Equation (2-4b) explicitly gives L in terms of wave period T and is suffi- 

 ciently accurate for many engineering calculations. The maximum error of 5 

 percent occurs when Zird/L^l . 



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

 travel. The following classifications are made according to the magnitude 

 of d/L and the resulting limiting values taken by the function tanh (Zird/L): 



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



reduce to 



"gL L 



2lT 



o o 

 T~ 



and 



C =^ 

 o 2tt 



(2-5) 



(2-6) 



Although deep Dater actually occurs at an infinite depth, tanh (2iTd/L), 

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

 relative depth of one-half (i.e., when the depth is one-half the wavelength), 

 tanh (2TTd/L) = 0.9964. 



Thus, when the relative depth d/L is greater than one-half, the wave 

 characteristics are virtually independent of depth. Deepwater conditions are 

 indicated by the subscript o as in L^ and Cq. The period T remains 

 constant and independent of depth for oscillatory waves; hence, the subscript 

 is omitted (Ippen, 1966b, pp. 21-24). If units of meters and seconds are 

 specified, the constant g/2Tr is equal to 1.56 meters per second squared and 



and 



C = 



L = 



§1 

 2Tr 



gT2 



2Tr 



9.8 



2tt 



T = 1.56T m/s 



9.8 



2Tr 



t2 = 1.56t2 m 



(2-7a) 



(2-8a) 



If units of feet and seconds are specified, the constant g/2TT is equal to 

 5.12 feet per second squared and 



C = -^ = 5.12T ft/s 



O 2lT 



(2-7b) 



2-9 



