Diagrams of Wave Function s 



Relationship Between Depth and the Height, Period, Length, and Velocity 

 of leaves ; Plates 1-9, inclusive, present the relationship between wave 

 period, length, velocity, and depth- These curves have been plotted from 

 the following equations; 



V 27T 



tanh 27Td_ 



L (1) 



L = CT (2) 



On Plate 1 velocity has been eliminated, giving the relationship 

 between wave period and length for curves of constant deptho Plate 2 is a 

 large scale plot of the region on Plate 1 where the wave length is less than 

 70 feet and the wave period is less than 5 seconds. In Plate 3 wave length 

 has been eliminated to give a relationship between period and velocity for 

 constant depths- Plate 4- is a large scale plot of the portion of Plate 3 

 where the period is less than 1..8 second and the wave velocity is less than 

 5 feet per second- Plate 5 shows velocity plotted against depth with period 

 as a parameter- 



Plate 6 is from Breakers and Surf, Hydrographic Office Publication No„ 

 234- and gives the relationship between wave velocity, wave period, and 

 depth- These curves differ from those in Plate 5 because a small correction 

 for deep water steepness has been made- 



Plate 7 shows depths in fathoms plotted against wave period in minutes 

 with curves of constant velocity and curves of constant d/L. Velocity is in 

 knots- The equations for these curves are derived from equations (1) and 

 (2)j thus, substituting CT for L in equation (1); 



inh 



Solving for d% 



27T uami CT (3) 



d = CT x -1 27TC 



-tanh — 



27T ^ Lil gT (4) 



Putting in the proper constants to change d from feet to fathoms, C from 

 feet per second to knots, and T from seconds to minutes: 



d =2-69 CT tanh -1 (0-00548 C/T) 

 or 



d = 1-343 CT [log e (1 + 0-00548 C/T) - log e (1 - 0-00548 C/tJ (5) 



