S = S = transformed component in x-direction 



S„„ = S = transformed component in y-direction 



S, „ = S„-^ = S = transformed shear stress component 

 12 21 xy 



and given by equations (23), (24), and (25), respectively. The validity of 

 this approach improves for narrow frequency and directional spectra. 



Another model for predicting irregular wave height distributions near- 

 shore on continuously decreasing depths was proposed by Goda (1975). The 

 following assumptions are made: (a) the equivalent significant wave height 

 and peak spectral period in deep water are known; (b) the Rayleigh distri- 

 bution applies in deep water for wave heights; (c) average beach slope is 

 known; (d) empirical formulas for wave setup, breaking limits, etc. are 

 applicable; (e) wave shoaling is nonlinear; and (f) broken waves can re- 

 form at smaller heights. A numerical procedure to use this model to predict 

 nearshore conditions, maximum wave heights, and critical water depths has 

 recently been developed (Seelig and Ahrens, 1980'*'* ; Seelig, 1980'+^). Goda's 

 model is similar to Battjes (1974a) but provides a smoother cutoff at break- 

 ing by use of a varying probability for the breaking ratio, y. 



Finally, as briefly mentioned earlier in Section IV of this chapter, 

 Battjes and Janssen (1976) used hydraulic jump bore theory to calculate the 

 energy loss rate in the surf zone for irregular waves. The same probability 

 theory as described above (Battjes, 1974a) is utilized except the probabil- 

 ities (Q, ) are expressed in terms of H and H to give a clearer physical 

 meaning. The local value of H is found by integrating the fundamental 

 surf zone energy equation (44) 



8F 

 X 



8x 



+ D = 



with F = ECgcosa 



X 



and E = ^DgH^ (123) 



8 '^ rms 



To close the system of equations for H^jng, the rate of energy dissipation 

 per unit width D was determined from classical hydraulic jump theory with 

 the depth across the jump approximately the local wave height. This gave 



D = K f Q, fpgH^ (124) 



4 b ° m 



for irregular waves with f the mean frequency df the energy spectrum and K, 

 a constant, near unity if the model is acceptable. 



'*'*SEELIG, W.N. , and AHRENS , J., "Estimating Nearshore Conditions for Irregular 

 Waves," TP 80-4, U.S. Army, Coirps of Engineers, Coastal Engineering Research 

 Center, Fort Belvoir, Va. , June 1980 (not in bibliography). 



'^^SEELIG, W.N., "Maximum Wave Heights and Critical Water Depths for Irregular 

 Waves in the Surf Zone," C2TA 80-1, U.S. Army, Corps of Engineers, Coastal 

 Engineering Research Center, Fort Belvoir, Va., Feb. 1980 (not in bibliography) 



136 



