From Equation 2-1, it is seen that 2-2 can be written as 



gT , /27rd 



C = — tanh 



2iT \ L > 



(2-3) 



The values 2Tr/L and 2Tr/T are called the wave number k and wave angular 

 frequency w, respectively. From Equations 2-1 and 2-3 an expression 

 for wavelength as a function of depth and wave period may be obtained. 



L = 



2-n 



tanh 



(2-4) 



Use of Equation 2-4 involves some difficulty since the unknown L, appears 

 on both sides of the equation. Tabulated values in Appendix C may be used 

 to simplify the solution of Equation 2-4. 



Gravity waves may also be classified by the depth of water in which 

 they travel. Classification is made according to the magnitude of d/L 

 and the resulting limiting values taken by the function tanh(27rd/L) . 

 Classifications are: 



In deep water, tanh(2TTd/L) approaches unity and Equations 2-2 and 2-3 

 reduce to 



and 



"gLT L, 



^o V 27r T 



° lit 



(2-5) 



(2-6) 



Although deep water actually occurs at infinite depth, tanh(2ird/L) , 

 for most practical purposes, approaches unity at a much smaller d/L. For 

 a relative depth of 1/2 (that is, when the depth is one-half the wavelength), 

 tanh(2Trd/L) = 0.9964. 



Thus, when the relative depth d/L, is greater than 1/2, the wave 

 characteristics are virtually independent of depth. Deepwater conditions 



are indicated by the subscript 



as in 



and Cq. The period T, 



remains constant and independent of depth for oscillatory waves; hence the 



2-9 



