which would vary in an irregular sea. By assuming that R can be approxi- 

 mated by Hunt's formula (R = VHL Q tan 9), and by assuming that both H and 

 L are jointly Rayleigh distributed in an irregular sea, Battjes analytical 

 derives an expression for the average overtopping rate created by irregular 



waves , 



where 



(1*K) 3/2 



VT 



v^F «p (- \ r£) - ^ <•"» (t*ts <) 



(16) 



S = Battjes' dimensionless-overtopping volume per average wave period 



= B/(o.1 H L Vtan e) 



B = average overtopping volume per average wave period 



H = average wave height 



L = average deepwater wavelength 



k = statistical parameter which is directly related to 

 X (0 < < < 1) 



X = the coefficient of linear correlation of H and L Q 



x, - dimensionless freeboard 



= F/ (V H L tan e) 



erfc = complementary error function (Abramowitz and Stegun 1965) 



To calculate volumetric overtopping rate, B is divided by the average wave 

 period, T , 



o b(0.1HL Vtan 9) 



o -J! ^ 5 / (17 ) 



g Battjes t " t 



Equation 8 is shown graphically in Figure 9. 



31. Battjes shows that his statistical parameter < is a function of 

 the linear correlation between H and L , X . The relationship between X 

 and k is shown graphically in Figure 10. When H and L Q are completely 

 uncorrelated, X = and k = . When H and L Q are perfectly cor- 

 related, X = 1 and k = 1 . 



Example ^ 



32. Using Battjes method, an estimation can be made of the volume rate 

 of water which will overtop a smooth 1:6-slope sea dike with a 5-ft freeboard 

 in 10 ft of water caused by waves with an average wave height of H = 3 ft, 

 and an average wave period of T = 8 sec (Figure 11). 



18 



