k2 = 1 - 10"5.10 

 Entering Figure 2-12 with the value of k gives 



l2h 



= 290 



or 



From Airy theory, 



290 d3 _ / 290(3)3 

 L = 88.5 m (290.3 ft) 



gT2 /2Tid\ 



L =- — tanh = 80.6 m (264.5 ft) 



2tt I L / 



To check whether the wave conditions are in the range for which cnoidal wave 

 theory is valid, calculate d/L and the Ursell or Stokes parameter L^H/d^. 



Therefore, cnoidal theory is applicable, 

 (b) Wave celerity is given by 



L 88 5 



C = - = — = 5.90 m/s (19.36 ft/s) 



T 15 



while the Airy theory predicts 



C = - = -^^ = 5.37 m/s (17.63 ft/s) 



Thus if it is assumed that the wave period is the same for cnoidal and Airy 

 theories then 



C L 



cnoidal cnoidal 



= m 1 



C L 



Airy Airy 



(c) The percentage of the wave height above the SWL may be determined from 

 Figure 2-13. Entering the figure with L^H/d^ = 290, the value of (y^. - 

 d)/H is found to be 0.865 or 86.5 percent. Therefore, 



2-54 



