained „ In order to build up a 

 table of d/Lo vs L/Lq and C/0 o a series of expanded accurate graphs were 

 made by plotting 6,/Lq vs d/L and then for the interval of d/L Q chosen, the 

 corresponding values of d/L were read off „ Then the values of L/Lq and 

 0/C o were recomputed „ 



In addition, in shallow water, the orbital motion is elliptical and 

 the ratio of the semi-minor (b s ) and the semi-major (a s ) of the surface 

 orbit is equal to the tanh 2 7T d/L, i.e., b s / a s = "tanh 2 "^ d/L. In the 

 tables to follow values of tanh 2 77 d/L (which is equal to b g /a , C/G , 

 and L/L ) are given in column 4 as a function of d/L_ or d/L» 



Pressure Response Factor; In order to make use of under-water pressure 

 instruments, it is necessary to know what height of wave give a particular 

 pressure response at some depth below the still water level „ It has been 

 found*-* that 



Z 

 K = H'/fe » P/P - cosh 2 7T d/L (1-d) 



cosh 2 77 d/L (15) 



where P is the pressure fluctuation at a depth Z below still water, P is 

 the surface pressure fluctuation, d is the depth of water (from still 

 water level to the ocean bottom), L is the wave length in any particular 

 depth of water, H is the height of wave at the surface, and H' is the 

 corresponding variation of head at a depth g a 



*- Breakers and Surf, Principles of Forecasting, Hydrographic Office 

 Publication No „ 234o 



*-*- Sub-surface Pressures Due to Oscillatory Waves, by R. Go Folsom. 

 Trans o American Geophysical Union, Volo 28, No. 6, December 194-7, 

 pp 875-381 o 



