A STATISTICAL STUDY OF THE EFFECT OF WAVE 

 STEEPNESS ON WAVE VELOCITY 



by 



Rudolph P. Sav a ge, Hydraulic Engineer 

 Research Division, Beach Erosion Board 



Theoretical investigations of the velocities of ocean waves have 

 in general concluded that wave steepness (H/l) has a negligible effect 

 on wave velocity when the wave steepness is small. Under these con- 

 ditions, the wave velocity is given by 



C H _ =|~_i tanh kdl* (l) 



where C^_q is the wave velocity neglecting wave steepness (Airy 

 Theory) (ft/sec.) 

 g = Acceleration of gravity (ft/sec^) 



k = 2^/L (1/ft.) 



d = Water depth (ft.) 



This result can be derived from the AIRY theory(l)*, which neglects 

 wave steepness, and from the theories of STOKES (1) and GERSTNER(l), 

 which consider wave steepness. 



When the wave steepness becomes large, Stokes theory as modified by 

 STRUIK (2) and W0LF(3) predicts that the wave velocity will increase 

 and gives the velocity to the second approximation as 



£1\- . „ .T>* 



C T = C H=0 



(2) 



where C^ = the wave velocity considering wave steepness (Stokes theory) 

 (ft/sec) 

 H = Wave height (ft) 



L = Wave length (ft.) 



and f (d/L) is given by 



2 cosh^ ~ T + 2 cosh — i — + 5 



f(d/l) 



lh^ 



2 77-d 



The present investigation seeks to determine the comparative degree of 

 reliability of these theories in predicting the wave velocity. 



* Numbers in parentheses refer to list at end of paper. 



