exceed unity, then according to the equations of motion, the pressure beneath the wave 

 crest would be negative which is unrealistic and would indicate an unstable water surface. 



It should be noted that the theory employed in the study is composed of a finite series of 

 terms. To adequately define an instabiUty formally, it may be necessary to extend the 

 representation to include an infinite number of terms. The results presented here for the 

 free surface breaking parameters should be interpreted accordingly. For the sample output 

 (Case 4-D, Table XI, Item 14) shows that the kinematic free surface breaking parameters for 

 the linear and Stream -function representations are 0.429 and 0.733, respectively. The 

 corresponding values (Table XI, Item 15) for the dynamic free surface breaking parameter 

 are 0.0409 and 0.286, respectively. The wave height associated with this case is 

 approximately 0.78 of the depth and according to the McCowan criterion, the wave would 

 be breaking. 



Example 6— Combined Shoaling-Refraction 



The shoaUng-refraction results were not tabulated, but are presented for various 

 deepwater directions in graphical form as Figures 25 through 29 of this report. 



Example 6-a 



Consider a deepwater wave propagating over bathymetry characterized by straight and 

 parallel contours; the deepwater wave conditions considered are: 



Ho = 11.52 ft 

 T = 15 sec 

 ao = 40° 



Suppose that we wish to find the wave height and direction in a water depth of 30 feet and 

 also the wave height, water depth and wave direction at breaking. Figure 28 is applicable for 

 a deepwater wave direction of 40°. The deepwater wavelength L^ is calculated as: 



^0 =^^' =17^2 (15)^ = 1152 ft 



therefore 



and for h = 30 ft 



Ho 



Lo 





0.01 



h 

 Lo 



= 



30 

 1152 



= 0.0260 



84 



