Yan Mater and Neat 



the water depth, h. In addition expressions are needed which deter- 

 mine the wave height decay after breaking and the point at which 

 spilling waves regain their stability. In the absence of an adequate 

 theoretical base a purely empirical approach will be used. 



Experimental evidence has been plentiful. Iverson [ 1952] 

 and Morison and Crooke [1953] made classical contributions. 

 Nakamura, Shiraishi, and Sasaki [ 1966] presented what is perhaps 

 the broadest range of data on breaking and decay after breaking. A 

 fairly complete bibliography of other works on the subject appears 

 in Van Mater [ 1970] . 



No uniformly satisfactory criterion which predicts both the 

 occurrence and the location of wave breaking has yet been developed. 

 A commonly used but crude criterion is that a wave breaks when the 

 wave height-to-water-depth ratio is equal to or greater than 0.78. 

 The Nakamura et al, paper previously alluded to contains all this 

 information covering a rather broad range of beach slopes and wave 

 conditions, and on this basis it was selected to develop the criteria 

 needed for this application. The paper is essentially a report of 

 experimental data with no analytical comparisons or proposals. A 

 comparison of the shoaling coefficients inferred from the Nakamura 

 data shows lower values for the gentler bottom slopes than would be 

 obtained by linear theory. This gives rise to suspicion of prominent 

 frictional effects in the experiments. Although the wave height may 

 have been attenuated by friction as the waves moved inshore it seems 

 reasonable to assume that the characteristics, w, H, and h, at the 

 breaking point would not be severely affected. More vulnerable, 

 perhaps, is the rate of decay after breaking and the length of the surf 

 zone reported in the paper. Nevertheless, the scale of the experi- 

 ments is approximately the size of those with which we are concerned. 

 The following formulas are a result of reworking and fitting curves 

 to the Nakamura data, 



(a) Wave breaking occurs if: 



2, 1/4 



< (loiii^ -i.if +log|J^i|^)'^'*+0,10 (wVg< 0-13, S > O.Oi) 



(19) 



where S = tangent of the angle of bottomi slope. A plot of this criteria 

 for several bottom slopes is given in Fig. 4, 



252 



