T = wave period 



k = 27r/L , radian wave number with 



L = wavelength 



6'= InB/ZdO , direction (in radians counterclockwise from the 

 negative x-axis) from which waves are coming 



6 = (the same) wave direction in degrees 



^ = initial phase or location in the wave cycle at some fixed 

 point in space and time 



41. Wherever possible in this report, wave direction will be given in 

 degrees; therefore, the variable 9 will be used. Conversion to 6' is only 

 necessary in arguments of trigonometric functions. 



42. In linear theory, wave number k is uniquely related to frequency 

 f for a given water depth. The formula is known as the dispersion relation 

 and is given by 



47r2f2 = gk tanh kd (2) 



where g equals acceleration as a result of gravity, and d equals water 

 depth. 



43. Though there are many variables involved in Equations 1 and 2, most 

 are known or can readily be computed. Generally, for a given depth of water, 



a complete description of the sea surface and all the other properties of a 

 single wave train are known if the variables a , f , ^ , and <j> are 

 specified. In particular, the mean wave energy per unit crestlength E 

 available to do work (on a beach or structure) can be found. It is given by 



E(f,0) = ipga^ (3) 



where p equals water density (mass per unit volume) . In the ocean, the 

 factors p and g vary by less than 3 percent. It is conventional to drop 

 them from expressions which refer to energy (as in spectral formulations) with 

 the understanding that they are to be reintroduced when actual energies are 

 computed. This abbreviated expression for mean wave energy per unit crest- 

 length has units of length squared and is given by 



19 



