water-wave research on this problem would be improved measurements. If however, the 

 disagreement between theory and experiment is much larger than can be attributed to 

 experimental error, and especially if this difference were of engineering significance, then 

 additional efforts on the formulation and solution of water wave theories would be 

 indicated. 



The availability of data is inadequate to carry out a comprehensive evaluation of 

 experimental vahdity over all ranges of relative depth and heights of engineering importance, 

 LeMehaute,Divorky, and Lin (1968) have carried out a measurement program in which 

 distributions over depth of horizontal water particle velocities were measured under the 

 crest phase position of fairly high waves in the shallow and transitional depth ranges. The 

 results included measured horizontal water particle velocity distributions for eight cases, and 

 also a vertical water particle velocity distribution for one case, and one measured wave 

 profile. Le Mehaute, Divorky, and Lin compared a number of wave theories with their data; 

 however the Stream-function theory was not included. The experimental validity reported 

 in this study was based on a comparison of the Stream-function theory with the data 

 described earher. 



It should be emphasized that the only addition to the paper by Le Mehaute, Divorky, and 

 Lin (1968) is (1) comparison of the Stream-function theory with the data and 

 (2) calculations which represent the overall agreement between the data and several of the 

 theories. In the Stream-function horizontal velocity component profiles presented, a 

 uniform mass transport velocity has been subtracted out, whereas due to time Umitations, 

 the other theoretical velocity distributions were simply plotted from Le Mehaute, Divorky, 

 and Lin. It is not clear whether or not the mass transport term should be subtracted out. 

 Although the experiments were conducted in a closed tank, the data were taken before 

 waves reflected from the beach had propagated back to the tank test section, and the zero 

 net flow over depth had probably not been estabUshed completely. 



In all, data for 10 different wave conditions are available. These waves are in the shallow 

 and transitional depth regions, and according to the conventional breaking criteria, the wave 

 heights range from 0.43 to 0.70 of the breaking height. The wave conditions are shown as 

 points in Figure 12 where isohnes representing various ratios of wave height to breaking 

 wave height are also presented. It is emphasized that the breaking wave height in Figure 12 

 is the conventional breaking height: i.e., H/h = 0.78 in shallow water (McCowan reviewed by 

 Munk, 1949); H/L = 0.142 in deep water (Michell, 1893); in the transitional range, the 

 breaking limit was first established by Reid and Bretschneider (1953) by interpolating on 

 the basis of measured data and is presented in several more available references, e.g. (Ippen, 

 1966) and (Bretschneider, 1960). A recent paper by Divoky, Le Mehaute, and Lin (1970) 

 reports an experimentally determined shallow-water breaking Umit of approximately 

 Hg/h = 0.60 to 0.66 as compared to the conventional value of 0.78. The recent experiments 

 resulting in the lower value were obtained with a laterally converging wave channel. 

 Certainly it is apparent that more work is needed to better resolve wave breaking Umits. 



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