APPENDIX B 



DISTINCTION BETWEEN SIGNIFICANT AND ROOT -MEAN -SQUARE WAVE HEIGHTS 

 IN PREDICTING LONGSHORE TRANSPORT RATES 



The four equivalent expressions for longshore energy flux, Pjj^, given 

 in Table 4-7 of the SPM are developed from small -amplitude linear theory ^see 

 App. A), and each expression for P^ contains the wave energy density, E, 

 as a linear factor. The energy density per wave is 



^h2 



(B-1) 



where w is the weight density of seawater, and H is the wave height measured 

 from crest to trough (see Fig. B-1). For a group of waves, N in number, each 

 with wave height H^ , for i = 1 to N, the average energy density is given by 



(E) = L Y. - H^ 



- CH 12 



(■B-2) 



where H is the root -mean- square (rms) wave height given by 



(B-3) 



Still- 

 Woter 

 Leve 



•-Time, t 



Figure B-1. Definition of wave height and amplitude for 

 simple sinusoidal wave function. 



Thus, the rms wave height is the proper wave height to use in evaluating 

 F and hence P. . In conditions where a uniform train of periodic waves exists, 

 approximated in some laboratory experiments, all of the H^ are equal. Thus, 

 by equation (B-3), H- is identical to Hp^g . In such cases H^ is inter- 

 changeable with Hp^g^ in equation (B-2). In natural conditions, however, such 

 as ocean waves approaching a shore, the wave heights are usually not uniform. 

 In such cases, the entire distribution of wave heights to determine Hp^g must 

 be considered or some other type of average wave height computed. It has been 

 the general practice of coastal engineers to use an average wave height called 

 the significant wave height, H , assumed equivalent to the mean of the highest 



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