Table B presents the comparison results included in the experimental validity evaluation. 

 The eight comparisons of horizontal water particle velocity are presented in Figures 13 

 through 20; the vertical velocity comparison is presented in Figure 21; and the wave profile 

 is presented in Figure 22. 



Figures 13 through 20 indicate that the Stream -function theory is in reasonable 

 agreement with the data. It is noteworthy that the shallow-water wave theories which 

 should provide good fits to the data are so poor. Another interesting feature of the 

 comparison is that the Unear (Airy) wave theory agrees better with the data than would be 

 expected. 



Of the 12 theories included in the comparison, the better agreements with data were 

 provided by the following five theories: Airy, Keulegan and Patterson Cnoidal wave theory, 

 Goda, Long- Wave, and Stream -function. These five theories were then selected for further 

 examination of their agreement with the data. The standard deviations between each of 

 these theories and the data were calculated, and are presented in Table C where it is seen 

 that the Stream-function theory provided the best fit to the data, followed, in order, by the 

 Goda, Keulegan and Patterson Cnoidal, Airy, and the Long- Wave Theories. 



The Goda "theory" is actually a series representation in which the analytical forms of the 

 terms comprising the series are the same as the hyperboUc and trigonometric functions in 

 the Stokes theories. However, the coefficients modifying these terms were determined 

 empirically by wave tank experiments. 



Additional calculations not presented here showed that, assuming the data were vaUd, the 

 Stream-function wave theory would on the average overpredict the maximum total drag 

 force on a vertical cyhnder by 21 percent. 



Data representing the vertical velocity distribution with depth are available for only one 

 set of wave conditions, (see Figure 21). The McCowan theory provides the best fit to the 

 data; the next best fit is associated with the Stream-function theory. Differences between 

 the McCowan and Stream-function theories, however, are quite small and it is probably not 

 justified to draw conclusions from only one set of data. Interpreted in terms of vertical drag 

 forces on a horizontal cylinder, the Stream-function would underpredict the forces by 30 

 percent. 



The one set of wave profile data are compared with the various theories in Figure 22. 

 Although no detailed comparisons were made, it appears that the Stream -function theory is 

 in as good or better agreement than any of the other theories shown. 



Conclusions Resulting from the Experimental Validity Study 



Comparisons of Stream-function theory predictions with measurements of velocity 

 components and one wave form representing transitional and shallow -water waves indicate 

 reasonably good agreement. Interpreted on the basis of maximum horizontal drag force 

 components, the Stream-function theory would over predict by an average of 21 percent. 

 Recognizing that the experimental accuracy is approximately 5 percent these results are 

 considered reasonable for engineering apphcations. The predicted maximum vertical drag 



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